research hypotheses definition

Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

Related Articles

Research Methodology

Qualitative Data Coding

What Is a Focus Group?

Cross-Cultural Research Methodology In Psychology

What Is Internal Validity In Research?

Research Methodology , Statistics

What Is Face Validity In Research? Importance & How To Measure

Criterion Validity: Definition & Examples

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Guided Meditations
• Verywell Mind Insights
• 2024 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
• "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

• Skip to main content
• Skip to primary sidebar
• Skip to footer
• QuestionPro

• Solutions Industries Gaming Automotive Sports and events Education Government Travel & Hospitality Financial Services Healthcare Cannabis Technology Use Case NPS+ Communities Audience Contactless surveys Mobile LivePolls Member Experience GDPR Positive People Science 360 Feedback Surveys
• Resources Blog eBooks Survey Templates Case Studies Training Help center

Home Market Research

Research Hypothesis: What It Is, Types + How to Develop?

A research study starts with a question. Researchers worldwide ask questions and create research hypotheses. The effectiveness of research relies on developing a good research hypothesis. Examples of research hypotheses can guide researchers in writing effective ones.

In this blog, we’ll learn what a research hypothesis is, why it’s important in research, and the different types used in science. We’ll also guide you through creating your research hypothesis and discussing ways to test and evaluate it.

What is a Research Hypothesis?

A hypothesis is like a guess or idea that you suggest to check if it’s true. A research hypothesis is a statement that brings up a question and predicts what might happen.

It’s really important in the scientific method and is used in experiments to figure things out. Essentially, it’s an educated guess about how things are connected in the research.

A research hypothesis usually includes pointing out the independent variable (the thing they’re changing or studying) and the dependent variable (the result they’re measuring or watching). It helps plan how to gather and analyze data to see if there’s evidence to support or deny the expected connection between these variables.

Importance of Hypothesis in Research

Hypotheses are really important in research. They help design studies, allow for practical testing, and add to our scientific knowledge. Their main role is to organize research projects, making them purposeful, focused, and valuable to the scientific community. Let’s look at some key reasons why they matter:

• A research hypothesis helps test theories.

A hypothesis plays a pivotal role in the scientific method by providing a basis for testing existing theories. For example, a hypothesis might test the predictive power of a psychological theory on human behavior.

• It serves as a great platform for investigation activities.

It serves as a launching pad for investigation activities, which offers researchers a clear starting point. A research hypothesis can explore the relationship between exercise and stress reduction.

• Hypothesis guides the research work or study.

A well-formulated hypothesis guides the entire research process. It ensures that the study remains focused and purposeful. For instance, a hypothesis about the impact of social media on interpersonal relationships provides clear guidance for a study.

• Hypothesis sometimes suggests theories.

In some cases, a hypothesis can suggest new theories or modifications to existing ones. For example, a hypothesis testing the effectiveness of a new drug might prompt a reconsideration of current medical theories.

• It helps in knowing the data needs.

A hypothesis clarifies the data requirements for a study, ensuring that researchers collect the necessary information—a hypothesis guiding the collection of demographic data to analyze the influence of age on a particular phenomenon.

• The hypothesis explains social phenomena.

Hypotheses are instrumental in explaining complex social phenomena. For instance, a hypothesis might explore the relationship between economic factors and crime rates in a given community.

• Hypothesis provides a relationship between phenomena for empirical Testing.

Hypotheses establish clear relationships between phenomena, paving the way for empirical testing. An example could be a hypothesis exploring the correlation between sleep patterns and academic performance.

• It helps in knowing the most suitable analysis technique.

A hypothesis guides researchers in selecting the most appropriate analysis techniques for their data. For example, a hypothesis focusing on the effectiveness of a teaching method may lead to the choice of statistical analyses best suited for educational research.

Characteristics of a Good Research Hypothesis

A hypothesis is a specific idea that you can test in a study. It often comes from looking at past research and theories. A good hypothesis usually starts with a research question that you can explore through background research. For it to be effective, consider these key characteristics:

• Clear and Focused Language: A good hypothesis uses clear and focused language to avoid confusion and ensure everyone understands it.
• Related to the Research Topic: The hypothesis should directly relate to the research topic, acting as a bridge between the specific question and the broader study.
• Testable: An effective hypothesis can be tested, meaning its prediction can be checked with real data to support or challenge the proposed relationship.
• Potential for Exploration: A good hypothesis often comes from a research question that invites further exploration. Doing background research helps find gaps and potential areas to investigate.
• Includes Variables: The hypothesis should clearly state both the independent and dependent variables, specifying the factors being studied and the expected outcomes.
• Ethical Considerations: Check if variables can be manipulated without breaking ethical standards. It’s crucial to maintain ethical research practices.
• Predicts Outcomes: The hypothesis should predict the expected relationship and outcome, acting as a roadmap for the study and guiding data collection and analysis.
• Simple and Concise: A good hypothesis avoids unnecessary complexity and is simple and concise, expressing the essence of the proposed relationship clearly.
• Clear and Assumption-Free: The hypothesis should be clear and free from assumptions about the reader’s prior knowledge, ensuring universal understanding.
• Observable and Testable Results: A strong hypothesis implies research that produces observable and testable results, making sure the study’s outcomes can be effectively measured and analyzed.

When you use these characteristics as a checklist, it can help you create a good research hypothesis. It’ll guide improving and strengthening the hypothesis, identifying any weaknesses, and making necessary changes. Crafting a hypothesis with these features helps you conduct a thorough and insightful research study.

Types of Research Hypotheses

The research hypothesis comes in various types, each serving a specific purpose in guiding the scientific investigation. Knowing the differences will make it easier for you to create your own hypothesis. Here’s an overview of the common types:

01. Null Hypothesis

The null hypothesis states that there is no connection between two considered variables or that two groups are unrelated. As discussed earlier, a hypothesis is an unproven assumption lacking sufficient supporting data. It serves as the statement researchers aim to disprove. It is testable, verifiable, and can be rejected.

For example, if you’re studying the relationship between Project A and Project B, assuming both projects are of equal standard is your null hypothesis. It needs to be specific for your study.

02. Alternative Hypothesis

The alternative hypothesis is basically another option to the null hypothesis. It involves looking for a significant change or alternative that could lead you to reject the null hypothesis. It’s a different idea compared to the null hypothesis.

When you create a null hypothesis, you’re making an educated guess about whether something is true or if there’s a connection between that thing and another variable. If the null view suggests something is correct, the alternative hypothesis says it’s incorrect. 

For instance, if your null hypothesis is “I’m going to be $1000 richer,” the alternative hypothesis would be “I’m not going to get $1000 or be richer.”

03. Directional Hypothesis

The directional hypothesis predicts the direction of the relationship between independent and dependent variables. They specify whether the effect will be positive or negative.

If you increase your study hours, you will experience a positive association with your exam scores. This hypothesis suggests that as you increase the independent variable (study hours), there will also be an increase in the dependent variable (exam scores).

04. Non-directional Hypothesis

The non-directional hypothesis predicts the existence of a relationship between variables but does not specify the direction of the effect. It suggests that there will be a significant difference or relationship, but it does not predict the nature of that difference.

For example, you will find no notable difference in test scores between students who receive the educational intervention and those who do not. However, once you compare the test scores of the two groups, you will notice an important difference.

05. Simple Hypothesis

A simple hypothesis predicts a relationship between one dependent variable and one independent variable without specifying the nature of that relationship. It’s simple and usually used when we don’t know much about how the two things are connected.

For example, if you adopt effective study habits, you will achieve higher exam scores than those with poor study habits.

06. Complex Hypothesis

A complex hypothesis is an idea that specifies a relationship between multiple independent and dependent variables. It is a more detailed idea than a simple hypothesis.

While a simple view suggests a straightforward cause-and-effect relationship between two things, a complex hypothesis involves many factors and how they’re connected to each other.

For example, when you increase your study time, you tend to achieve higher exam scores. The connection between your study time and exam performance is affected by various factors, including the quality of your sleep, your motivation levels, and the effectiveness of your study techniques.

If you sleep well, stay highly motivated, and use effective study strategies, you may observe a more robust positive correlation between the time you spend studying and your exam scores, unlike those who may lack these factors.

07. Associative Hypothesis

An associative hypothesis proposes a connection between two things without saying that one causes the other. Basically, it suggests that when one thing changes, the other changes too, but it doesn’t claim that one thing is causing the change in the other.

For example, you will likely notice higher exam scores when you increase your study time. You can recognize an association between your study time and exam scores in this scenario.

Your hypothesis acknowledges a relationship between the two variables—your study time and exam scores—without asserting that increased study time directly causes higher exam scores. You need to consider that other factors, like motivation or learning style, could affect the observed association.

08. Causal Hypothesis

A causal hypothesis proposes a cause-and-effect relationship between two variables. It suggests that changes in one variable directly cause changes in another variable.

For example, when you increase your study time, you experience higher exam scores. This hypothesis suggests a direct cause-and-effect relationship, indicating that the more time you spend studying, the higher your exam scores. It assumes that changes in your study time directly influence changes in your exam performance.

09. Empirical Hypothesis

An empirical hypothesis is a statement based on things we can see and measure. It comes from direct observation or experiments and can be tested with real-world evidence. If an experiment proves a theory, it supports the idea and shows it’s not just a guess. This makes the statement more reliable than a wild guess.

For example, if you increase the dosage of a certain medication, you might observe a quicker recovery time for patients. Imagine you’re in charge of a clinical trial. In this trial, patients are given varying dosages of the medication, and you measure and compare their recovery times. This allows you to directly see the effects of different dosages on how fast patients recover.

This way, you can create a research hypothesis: “Increasing the dosage of a certain medication will lead to a faster recovery time for patients.”

10. Statistical Hypothesis

A statistical hypothesis is a statement or assumption about a population parameter that is the subject of an investigation. It serves as the basis for statistical analysis and testing. It is often tested using statistical methods to draw inferences about the larger population.

In a hypothesis test, statistical evidence is collected to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis due to insufficient evidence.

For example, let’s say you’re testing a new medicine. Your hypothesis could be that the medicine doesn’t really help patients get better. So, you collect data and use statistics to see if your guess is right or if the medicine actually makes a difference.

If the data strongly shows that the medicine does help, you say your guess was wrong, and the medicine does make a difference. But if the proof isn’t strong enough, you can stick with your original guess because you didn’t get enough evidence to change your mind.

How to Develop a Research Hypotheses?

Step 1: identify your research problem or topic..

Define the area of interest or the problem you want to investigate. Make sure it’s clear and well-defined.

Start by asking a question about your chosen topic. Consider the limitations of your research and create a straightforward problem related to your topic. Once you’ve done that, you can develop and test a hypothesis with evidence.

Step 2: Conduct a literature review

Review existing literature related to your research problem. This will help you understand the current state of knowledge in the field, identify gaps, and build a foundation for your hypothesis. Consider the following questions:

• What existing research has been conducted on your chosen topic?
• Are there any gaps or unanswered questions in the current literature?
• How will the existing literature contribute to the foundation of your research?

Step 3: Formulate your research question

Based on your literature review, create a specific and concise research question that addresses your identified problem. Your research question should be clear, focused, and relevant to your field of study.

Step 4: Identify variables

Determine the key variables involved in your research question. Variables are the factors or phenomena that you will study and manipulate to test your hypothesis.

• Independent Variable: The variable you manipulate or control.
• Dependent Variable: The variable you measure to observe the effect of the independent variable.

Step 5: State the Null hypothesis

The null hypothesis is a statement that there is no significant difference or effect. It serves as a baseline for comparison with the alternative hypothesis.

Step 6: Select appropriate methods for testing the hypothesis

Choose research methods that align with your study objectives, such as experiments, surveys, or observational studies. The selected methods enable you to test your research hypothesis effectively.

Creating a research hypothesis usually takes more than one try. Expect to make changes as you collect data. It’s normal to test and say no to a few hypotheses before you find the right answer to your research question.

Testing and Evaluating Hypotheses

Testing hypotheses is a really important part of research. It’s like the practical side of things. Here, real-world evidence will help you determine how different things are connected. Let’s explore the main steps in hypothesis testing:

• State your research hypothesis.

Before testing, clearly articulate your research hypothesis. This involves framing both a null hypothesis, suggesting no significant effect or relationship, and an alternative hypothesis, proposing the expected outcome.

• Collect data strategically.

Plan how you will gather information in a way that fits your study. Make sure your data collection method matches the things you’re studying.

Whether through surveys, observations, or experiments, this step demands precision and adherence to the established methodology. The quality of data collected directly influences the credibility of study outcomes.

• Perform an appropriate statistical test.

Choose a statistical test that aligns with the nature of your data and the hypotheses being tested. Whether it’s a t-test, chi-square test, ANOVA, or regression analysis, selecting the right statistical tool is paramount for accurate and reliable results.

• Decide if your idea was right or wrong.

Following the statistical analysis, evaluate the results in the context of your null hypothesis. You need to decide if you should reject your null hypothesis or not.

• Share what you found.

When discussing what you found in your research, be clear and organized. Say whether your idea was supported or not, and talk about what your results mean. Also, mention any limits to your study and suggest ideas for future research.

The Role of QuestionPro to Develop a Good Research Hypothesis

QuestionPro is a survey and research platform that provides tools for creating, distributing, and analyzing surveys. It plays a crucial role in the research process, especially when you’re in the initial stages of hypothesis development. Here’s how QuestionPro can help you to develop a good research hypothesis:

• Survey design and data collection: You can use the platform to create targeted questions that help you gather relevant data.
• Exploratory research: Through surveys and feedback mechanisms on QuestionPro, you can conduct exploratory research to understand the landscape of a particular subject.
• Literature review and background research: QuestionPro surveys can collect sample population opinions, experiences, and preferences. This data and a thorough literature evaluation can help you generate a well-grounded hypothesis by improving your research knowledge.
• Identifying variables: Using targeted survey questions, you can identify relevant variables related to their research topic.
• Testing assumptions: You can use surveys to informally test certain assumptions or hypotheses before formalizing a research hypothesis.
• Data analysis tools: QuestionPro provides tools for analyzing survey data. You can use these tools to identify the collected data’s patterns, correlations, or trends.
• Refining your hypotheses: As you collect data through QuestionPro, you can adjust your hypotheses based on the real-world responses you receive.

A research hypothesis is like a guide for researchers in science. It’s a well-thought-out idea that has been thoroughly tested. This idea is crucial as researchers can explore different fields, such as medicine, social sciences, and natural sciences. The research hypothesis links theories to real-world evidence and gives researchers a clear path to explore and make discoveries.

QuestionPro Research Suite is a helpful tool for researchers. It makes creating surveys, collecting data, and analyzing information easily. It supports all kinds of research, from exploring new ideas to forming hypotheses. With a focus on using data, it helps researchers do their best work.

Are you interested in learning more about QuestionPro Research Suite? Take advantage of QuestionPro’s free trial to get an initial look at its capabilities and realize the full potential of your research efforts.

LEARN MORE         FREE TRIAL

MORE LIKE THIS

Data Information vs Insight: Essential differences

May 14, 2024

Pricing Analytics Software: Optimize Your Pricing Strategy

May 13, 2024

Relationship Marketing: What It Is, Examples & Top 7 Benefits

May 8, 2024

The Best Email Survey Tool to Boost Your Feedback Game

May 7, 2024

Other categories

• Academic Research
• Artificial Intelligence
• Assessments
• Brand Awareness
• Case Studies
• Communities
• Consumer Insights
• Customer effort score
• Customer Engagement
• Customer Experience
• Customer Loyalty
• Customer Research
• Customer Satisfaction
• Employee Benefits
• Employee Engagement
• Employee Retention
• Friday Five
• General Data Protection Regulation
• Insights Hub
• Life@QuestionPro
• Market Research
• Mobile diaries
• Mobile Surveys
• New Features
• Online Communities
• Question Types
• Questionnaire
• QuestionPro Products
• Release Notes
• Research Tools and Apps
• Revenue at Risk
• Survey Templates
• Training Tips
• Uncategorized
• Video Learning Series
• What’s Coming Up
• Workforce Intelligence

• Privacy Policy

Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Data Collection – Methods Types and Examples

Delimitations in Research – Types, Examples and...

Research Process – Steps, Examples and Tips

Research Design – Types, Methods and Examples

Institutional Review Board – Application Sample...

Evaluating Research – Process, Examples and...

How to Write a Research Hypothesis

• Research Process
• Peer Review

Since grade school, we've all been familiar with hypotheses. The hypothesis is an essential step of the scientific method. But what makes an effective research hypothesis, how do you create one, and what types of hypotheses are there? We answer these questions and more.

Updated on April 27, 2022

What is a research hypothesis?

General hypothesis.

Since grade school, we've all been familiar with the term “hypothesis.” A hypothesis is a fact-based guess or prediction that has not been proven. It is an essential step of the scientific method. The hypothesis of a study is a drive for experimentation to either prove the hypothesis or dispute it.

Research Hypothesis

A research hypothesis is more specific than a general hypothesis. It is an educated, expected prediction of the outcome of a study that is testable.

What makes an effective research hypothesis?

A good research hypothesis is a clear statement of the relationship between a dependent variable(s) and independent variable(s) relevant to the study that can be disproven.

Research hypothesis checklist

Once you've written a possible hypothesis, make sure it checks the following boxes:

• It must be testable: You need a means to prove your hypothesis. If you can't test it, it's not a hypothesis.
• It must include a dependent and independent variable: At least one independent variable ( cause ) and one dependent variable ( effect ) must be included.
• The language must be easy to understand: Be as clear and concise as possible. Nothing should be left to interpretation.
• It must be relevant to your research topic: You probably shouldn't be talking about cats and dogs if your research topic is outer space. Stay relevant to your topic.

How to create an effective research hypothesis

Pose it as a question first.

Start your research hypothesis from a journalistic approach. Ask one of the five W's: Who, what, when, where, or why.

A possible initial question could be: Why is the sky blue?

Do the preliminary research

Once you have a question in mind, read research around your topic. Collect research from academic journals.

If you're looking for information about the sky and why it is blue, research information about the atmosphere, weather, space, the sun, etc.

Write a draft hypothesis

Once you're comfortable with your subject and have preliminary knowledge, create a working hypothesis. Don't stress much over this. Your first hypothesis is not permanent. Look at it as a draft.

Your first draft of a hypothesis could be: Certain molecules in the Earth's atmosphere are responsive to the sky being the color blue.

Make your working draft perfect

Take your working hypothesis and make it perfect. Narrow it down to include only the information listed in the “Research hypothesis checklist” above.

Now that you've written your working hypothesis, narrow it down. Your new hypothesis could be: Light from the sun hitting oxygen molecules in the sky makes the color of the sky appear blue.

Write a null hypothesis

Your null hypothesis should be the opposite of your research hypothesis. It should be able to be disproven by your research.

In this example, your null hypothesis would be: Light from the sun hitting oxygen molecules in the sky does not make the color of the sky appear blue.

Why is it important to have a clear, testable hypothesis?

One of the main reasons a manuscript can be rejected from a journal is because of a weak hypothesis. “Poor hypothesis, study design, methodology, and improper use of statistics are other reasons for rejection of a manuscript,” says Dr. Ish Kumar Dhammi and Dr. Rehan-Ul-Haq in Indian Journal of Orthopaedics.

According to Dr. James M. Provenzale in American Journal of Roentgenology , “The clear declaration of a research question (or hypothesis) in the Introduction is critical for reviewers to understand the intent of the research study. It is best to clearly state the study goal in plain language (for example, “We set out to determine whether condition x produces condition y.”) An insufficient problem statement is one of the more common reasons for manuscript rejection.”

Characteristics that make a hypothesis weak include:

• Unclear variables
• Unoriginality
• Too general
• Too specific

A weak hypothesis leads to weak research and methods . The goal of a paper is to prove or disprove a hypothesis - or to prove or disprove a null hypothesis. If the hypothesis is not a dependent variable of what is being studied, the paper's methods should come into question.

A strong hypothesis is essential to the scientific method. A hypothesis states an assumed relationship between at least two variables and the experiment then proves or disproves that relationship with statistical significance. Without a proven and reproducible relationship, the paper feeds into the reproducibility crisis. Learn more about writing for reproducibility .

In a study published in The Journal of Obstetrics and Gynecology of India by Dr. Suvarna Satish Khadilkar, she reviewed 400 rejected manuscripts to see why they were rejected. Her studies revealed that poor methodology was a top reason for the submission having a final disposition of rejection.

Aside from publication chances, Dr. Gareth Dyke believes a clear hypothesis helps efficiency.

“Developing a clear and testable hypothesis for your research project means that you will not waste time, energy, and money with your work,” said Dyke. “Refining a hypothesis that is both meaningful, interesting, attainable, and testable is the goal of all effective research.”

Types of research hypotheses

There can be overlap in these types of hypotheses.

Simple hypothesis

A simple hypothesis is a hypothesis at its most basic form. It shows the relationship of one independent and one independent variable.

Example: Drinking soda (independent variable) every day leads to obesity (dependent variable).

Complex hypothesis

A complex hypothesis shows the relationship of two or more independent and dependent variables.

Example: Drinking soda (independent variable) every day leads to obesity (dependent variable) and heart disease (dependent variable).

Directional hypothesis

A directional hypothesis guesses which way the results of an experiment will go. It uses words like increase, decrease, higher, lower, positive, negative, more, or less. It is also frequently used in statistics.

Example: Humans exposed to radiation have a higher risk of cancer than humans not exposed to radiation.

Non-directional hypothesis

A non-directional hypothesis says there will be an effect on the dependent variable, but it does not say which direction.

Associative hypothesis

An associative hypothesis says that when one variable changes, so does the other variable.

Alternative hypothesis

An alternative hypothesis states that the variables have a relationship.

• The opposite of a null hypothesis

Example: An apple a day keeps the doctor away.

Null hypothesis

A null hypothesis states that there is no relationship between the two variables. It is posed as the opposite of what the alternative hypothesis states.

Researchers use a null hypothesis to work to be able to reject it. A null hypothesis:

• Can never be proven
• Can only be rejected
• Is the opposite of an alternative hypothesis

Example: An apple a day does not keep the doctor away.

Logical hypothesis

A logical hypothesis is a suggested explanation while using limited evidence.

Example: Bats can navigate in the dark better than tigers.

In this hypothesis, the researcher knows that tigers cannot see in the dark, and bats mostly live in darkness.

Empirical hypothesis

An empirical hypothesis is also called a “working hypothesis.” It uses the trial and error method and changes around the independent variables.

• An apple a day keeps the doctor away.
• Two apples a day keep the doctor away.
• Three apples a day keep the doctor away.

In this case, the research changes the hypothesis as the researcher learns more about his/her research.

Statistical hypothesis

A statistical hypothesis is a look of a part of a population or statistical model. This type of hypothesis is especially useful if you are making a statement about a large population. Instead of having to test the entire population of Illinois, you could just use a smaller sample of people who live there.

Example: 70% of people who live in Illinois are iron deficient.

Causal hypothesis

A causal hypothesis states that the independent variable will have an effect on the dependent variable.

Example: Using tobacco products causes cancer.

Final thoughts

Make sure your research is error-free before you send it to your preferred journal . Check our our English Editing services to avoid your chances of desk rejection.

Jonny Rhein, BA

See our "Privacy Policy"

The Research Hypothesis: Role and Construction

• First Online: 01 January 2012

Cite this chapter

• Phyllis G. Supino EdD 3  

6014 Accesses

A hypothesis is a logical construct, interposed between a problem and its solution, which represents a proposed answer to a research question. It gives direction to the investigator’s thinking about the problem and, therefore, facilitates a solution. There are three primary modes of inference by which hypotheses are developed: deduction (reasoning from a general propositions to specific instances), induction (reasoning from specific instances to a general proposition), and abduction (formulation/acceptance on probation of a hypothesis to explain a surprising observation).

A research hypothesis should reflect an inference about variables; be stated as a grammatically complete, declarative sentence; be expressed simply and unambiguously; provide an adequate answer to the research problem; and be testable. Hypotheses can be classified as conceptual versus operational, single versus bi- or multivariable, causal or not causal, mechanistic versus nonmechanistic, and null or alternative. Hypotheses most commonly entail statements about “variables” which, in turn, can be classified according to their level of measurement (scaling characteristics) or according to their role in the hypothesis (independent, dependent, moderator, control, or intervening).

A hypothesis is rendered operational when its broadly (conceptually) stated variables are replaced by operational definitions of those variables. Hypotheses stated in this manner are called operational hypotheses, specific hypotheses, or predictions and facilitate testing.

Wrong hypotheses, rightly worked from, have produced more results than unguided observation

—Augustus De Morgan, 1872[ 1 ]—

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

• Available as EPUB and PDF
• Read on any device
• Instant download
• Own it forever
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info
• Durable hardcover edition

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

The Nature and Logic of Science: Testing Hypotheses

Abductive Research Methods in Psychological Science

Abductive Research Methods in Psychological Science

De Morgan A, De Morgan S. A budget of paradoxes. London: Longmans Green; 1872.

Google Scholar  

Leedy Paul D. Practical research. Planning and design. 2nd ed. New York: Macmillan; 1960.

Bernard C. Introduction to the study of experimental medicine. New York: Dover; 1957.

Erren TC. The quest for questions—on the logical force of science. Med Hypotheses. 2004;62:635–40.

Article   PubMed   Google Scholar  

Peirce CS. Collected papers of Charles Sanders Peirce, vol. 7. In: Hartshorne C, Weiss P, editors. Boston: The Belknap Press of Harvard University Press; 1966.

Aristotle. The complete works of Aristotle: the revised Oxford Translation. In: Barnes J, editor. vol. 2. Princeton/New Jersey: Princeton University Press; 1984.

Polit D, Beck CT. Conceptualizing a study to generate evidence for nursing. In: Polit D, Beck CT, editors. Nursing research: generating and assessing evidence for nursing practice. 8th ed. Philadelphia: Wolters Kluwer/Lippincott Williams and Wilkins; 2008. Chapter 4.

Jenicek M, Hitchcock DL. Evidence-based practice. Logic and critical thinking in medicine. Chicago: AMA Press; 2005.

Bacon F. The novum organon or a true guide to the interpretation of nature. A new translation by the Rev G.W. Kitchin. Oxford: The University Press; 1855.

Popper KR. Objective knowledge: an evolutionary approach (revised edition). New York: Oxford University Press; 1979.

Morgan AJ, Parker S. Translational mini-review series on vaccines: the Edward Jenner Museum and the history of vaccination. Clin Exp Immunol. 2007;147:389–94.

Article   PubMed   CAS   Google Scholar  

Pead PJ. Benjamin Jesty: new light in the dawn of vaccination. Lancet. 2003;362:2104–9.

Lee JA. The scientific endeavor: a primer on scientific principles and practice. San Francisco: Addison-Wesley Longman; 2000.

Allchin D. Lawson’s shoehorn, or should the philosophy of science be rated, ‘X’? Science and Education. 2003;12:315–29.

Article   Google Scholar  

Lawson AE. What is the role of induction and deduction in reasoning and scientific inquiry? J Res Sci Teach. 2005;42:716–40.

Peirce CS. Collected papers of Charles Sanders Peirce, vol. 2. In: Hartshorne C, Weiss P, editors. Boston: The Belknap Press of Harvard University Press; 1965.

Bonfantini MA, Proni G. To guess or not to guess? In: Eco U, Sebeok T, editors. The sign of three: Dupin, Holmes, Peirce. Bloomington: Indiana University Press; 1983. Chapter 5.

Peirce CS. Collected papers of Charles Sanders Peirce, vol. 5. In: Hartshorne C, Weiss P, editors. Boston: The Belknap Press of Harvard University Press; 1965.

Flach PA, Kakas AC. Abductive and inductive reasoning: background issues. In: Flach PA, Kakas AC, ­editors. Abduction and induction. Essays on their relation and integration. The Netherlands: Klewer; 2000. Chapter 1.

Murray JF. Voltaire, Walpole and Pasteur: variations on the theme of discovery. Am J Respir Crit Care Med. 2005;172:423–6.

Danemark B, Ekstrom M, Jakobsen L, Karlsson JC. Methodological implications, generalization, scientific inference, models (Part II) In: explaining society. Critical realism in the social sciences. New York: Routledge; 2002.

Pasteur L. Inaugural lecture as professor and dean of the faculty of sciences. In: Peterson H, editor. A treasury of the world’s greatest speeches. Douai, France: University of Lille 7 Dec 1954.

Swineburne R. Simplicity as evidence for truth. Milwaukee: Marquette University Press; 1997.

Sakar S, editor. Logical empiricism at its peak: Schlick, Carnap and Neurath. New York: Garland; 1996.

Popper K. The logic of scientific discovery. New York: Basic Books; 1959. 1934, trans. 1959.

Caws P. The philosophy of science. Princeton: D. Van Nostrand Company; 1965.

Popper K. Conjectures and refutations. The growth of scientific knowledge. 4th ed. London: Routledge and Keegan Paul; 1972.

Feyerabend PK. Against method, outline of an anarchistic theory of knowledge. London, UK: Verso; 1978.

Smith PG. Popper: conjectures and refutations (Chapter IV). In: Theory and reality: an introduction to the philosophy of science. Chicago: University of Chicago Press; 2003.

Blystone RV, Blodgett K. WWW: the scientific method. CBE Life Sci Educ. 2006;5:7–11.

Kleinbaum DG, Kupper LL, Morgenstern H. Epidemiological research. Principles and quantitative methods. New York: Van Nostrand Reinhold; 1982.

Fortune AE, Reid WJ. Research in social work. 3rd ed. New York: Columbia University Press; 1999.

Kerlinger FN. Foundations of behavioral research. 1st ed. New York: Hold, Reinhart and Winston; 1970.

Hoskins CN, Mariano C. Research in nursing and health. Understanding and using quantitative and qualitative methods. New York: Springer; 2004.

Tuckman BW. Conducting educational research. New York: Harcourt, Brace, Jovanovich; 1972.

Wang C, Chiari PC, Weihrauch D, Krolikowski JG, Warltier DC, Kersten JR, Pratt Jr PF, Pagel PS. Gender-specificity of delayed preconditioning by isoflurane in rabbits: potential role of endothelial nitric oxide synthase. Anesth Analg. 2006;103:274–80.

Beyer ME, Slesak G, Nerz S, Kazmaier S, Hoffmeister HM. Effects of endothelin-1 and IRL 1620 on myocardial contractility and myocardial energy metabolism. J Cardiovasc Pharmacol. 1995;26(Suppl 3):S150–2.

PubMed   CAS   Google Scholar  

Stone J, Sharpe M. Amnesia for childhood in patients with unexplained neurological symptoms. J Neurol Neurosurg Psychiatry. 2002;72:416–7.

Naughton BJ, Moran M, Ghaly Y, Michalakes C. Computer tomography scanning and delirium in elder patients. Acad Emerg Med. 1997;4:1107–10.

Easterbrook PJ, Berlin JA, Gopalan R, Matthews DR. Publication bias in clinical research. Lancet. 1991;337:867–72.

Stern JM, Simes RJ. Publication bias: evidence of delayed publication in a cohort study of clinical research projects. BMJ. 1997;315:640–5.

Stevens SS. On the theory of scales and measurement. Science. 1946;103:677–80.

Knapp TR. Treating ordinal scales as interval scales: an attempt to resolve the controversy. Nurs Res. 1990;39:121–3.

The Cochrane Collaboration. Open Learning Material. www.cochrane-net.org/openlearning/html/mod14-3.htm . Accessed 12 Oct 2009.

MacCorquodale K, Meehl PE. On a distinction between hypothetical constructs and intervening ­variables. Psychol Rev. 1948;55:95–107.

Baron RM, Kenny DA. The moderator-mediator variable distinction in social psychological research: ­conceptual, strategic and statistical considerations. J Pers Soc Psychol. 1986;51:1173–82.

Williamson GM, Schultz R. Activity restriction mediates the association between pain and depressed affect: a study of younger and older adult cancer patients. Psychol Aging. 1995;10:369–78.

Song M, Lee EO. Development of a functional capacity model for the elderly. Res Nurs Health. 1998;21:189–98.

MacKinnon DP. Introduction to statistical mediation analysis. New York: Routledge; 2008.

Download references

Author information

Authors and affiliations.

Department of Medicine, College of Medicine, SUNY Downstate Medical Center, 450 Clarkson Avenue, 1199, Brooklyn, NY, 11203, USA

Phyllis G. Supino EdD

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Phyllis G. Supino EdD .

Editor information

Editors and affiliations.

, Cardiovascular Medicine, SUNY Downstate Medical Center, Clarkson Avenue, box 1199 450, Brooklyn, 11203, USA

Phyllis G. Supino

, Cardiovascualr Medicine, SUNY Downstate Medical Center, Clarkson Avenue 450, Brooklyn, 11203, USA

Jeffrey S. Borer

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media, LLC

About this chapter

Supino, P.G. (2012). The Research Hypothesis: Role and Construction. In: Supino, P., Borer, J. (eds) Principles of Research Methodology. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3360-6_3

Download citation

DOI : https://doi.org/10.1007/978-1-4614-3360-6_3

Published : 18 April 2012

Publisher Name : Springer, New York, NY

Print ISBN : 978-1-4614-3359-0

Online ISBN : 978-1-4614-3360-6

eBook Packages : Medicine Medicine (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

• Manuscript Preparation

What is and How to Write a Good Hypothesis in Research?

• 4 minute read
• 314.1K views

Table of Contents

One of the most important aspects of conducting research is constructing a strong hypothesis. But what makes a hypothesis in research effective? In this article, we’ll look at the difference between a hypothesis and a research question, as well as the elements of a good hypothesis in research. We’ll also include some examples of effective hypotheses, and what pitfalls to avoid.

What is a Hypothesis in Research?

Simply put, a hypothesis is a research question that also includes the predicted or expected result of the research. Without a hypothesis, there can be no basis for a scientific or research experiment. As such, it is critical that you carefully construct your hypothesis by being deliberate and thorough, even before you set pen to paper. Unless your hypothesis is clearly and carefully constructed, any flaw can have an adverse, and even grave, effect on the quality of your experiment and its subsequent results.

Research Question vs Hypothesis

It’s easy to confuse research questions with hypotheses, and vice versa. While they’re both critical to the Scientific Method, they have very specific differences. Primarily, a research question, just like a hypothesis, is focused and concise. But a hypothesis includes a prediction based on the proposed research, and is designed to forecast the relationship of and between two (or more) variables. Research questions are open-ended, and invite debate and discussion, while hypotheses are closed, e.g. “The relationship between A and B will be C.”

A hypothesis is generally used if your research topic is fairly well established, and you are relatively certain about the relationship between the variables that will be presented in your research. Since a hypothesis is ideally suited for experimental studies, it will, by its very existence, affect the design of your experiment. The research question is typically used for new topics that have not yet been researched extensively. Here, the relationship between different variables is less known. There is no prediction made, but there may be variables explored. The research question can be casual in nature, simply trying to understand if a relationship even exists, descriptive or comparative.

How to Write Hypothesis in Research

Writing an effective hypothesis starts before you even begin to type. Like any task, preparation is key, so you start first by conducting research yourself, and reading all you can about the topic that you plan to research. From there, you’ll gain the knowledge you need to understand where your focus within the topic will lie.

Remember that a hypothesis is a prediction of the relationship that exists between two or more variables. Your job is to write a hypothesis, and design the research, to “prove” whether or not your prediction is correct. A common pitfall is to use judgments that are subjective and inappropriate for the construction of a hypothesis. It’s important to keep the focus and language of your hypothesis objective.

An effective hypothesis in research is clearly and concisely written, and any terms or definitions clarified and defined. Specific language must also be used to avoid any generalities or assumptions.

Use the following points as a checklist to evaluate the effectiveness of your research hypothesis:

• Predicts the relationship and outcome
• Simple and concise – avoid wordiness
• Clear with no ambiguity or assumptions about the readers’ knowledge
• Observable and testable results
• Relevant and specific to the research question or problem

Research Hypothesis Example

Perhaps the best way to evaluate whether or not your hypothesis is effective is to compare it to those of your colleagues in the field. There is no need to reinvent the wheel when it comes to writing a powerful research hypothesis. As you’re reading and preparing your hypothesis, you’ll also read other hypotheses. These can help guide you on what works, and what doesn’t, when it comes to writing a strong research hypothesis.

Here are a few generic examples to get you started.

Eating an apple each day, after the age of 60, will result in a reduction of frequency of physician visits.

Budget airlines are more likely to receive more customer complaints. A budget airline is defined as an airline that offers lower fares and fewer amenities than a traditional full-service airline. (Note that the term “budget airline” is included in the hypothesis.

Workplaces that offer flexible working hours report higher levels of employee job satisfaction than workplaces with fixed hours.

Each of the above examples are specific, observable and measurable, and the statement of prediction can be verified or shown to be false by utilizing standard experimental practices. It should be noted, however, that often your hypothesis will change as your research progresses.

Language Editing Plus

Elsevier’s Language Editing Plus service can help ensure that your research hypothesis is well-designed, and articulates your research and conclusions. Our most comprehensive editing package, you can count on a thorough language review by native-English speakers who are PhDs or PhD candidates. We’ll check for effective logic and flow of your manuscript, as well as document formatting for your chosen journal, reference checks, and much more.

• Research Process

Systematic Literature Review or Literature Review?

What is a Problem Statement? [with examples]

You may also like.

Make Hook, Line, and Sinker: The Art of Crafting Engaging Introductions

Can Describing Study Limitations Improve the Quality of Your Paper?

A Guide to Crafting Shorter, Impactful Sentences in Academic Writing

6 Steps to Write an Excellent Discussion in Your Manuscript

How to Write Clear and Crisp Civil Engineering Papers? Here are 5 Key Tips to Consider

The Clear Path to An Impactful Paper: ②

The Essentials of Writing to Communicate Research in Medicine

Changing Lines: Sentence Patterns in Academic Writing

Input your search keywords and press Enter.

Research Hypothesis: Elements, Format, Types

When a proposition is formulated for empirical testing, we call it a hypothesis. Almost all studies begin with one or more hypotheses.

Let’s Understand Research Hypothesis.

What is a hypothesis.

A hypothesis, specifically a research hypothesis, is formulated to predict an assumed relationship between two or more variables of interest.

If we reasonably guess that a relationship exists between the variables of interest, we first state it as a hypothesis and then test it in the field.

Hypotheses are stated in terms of the particular dependent and independent variables that are going to be used in the study.

Research Hypothesis Definition

A research hypothesis is a conjectural statement, a logical supposition, a reasonable guess, and an educated prediction about the nature of the relationship between two or more variables that we expect to happen in our study.

Unless you are creating an exploratory study, your hypothesis should always explain what you expect to happen during your experiment or research.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the research aims to determine whether this guess is right or wrong.

When experimenting, researchers might explore different factors to determine which ones might contribute to the outcome.

In many cases, researchers may find that the results of an experiment do not support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

Elements of a Good Hypothesis

Regardless of the type of hypothesis, the goal of a good hypothesis is to help explain the focus and direction of the experiment or research. As such, a good hypothesis will

• State the purpose of the research.
• Identify which variables are to be used.

A good hypothesis;

• Needs to be logical.
• Must be precise in language.
• It should be testable with research or experimentation.

A hypothesis is usually written in a form where it proposes that if something is done, then something will occur.

Finally, when you are trying to come up with a good hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on any previous research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research on your topic.

Once you have completed a literature review, start thinking of potential questions you still have. Pay attention to the discussion section in the journal articles you read. Many authors will suggest questions that still need to be explored.

Basic Format of a Good Hypothesis

A hypothesis often follows a basic format of “If {this happens}, then {this will happen}.” One way to structure your hypothesis is to describe what will happen to the dependent variable if you change the independent variable.

The basic format might be:

“If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}.”

A few examples:

• Students who eat breakfast will perform better on a math test than students who do not eat breakfast.
• Students who experience test anxiety before an exam get higher scores than students who do not experience test anxiety.
• Drivers who talk on their mobile phones while driving will be more likely to make errors when driving than those who do not talk on the phone.
• People with high exposure to ultraviolet light will have a higher frequency of skin cancer than those who do not have such exposure.

Look at the last example.

Here is the independent variable (exposure to ultraviolet light)) is specified, and the dependent variable (skin cancer) is also specified.

Notice also that this research hypothesis specifies a direction in that it predicts that people exposed to ultraviolet light will have a higher risk of cancer.

This is not always the case. Research hypotheses can also specify a difference without saying which group will be better or higher than the other.

For example, one might formulate a hypothesis of the type: ‘Religion does not make any significant difference in the performance of cultural activities.’

In general, however, it is considered a better hypothesis if you can specify a direction.

Research hypotheses serve several important functions. The most important one is to direct and guide the research.

A few of the other functions of the research hypothesis are enumerated below:

• A research hypothesis indicates the major independent variables to be included in the study;
• A research hypothesis suggests the type of data that must be collected and the type of analysis that must be conducted to measure the relationship;
• A research hypothesis identifies facts that are relevant and that are not;
• A research hypothesis suggests the type of research design to be employed.

Types of Research Hypothesis

Two types of research hypotheses are;

• Descriptive hypothesis.
• Relational hypothesis.

Descriptive Hypotheses

Descriptive hypotheses are propositions that typically state some variables’ existence, size, form, or distribution.

These hypotheses are formulated in the form of statements in which we assign variables to cases.

For example,

• The prevalence of contraceptive use among currently married women in India exceeds 60%.

In this example, the case is ‘currently married women,’ and the variable is ‘prevalence of contraceptives.’ As a second example,

• The public universities are currently experiencing budget difficulties.

Here,’ public universities’ is the case, and ‘budget difficulties’ is the variable.

• The National Board of Revenue claims that over 15% of potential taxpayers falsify in their income tax returns.
• At most, 75% of the pre-school children in community A have a protein-deficient diet.
• The average sales in a superstore exceed taka 25 lac per month.
• Smoking increases the risk of lung cancer.
• The average longevity of women is higher among females than among males.
• Gainfully employed women tend to have lower than average fertility.
• Women with child loss experience will have higher fertility than those who do not have such experiences.

All examples of descriptive hypotheses.

It is important to note that the Descriptive hypothesis does not always have variables that can be designated as independent or dependent.

Relational Hypotheses

Relational hypotheses, on the other hand, are statements that describe the relationship between variables concerning some cases.

• Communities with many modern facilities will have a higher rate of contraception than communities with few modern facilities.

In this instance, the case is ‘communities,’ and the variables are ‘rate of contraception’ and ‘modern facilities.’

Similarly, “People who use chewing tobacco have a higher risk of oral carcinoma than people who have never used chewing tobacco” is a relational hypothesis.

A relational hypothesis is again of two types: correlational hypothesis and the causal hypothesis.

A correlational hypothesis states that variables occur in some predictable relationships without implying that one variable causes the other to change or take on different values.

Here is an example of a co-relational hypothesis:

• Males are more efficient than their female counterparts in typing.

In making such a statement, we do not claim that sex (male-female) as a variable influences the other variable,’ typing efficiency’ (less efficient-more efficient). Here is one more example of a correlational hypothesis:

• Saving habit is more pronounced among Christians than the people of other religions.

Once again, religion is not believed to be a factor in saving habits, although a positive relationship has been observed.

Look at the following example:

• The participation of women in household decision making increases with age, their level of education, and the number of surviving children.

Here too, women’s education, several surviving children, or education does not guarantee their decision-making autonomy.

With causal hypotheses (also called explanatory hypotheses), on the other hand, there is an implication that a change in one variable causes a change or leads to an effect on the other variable.

A causal variable is typically called an independent variable, and the other is the dependent variable. It is important to note that the term “cause” roughly means “help make happen.” So, the independent variable need not be the sole reason for the existence of or change in the dependent variable. Here are some examples of causal hypotheses:

• An increase in family income leads to an increase in the income saved.
• Exposure of mothers to mass media increases their knowledge of malnutrition among their children.
• An offer of a discount in a department store enhances the sales volume.
• Chewing tobacco increases the risk of oral carcinoma.
• Goat farming contributes to poverty alleviation of rural people.
• The utilization of child welfare clinics is the lowest in those clinics in which the clinic personnel are poorly motivated to provide preventive services.
• An increase in bank interest rate encourages the customers for increased savings.

In the above example, we have ample reasons to believe that one variable (family income and savings, misuse of credit, and farm size) has a bearing on the other variable.

We cite two more examples to illustrate the hypothesis, general objective, ultimate objective, and a few specific objectives.

General objective:

• To compare the complications of acceptors of laparoscopic sterilization and mini-laparotomy among American women.

Research hypothesis:

• The risk of complications is higher in the mini-laparotomy method of sterilization than in laparoscopic sterilization.

Specific objectives:

• To assess the complications of laparoscopic sterilization and mini-laparotomy.
• To assess service providers’ knowledge and perception regarding the complications, preferences, and convenience of the two methods.

Ultimate Objectives:

• To introduce and popularize the laparoscopic female sterilization method in the National Family Planning Program to reduce the rapid population growth rate.

In a study designed to examine the living and working conditions of the overseas migrant workers from India and the pattern of remittances from overseas migrant workers, the general objective, specific objectives, and the ultimate objective were formulated as follows:

• To examine the living and working conditions of the overseas migrant workers from India.”
• Characteristics of migrant workers by significant migration channels;
• Countries of destination;
• The occupational skill of the workers;
• Pattern and procedures of remittances;
• Impact of remittances on government revenue;
• Better utilization of remittances.

Ultimate objective:

• To suggest ways and means to minimize the differences in the policy adopted by the public and private sectors in their recruitment process in the interest of the workers;
• To ascertain the possible exploitation of the workers by the private agencies and suggest remedies for such exploitation.
• Private agencies, in most cases, exploit migrant workers.

What are the elements of a good hypothesis?

A good hypothesis should state the purpose of the research, identify which variables are to be used, be logical, precise in language, and be testable with research or experimentation.

How is a hypothesis typically structured?

A hypothesis often follows a basic format of “If {this happens}, then {this will happen}.” It proposes that if something is done, then a specific outcome will occur.

What is a Descriptive hypothesis?

Descriptive hypotheses are propositions that typically state some variables’ existence, size, form, or distribution. They are formulated in the form of statements in which variables are assigned to cases.

What distinguishes a Relational hypothesis?

Relational hypotheses describe the relationship between variables concerning some cases. They can be correlational, where variables occur in a predictable relationship without implying causation, or causal, where a change in one variable causes a change in another.

What is the difference between a correlational hypothesis and a causal hypothesis?

A correlational hypothesis states that variables occur in some predictable relationships without implying that one variable causes the other to change. A causal hypothesis, on the other hand, implies that a change in one variable causes a change or leads to an effect on the other variable.

What are the two main types of research hypotheses?

The two main types of research hypotheses are Descriptive hypothesis and Relational hypothesis

What is a hypothesis in the context of academic research?

A hypothesis is a statement about an expected relationship between variables or an explanation of an occurrence that is clear, specific, and testable.

How does a research hypothesis differ from a general hypothesis?

A research hypothesis is more specific and clear about what’s being assessed and the expected outcome. It must also be testable, meaning there should be a way to prove or disprove it.

What are the essential attributes of a good research hypothesis?

A good research hypothesis should have specificity, clarity, and testability.

Why is testability crucial for a research hypothesis?

Testability ensures that empirical research can prove or disproven the hypothesis. If a statement isn’t testable, it doesn’t qualify as a research hypothesis.

What is the null hypothesis?

The null hypothesis is the counter-proposal to the original hypothesis. It predicts that there is no relationship between the variables in question.

How can one ensure that a hypothesis is clear and specific?

A hypothesis should clearly identify the variables involved, the parties involved, and the expected relationship type, leaving no ambiguity about its intent or meaning.

Why is it essential to avoid value judgments in a research hypothesis?

Value judgments are subjective and not appropriate for a hypothesis. A research hypothesis should strive to be objective, avoiding personal opinions.

What is the basic definition of a hypothesis in research?

A research hypothesis is a statement about an expected relationship between variables, or an explanation of an occurrence, that is clear, specific, and testable.

While a general hypothesis is an idea or explanation based on known facts but not yet proven, a research hypothesis is a clear, specific, and testable statement about the expected outcome of a study.

What are the essential characteristics of a good research hypothesis?

A good research hypothesis should possess specificity, clarity, and testability. It should clearly define what’s being assessed and the expected outcome, and it must be possible to prove or disprove the statement through experimentation.

How can one ensure that a hypothesis is testable?

A hypothesis is testable if there’s a possibility to prove both its truth and falsity. The results of the hypothesis should be reproducible, and it should be specific enough to allow for clear testing procedures.

What is the difference between a null hypothesis and an alternative hypothesis?

The null hypothesis proposes that no statistical significance exists in a set of observations, suggesting any differences are due to chance alone. The alternative hypothesis, on the other hand, predicts a relationship between the variables of the study and states that the results are significant to the research topic.

How should one formulate an effective research hypothesis?

To formulate an effective research hypothesis, one should state the problem clearly, use an ‘if-then’ statement structure, define the variables as dependent or independent, and scrutinize the hypothesis to ensure it meets the criteria of specificity, clarity, and testability.

What are some types of hypotheses in research?

Types of hypotheses include simple, complex, directional, non-directional, associative and causal, empirical, and statistical hypotheses. Each type serves a specific purpose and is used based on the nature of the research question or problem.

How to Develop a Good Research Hypothesis

The story of a research study begins by asking a question. Researchers all around the globe are asking curious questions and formulating research hypothesis. However, whether the research study provides an effective conclusion depends on how well one develops a good research hypothesis. Research hypothesis examples could help researchers get an idea as to how to write a good research hypothesis.

This blog will help you understand what is a research hypothesis, its characteristics and, how to formulate a research hypothesis

Table of Contents

What is Hypothesis?

Hypothesis is an assumption or an idea proposed for the sake of argument so that it can be tested. It is a precise, testable statement of what the researchers predict will be outcome of the study.  Hypothesis usually involves proposing a relationship between two variables: the independent variable (what the researchers change) and the dependent variable (what the research measures).

What is a Research Hypothesis?

Research hypothesis is a statement that introduces a research question and proposes an expected result. It is an integral part of the scientific method that forms the basis of scientific experiments. Therefore, you need to be careful and thorough when building your research hypothesis. A minor flaw in the construction of your hypothesis could have an adverse effect on your experiment. In research, there is a convention that the hypothesis is written in two forms, the null hypothesis, and the alternative hypothesis (called the experimental hypothesis when the method of investigation is an experiment).

Characteristics of a Good Research Hypothesis

As the hypothesis is specific, there is a testable prediction about what you expect to happen in a study. You may consider drawing hypothesis from previously published research based on the theory.

A good research hypothesis involves more effort than just a guess. In particular, your hypothesis may begin with a question that could be further explored through background research.

To help you formulate a promising research hypothesis, you should ask yourself the following questions:

• Is the language clear and focused?
• What is the relationship between your hypothesis and your research topic?
• Is your hypothesis testable? If yes, then how?
• What are the possible explanations that you might want to explore?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate your variables without hampering the ethical standards?
• Does your research predict the relationship and outcome?
• Is your research simple and concise (avoids wordiness)?
• Is it clear with no ambiguity or assumptions about the readers’ knowledge
• Is your research observable and testable results?
• Is it relevant and specific to the research question or problem?

The questions listed above can be used as a checklist to make sure your hypothesis is based on a solid foundation. Furthermore, it can help you identify weaknesses in your hypothesis and revise it if necessary.

Source: Educational Hub

How to formulate a research hypothesis.

A testable hypothesis is not a simple statement. It is rather an intricate statement that needs to offer a clear introduction to a scientific experiment, its intentions, and the possible outcomes. However, there are some important things to consider when building a compelling hypothesis.

1. State the problem that you are trying to solve.

Make sure that the hypothesis clearly defines the topic and the focus of the experiment.

2. Try to write the hypothesis as an if-then statement.

Follow this template: If a specific action is taken, then a certain outcome is expected.

3. Define the variables

Independent variables are the ones that are manipulated, controlled, or changed. Independent variables are isolated from other factors of the study.

Dependent variables , as the name suggests are dependent on other factors of the study. They are influenced by the change in independent variable.

4. Scrutinize the hypothesis

Evaluate assumptions, predictions, and evidence rigorously to refine your understanding.

Types of Research Hypothesis

The types of research hypothesis are stated below:

1. Simple Hypothesis

It predicts the relationship between a single dependent variable and a single independent variable.

2. Complex Hypothesis

It predicts the relationship between two or more independent and dependent variables.

3. Directional Hypothesis

It specifies the expected direction to be followed to determine the relationship between variables and is derived from theory. Furthermore, it implies the researcher’s intellectual commitment to a particular outcome.

4. Non-directional Hypothesis

It does not predict the exact direction or nature of the relationship between the two variables. The non-directional hypothesis is used when there is no theory involved or when findings contradict previous research.

5. Associative and Causal Hypothesis

The associative hypothesis defines interdependency between variables. A change in one variable results in the change of the other variable. On the other hand, the causal hypothesis proposes an effect on the dependent due to manipulation of the independent variable.

6. Null Hypothesis

Null hypothesis states a negative statement to support the researcher’s findings that there is no relationship between two variables. There will be no changes in the dependent variable due the manipulation of the independent variable. Furthermore, it states results are due to chance and are not significant in terms of supporting the idea being investigated.

7. Alternative Hypothesis

It states that there is a relationship between the two variables of the study and that the results are significant to the research topic. An experimental hypothesis predicts what changes will take place in the dependent variable when the independent variable is manipulated. Also, it states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

Research Hypothesis Examples of Independent and Dependent Variables

Research Hypothesis Example 1 The greater number of coal plants in a region (independent variable) increases water pollution (dependent variable). If you change the independent variable (building more coal factories), it will change the dependent variable (amount of water pollution).

Research Hypothesis Example 2 What is the effect of diet or regular soda (independent variable) on blood sugar levels (dependent variable)? If you change the independent variable (the type of soda you consume), it will change the dependent variable (blood sugar levels)

You should not ignore the importance of the above steps. The validity of your experiment and its results rely on a robust testable hypothesis. Developing a strong testable hypothesis has few advantages, it compels us to think intensely and specifically about the outcomes of a study. Consequently, it enables us to understand the implication of the question and the different variables involved in the study. Furthermore, it helps us to make precise predictions based on prior research. Hence, forming a hypothesis would be of great value to the research. Here are some good examples of testable hypotheses.

More importantly, you need to build a robust testable research hypothesis for your scientific experiments. A testable hypothesis is a hypothesis that can be proved or disproved as a result of experimentation.

Importance of a Testable Hypothesis

To devise and perform an experiment using scientific method, you need to make sure that your hypothesis is testable. To be considered testable, some essential criteria must be met:

• There must be a possibility to prove that the hypothesis is true.
• There must be a possibility to prove that the hypothesis is false.
• The results of the hypothesis must be reproducible.

Without these criteria, the hypothesis and the results will be vague. As a result, the experiment will not prove or disprove anything significant.

What are your experiences with building hypotheses for scientific experiments? What challenges did you face? How did you overcome these challenges? Please share your thoughts with us in the comments section.

Frequently Asked Questions

The steps to write a research hypothesis are: 1. Stating the problem: Ensure that the hypothesis defines the research problem 2. Writing a hypothesis as an 'if-then' statement: Include the action and the expected outcome of your study by following a ‘if-then’ structure. 3. Defining the variables: Define the variables as Dependent or Independent based on their dependency to other factors. 4. Scrutinizing the hypothesis: Identify the type of your hypothesis

Hypothesis testing is a statistical tool which is used to make inferences about a population data to draw conclusions for a particular hypothesis.

Hypothesis in statistics is a formal statement about the nature of a population within a structured framework of a statistical model. It is used to test an existing hypothesis by studying a population.

Research hypothesis is a statement that introduces a research question and proposes an expected result. It forms the basis of scientific experiments.

The different types of hypothesis in research are: • Null hypothesis: Null hypothesis is a negative statement to support the researcher’s findings that there is no relationship between two variables. • Alternate hypothesis: Alternate hypothesis predicts the relationship between the two variables of the study. • Directional hypothesis: Directional hypothesis specifies the expected direction to be followed to determine the relationship between variables. • Non-directional hypothesis: Non-directional hypothesis does not predict the exact direction or nature of the relationship between the two variables. • Simple hypothesis: Simple hypothesis predicts the relationship between a single dependent variable and a single independent variable. • Complex hypothesis: Complex hypothesis predicts the relationship between two or more independent and dependent variables. • Associative and casual hypothesis: Associative and casual hypothesis predicts the relationship between two or more independent and dependent variables. • Empirical hypothesis: Empirical hypothesis can be tested via experiments and observation. • Statistical hypothesis: A statistical hypothesis utilizes statistical models to draw conclusions about broader populations.

Wow! You really simplified your explanation that even dummies would find it easy to comprehend. Thank you so much.

Thanks a lot for your valuable guidance.

I enjoy reading the post. Hypotheses are actually an intrinsic part in a study. It bridges the research question and the methodology of the study.

Useful piece!

This is awesome.Wow.

It very interesting to read the topic, can you guide me any specific example of hypothesis process establish throw the Demand and supply of the specific product in market

Nicely explained

It is really a useful for me Kindly give some examples of hypothesis

It was a well explained content ,can you please give me an example with the null and alternative hypothesis illustrated

clear and concise. thanks.

So Good so Amazing

Good to learn

Thanks a lot for explaining to my level of understanding

Explained well and in simple terms. Quick read! Thank you

It awesome. It has really positioned me in my research project

Rate this article Cancel Reply

Your email address will not be published.

Enago Academy's Most Popular Articles

• Reporting Research

Choosing the Right Analytical Approach: Thematic analysis vs. content analysis for data interpretation

In research, choosing the right approach to understand data is crucial for deriving meaningful insights.…

Comparing Cross Sectional and Longitudinal Studies: 5 steps for choosing the right approach

The process of choosing the right research design can put ourselves at the crossroads of…

• Industry News

COPE Forum Discussion Highlights Challenges and Urges Clarity in Institutional Authorship Standards

The COPE forum discussion held in December 2023 initiated with a fundamental question — is…

• Career Corner

Unlocking the Power of Networking in Academic Conferences

Embarking on your first academic conference experience? Fear not, we got you covered! Academic conferences…

Research Recommendations – Guiding policy-makers for evidence-based decision making

Research recommendations play a crucial role in guiding scholars and researchers toward fruitful avenues of…

Choosing the Right Analytical Approach: Thematic analysis vs. content analysis for…

Comparing Cross Sectional and Longitudinal Studies: 5 steps for choosing the right…

How to Design Effective Research Questionnaires for Robust Findings

Sign-up to read more

Subscribe for free to get unrestricted access to all our resources on research writing and academic publishing including:

• 2000+ blog articles
• 50+ Webinars
• 10+ Expert podcasts
• 50+ Infographics
• 10+ Checklists
• Research Guides

We hate spam too. We promise to protect your privacy and never spam you.

I am looking for Editing/ Proofreading services for my manuscript Tentative date of next journal submission:

As a researcher, what do you consider most when choosing an image manipulation detector?

Ohio State nav bar

The Ohio State University

• BuckeyeLink
• Find People
• Search Ohio State

Research Questions & Hypotheses

Generally, in quantitative studies, reviewers expect hypotheses rather than research questions. However, both research questions and hypotheses serve different purposes and can be beneficial when used together.

Research Questions

Clarify the research’s aim (farrugia et al., 2010).

• Research often begins with an interest in a topic, but a deep understanding of the subject is crucial to formulate an appropriate research question.
• Descriptive: “What factors most influence the academic achievement of senior high school students?”
• Comparative: “What is the performance difference between teaching methods A and B?”
• Relationship-based: “What is the relationship between self-efficacy and academic achievement?”
• Increasing knowledge about a subject can be achieved through systematic literature reviews, in-depth interviews with patients (and proxies), focus groups, and consultations with field experts.
• Some funding bodies, like the Canadian Institute for Health Research, recommend conducting a systematic review or a pilot study before seeking grants for full trials.
• The presence of multiple research questions in a study can complicate the design, statistical analysis, and feasibility.
• It’s advisable to focus on a single primary research question for the study.
• The primary question, clearly stated at the end of a grant proposal’s introduction, usually specifies the study population, intervention, and other relevant factors.
• The FINER criteria underscore aspects that can enhance the chances of a successful research project, including specifying the population of interest, aligning with scientific and public interest, clinical relevance, and contribution to the field, while complying with ethical and national research standards.
• The P ICOT approach is crucial in developing the study’s framework and protocol, influencing inclusion and exclusion criteria and identifying patient groups for inclusion.
• Defining the specific population, intervention, comparator, and outcome helps in selecting the right outcome measurement tool.
• The more precise the population definition and stricter the inclusion and exclusion criteria, the more significant the impact on the interpretation, applicability, and generalizability of the research findings.
• A restricted study population enhances internal validity but may limit the study’s external validity and generalizability to clinical practice.
• A broadly defined study population may better reflect clinical practice but could increase bias and reduce internal validity.
• An inadequately formulated research question can negatively impact study design, potentially leading to ineffective outcomes and affecting publication prospects.

Checklist: Good research questions for social science projects (Panke, 2018)

Research Hypotheses

Present the researcher’s predictions based on specific statements.

• These statements define the research problem or issue and indicate the direction of the researcher’s predictions.
• Formulating the research question and hypothesis from existing data (e.g., a database) can lead to multiple statistical comparisons and potentially spurious findings due to chance.
• The research or clinical hypothesis, derived from the research question, shapes the study’s key elements: sampling strategy, intervention, comparison, and outcome variables.
• Hypotheses can express a single outcome or multiple outcomes.
• After statistical testing, the null hypothesis is either rejected or not rejected based on whether the study’s findings are statistically significant.
• Hypothesis testing helps determine if observed findings are due to true differences and not chance.
• Hypotheses can be 1-sided (specific direction of difference) or 2-sided (presence of a difference without specifying direction).
• 2-sided hypotheses are generally preferred unless there’s a strong justification for a 1-sided hypothesis.
• A solid research hypothesis, informed by a good research question, influences the research design and paves the way for defining clear research objectives.

Types of Research Hypothesis

• In a Y-centered research design, the focus is on the dependent variable (DV) which is specified in the research question. Theories are then used to identify independent variables (IV) and explain their causal relationship with the DV.
• Example: “An increase in teacher-led instructional time (IV) is likely to improve student reading comprehension scores (DV), because extensive guided practice under expert supervision enhances learning retention and skill mastery.”
• Hypothesis Explanation: The dependent variable (student reading comprehension scores) is the focus, and the hypothesis explores how changes in the independent variable (teacher-led instructional time) affect it.
• In X-centered research designs, the independent variable is specified in the research question. Theories are used to determine potential dependent variables and the causal mechanisms at play.
• Example: “Implementing technology-based learning tools (IV) is likely to enhance student engagement in the classroom (DV), because interactive and multimedia content increases student interest and participation.”
• Hypothesis Explanation: The independent variable (technology-based learning tools) is the focus, with the hypothesis exploring its impact on a potential dependent variable (student engagement).
• Probabilistic hypotheses suggest that changes in the independent variable are likely to lead to changes in the dependent variable in a predictable manner, but not with absolute certainty.
• Example: “The more teachers engage in professional development programs (IV), the more their teaching effectiveness (DV) is likely to improve, because continuous training updates pedagogical skills and knowledge.”
• Hypothesis Explanation: This hypothesis implies a probable relationship between the extent of professional development (IV) and teaching effectiveness (DV).
• Deterministic hypotheses state that a specific change in the independent variable will lead to a specific change in the dependent variable, implying a more direct and certain relationship.
• Example: “If the school curriculum changes from traditional lecture-based methods to project-based learning (IV), then student collaboration skills (DV) are expected to improve because project-based learning inherently requires teamwork and peer interaction.”
• Hypothesis Explanation: This hypothesis presumes a direct and definite outcome (improvement in collaboration skills) resulting from a specific change in the teaching method.
• Example : “Students who identify as visual learners will score higher on tests that are presented in a visually rich format compared to tests presented in a text-only format.”
• Explanation : This hypothesis aims to describe the potential difference in test scores between visual learners taking visually rich tests and text-only tests, without implying a direct cause-and-effect relationship.
• Example : “Teaching method A will improve student performance more than method B.”
• Explanation : This hypothesis compares the effectiveness of two different teaching methods, suggesting that one will lead to better student performance than the other. It implies a direct comparison but does not necessarily establish a causal mechanism.
• Example : “Students with higher self-efficacy will show higher levels of academic achievement.”
• Explanation : This hypothesis predicts a relationship between the variable of self-efficacy and academic achievement. Unlike a causal hypothesis, it does not necessarily suggest that one variable causes changes in the other, but rather that they are related in some way.

Tips for developing research questions and hypotheses for research studies

• Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
• Learn about current trends and technological advances on the topic.
• Seek careful input from experts, mentors, colleagues, and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
• Use the FINER criteria in the development of the research question.
• Ensure that the research question follows PICOT format.
• Develop a research hypothesis from the research question.
• Ensure that the research question and objectives are answerable, feasible, and clinically relevant.

If your research hypotheses are derived from your research questions, particularly when multiple hypotheses address a single question, it’s recommended to use both research questions and hypotheses. However, if this isn’t the case, using hypotheses over research questions is advised. It’s important to note these are general guidelines, not strict rules. If you opt not to use hypotheses, consult with your supervisor for the best approach.

Farrugia, P., Petrisor, B. A., Farrokhyar, F., & Bhandari, M. (2010). Practical tips for surgical research: Research questions, hypotheses and objectives.  Canadian journal of surgery. Journal canadien de chirurgie ,  53 (4), 278–281.

Hulley, S. B., Cummings, S. R., Browner, W. S., Grady, D., & Newman, T. B. (2007). Designing clinical research. Philadelphia.

Panke, D. (2018). Research design & method selection: Making good choices in the social sciences.  Research Design & Method Selection , 1-368.

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• v.53(4); 2010 Aug

Research questions, hypotheses and objectives

Patricia farrugia.

* Michael G. DeGroote School of Medicine, the

Bradley A. Petrisor

† Division of Orthopaedic Surgery and the

Forough Farrokhyar

‡ Departments of Surgery and

§ Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Ont

Mohit Bhandari

There is an increasing familiarity with the principles of evidence-based medicine in the surgical community. As surgeons become more aware of the hierarchy of evidence, grades of recommendations and the principles of critical appraisal, they develop an increasing familiarity with research design. Surgeons and clinicians are looking more and more to the literature and clinical trials to guide their practice; as such, it is becoming a responsibility of the clinical research community to attempt to answer questions that are not only well thought out but also clinically relevant. The development of the research question, including a supportive hypothesis and objectives, is a necessary key step in producing clinically relevant results to be used in evidence-based practice. A well-defined and specific research question is more likely to help guide us in making decisions about study design and population and subsequently what data will be collected and analyzed. 1

Objectives of this article

In this article, we discuss important considerations in the development of a research question and hypothesis and in defining objectives for research. By the end of this article, the reader will be able to appreciate the significance of constructing a good research question and developing hypotheses and research objectives for the successful design of a research study. The following article is divided into 3 sections: research question, research hypothesis and research objectives.

Research question

Interest in a particular topic usually begins the research process, but it is the familiarity with the subject that helps define an appropriate research question for a study. 1 Questions then arise out of a perceived knowledge deficit within a subject area or field of study. 2 Indeed, Haynes suggests that it is important to know “where the boundary between current knowledge and ignorance lies.” 1 The challenge in developing an appropriate research question is in determining which clinical uncertainties could or should be studied and also rationalizing the need for their investigation.

Increasing one’s knowledge about the subject of interest can be accomplished in many ways. Appropriate methods include systematically searching the literature, in-depth interviews and focus groups with patients (and proxies) and interviews with experts in the field. In addition, awareness of current trends and technological advances can assist with the development of research questions. 2 It is imperative to understand what has been studied about a topic to date in order to further the knowledge that has been previously gathered on a topic. Indeed, some granting institutions (e.g., Canadian Institute for Health Research) encourage applicants to conduct a systematic review of the available evidence if a recent review does not already exist and preferably a pilot or feasibility study before applying for a grant for a full trial.

In-depth knowledge about a subject may generate a number of questions. It then becomes necessary to ask whether these questions can be answered through one study or if more than one study needed. 1 Additional research questions can be developed, but several basic principles should be taken into consideration. 1 All questions, primary and secondary, should be developed at the beginning and planning stages of a study. Any additional questions should never compromise the primary question because it is the primary research question that forms the basis of the hypothesis and study objectives. It must be kept in mind that within the scope of one study, the presence of a number of research questions will affect and potentially increase the complexity of both the study design and subsequent statistical analyses, not to mention the actual feasibility of answering every question. 1 A sensible strategy is to establish a single primary research question around which to focus the study plan. 3 In a study, the primary research question should be clearly stated at the end of the introduction of the grant proposal, and it usually specifies the population to be studied, the intervention to be implemented and other circumstantial factors. 4

Hulley and colleagues 2 have suggested the use of the FINER criteria in the development of a good research question ( Box 1 ). The FINER criteria highlight useful points that may increase the chances of developing a successful research project. A good research question should specify the population of interest, be of interest to the scientific community and potentially to the public, have clinical relevance and further current knowledge in the field (and of course be compliant with the standards of ethical boards and national research standards).

FINER criteria for a good research question

Adapted with permission from Wolters Kluwer Health. 2

Whereas the FINER criteria outline the important aspects of the question in general, a useful format to use in the development of a specific research question is the PICO format — consider the population (P) of interest, the intervention (I) being studied, the comparison (C) group (or to what is the intervention being compared) and the outcome of interest (O). 3 , 5 , 6 Often timing (T) is added to PICO ( Box 2 ) — that is, “Over what time frame will the study take place?” 1 The PICOT approach helps generate a question that aids in constructing the framework of the study and subsequently in protocol development by alluding to the inclusion and exclusion criteria and identifying the groups of patients to be included. Knowing the specific population of interest, intervention (and comparator) and outcome of interest may also help the researcher identify an appropriate outcome measurement tool. 7 The more defined the population of interest, and thus the more stringent the inclusion and exclusion criteria, the greater the effect on the interpretation and subsequent applicability and generalizability of the research findings. 1 , 2 A restricted study population (and exclusion criteria) may limit bias and increase the internal validity of the study; however, this approach will limit external validity of the study and, thus, the generalizability of the findings to the practical clinical setting. Conversely, a broadly defined study population and inclusion criteria may be representative of practical clinical practice but may increase bias and reduce the internal validity of the study.

PICOT criteria 1

A poorly devised research question may affect the choice of study design, potentially lead to futile situations and, thus, hamper the chance of determining anything of clinical significance, which will then affect the potential for publication. Without devoting appropriate resources to developing the research question, the quality of the study and subsequent results may be compromised. During the initial stages of any research study, it is therefore imperative to formulate a research question that is both clinically relevant and answerable.

Research hypothesis

The primary research question should be driven by the hypothesis rather than the data. 1 , 2 That is, the research question and hypothesis should be developed before the start of the study. This sounds intuitive; however, if we take, for example, a database of information, it is potentially possible to perform multiple statistical comparisons of groups within the database to find a statistically significant association. This could then lead one to work backward from the data and develop the “question.” This is counterintuitive to the process because the question is asked specifically to then find the answer, thus collecting data along the way (i.e., in a prospective manner). Multiple statistical testing of associations from data previously collected could potentially lead to spuriously positive findings of association through chance alone. 2 Therefore, a good hypothesis must be based on a good research question at the start of a trial and, indeed, drive data collection for the study.

The research or clinical hypothesis is developed from the research question and then the main elements of the study — sampling strategy, intervention (if applicable), comparison and outcome variables — are summarized in a form that establishes the basis for testing, statistical and ultimately clinical significance. 3 For example, in a research study comparing computer-assisted acetabular component insertion versus freehand acetabular component placement in patients in need of total hip arthroplasty, the experimental group would be computer-assisted insertion and the control/conventional group would be free-hand placement. The investigative team would first state a research hypothesis. This could be expressed as a single outcome (e.g., computer-assisted acetabular component placement leads to improved functional outcome) or potentially as a complex/composite outcome; that is, more than one outcome (e.g., computer-assisted acetabular component placement leads to both improved radiographic cup placement and improved functional outcome).

However, when formally testing statistical significance, the hypothesis should be stated as a “null” hypothesis. 2 The purpose of hypothesis testing is to make an inference about the population of interest on the basis of a random sample taken from that population. The null hypothesis for the preceding research hypothesis then would be that there is no difference in mean functional outcome between the computer-assisted insertion and free-hand placement techniques. After forming the null hypothesis, the researchers would form an alternate hypothesis stating the nature of the difference, if it should appear. The alternate hypothesis would be that there is a difference in mean functional outcome between these techniques. At the end of the study, the null hypothesis is then tested statistically. If the findings of the study are not statistically significant (i.e., there is no difference in functional outcome between the groups in a statistical sense), we cannot reject the null hypothesis, whereas if the findings were significant, we can reject the null hypothesis and accept the alternate hypothesis (i.e., there is a difference in mean functional outcome between the study groups), errors in testing notwithstanding. In other words, hypothesis testing confirms or refutes the statement that the observed findings did not occur by chance alone but rather occurred because there was a true difference in outcomes between these surgical procedures. The concept of statistical hypothesis testing is complex, and the details are beyond the scope of this article.

Another important concept inherent in hypothesis testing is whether the hypotheses will be 1-sided or 2-sided. A 2-sided hypothesis states that there is a difference between the experimental group and the control group, but it does not specify in advance the expected direction of the difference. For example, we asked whether there is there an improvement in outcomes with computer-assisted surgery or whether the outcomes worse with computer-assisted surgery. We presented a 2-sided test in the above example because we did not specify the direction of the difference. A 1-sided hypothesis states a specific direction (e.g., there is an improvement in outcomes with computer-assisted surgery). A 2-sided hypothesis should be used unless there is a good justification for using a 1-sided hypothesis. As Bland and Atlman 8 stated, “One-sided hypothesis testing should never be used as a device to make a conventionally nonsignificant difference significant.”

The research hypothesis should be stated at the beginning of the study to guide the objectives for research. Whereas the investigators may state the hypothesis as being 1-sided (there is an improvement with treatment), the study and investigators must adhere to the concept of clinical equipoise. According to this principle, a clinical (or surgical) trial is ethical only if the expert community is uncertain about the relative therapeutic merits of the experimental and control groups being evaluated. 9 It means there must exist an honest and professional disagreement among expert clinicians about the preferred treatment. 9

Designing a research hypothesis is supported by a good research question and will influence the type of research design for the study. Acting on the principles of appropriate hypothesis development, the study can then confidently proceed to the development of the research objective.

Research objective

The primary objective should be coupled with the hypothesis of the study. Study objectives define the specific aims of the study and should be clearly stated in the introduction of the research protocol. 7 From our previous example and using the investigative hypothesis that there is a difference in functional outcomes between computer-assisted acetabular component placement and free-hand placement, the primary objective can be stated as follows: this study will compare the functional outcomes of computer-assisted acetabular component insertion versus free-hand placement in patients undergoing total hip arthroplasty. Note that the study objective is an active statement about how the study is going to answer the specific research question. Objectives can (and often do) state exactly which outcome measures are going to be used within their statements. They are important because they not only help guide the development of the protocol and design of study but also play a role in sample size calculations and determining the power of the study. 7 These concepts will be discussed in other articles in this series.

From the surgeon’s point of view, it is important for the study objectives to be focused on outcomes that are important to patients and clinically relevant. For example, the most methodologically sound randomized controlled trial comparing 2 techniques of distal radial fixation would have little or no clinical impact if the primary objective was to determine the effect of treatment A as compared to treatment B on intraoperative fluoroscopy time. However, if the objective was to determine the effect of treatment A as compared to treatment B on patient functional outcome at 1 year, this would have a much more significant impact on clinical decision-making. Second, more meaningful surgeon–patient discussions could ensue, incorporating patient values and preferences with the results from this study. 6 , 7 It is the precise objective and what the investigator is trying to measure that is of clinical relevance in the practical setting.

The following is an example from the literature about the relation between the research question, hypothesis and study objectives:

Study: Warden SJ, Metcalf BR, Kiss ZS, et al. Low-intensity pulsed ultrasound for chronic patellar tendinopathy: a randomized, double-blind, placebo-controlled trial. Rheumatology 2008;47:467–71.

Research question: How does low-intensity pulsed ultrasound (LIPUS) compare with a placebo device in managing the symptoms of skeletally mature patients with patellar tendinopathy?

Research hypothesis: Pain levels are reduced in patients who receive daily active-LIPUS (treatment) for 12 weeks compared with individuals who receive inactive-LIPUS (placebo).

Objective: To investigate the clinical efficacy of LIPUS in the management of patellar tendinopathy symptoms.

The development of the research question is the most important aspect of a research project. A research project can fail if the objectives and hypothesis are poorly focused and underdeveloped. Useful tips for surgical researchers are provided in Box 3 . Designing and developing an appropriate and relevant research question, hypothesis and objectives can be a difficult task. The critical appraisal of the research question used in a study is vital to the application of the findings to clinical practice. Focusing resources, time and dedication to these 3 very important tasks will help to guide a successful research project, influence interpretation of the results and affect future publication efforts.

Tips for developing research questions, hypotheses and objectives for research studies

• Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
• Learn about current trends and technological advances on the topic.
• Seek careful input from experts, mentors, colleagues and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
• Use the FINER criteria in the development of the research question.
• Ensure that the research question follows PICOT format.
• Develop a research hypothesis from the research question.
• Develop clear and well-defined primary and secondary (if needed) objectives.
• Ensure that the research question and objectives are answerable, feasible and clinically relevant.

FINER = feasible, interesting, novel, ethical, relevant; PICOT = population (patients), intervention (for intervention studies only), comparison group, outcome of interest, time.

Competing interests: No funding was received in preparation of this paper. Dr. Bhandari was funded, in part, by a Canada Research Chair, McMaster University.

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons

Margin Size

• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

7.3: The Research Hypothesis and the Null Hypothesis

• Last updated
• Save as PDF
• Page ID 18038

• Michelle Oja
• Taft College

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

Hypotheses are predictions of expected findings.

The Research Hypothesis

A research hypothesis is a mathematical way of stating a research question.  A research hypothesis names the groups (we'll start with a sample and a population), what was measured, and which we think will have a higher mean.  The last one gives the research hypothesis a direction.  In other words, a research hypothesis should include:

• The name of the groups being compared.  This is sometimes considered the IV.
• What was measured.  This is the DV.
• Which group are we predicting will have the higher mean.  

There are two types of research hypotheses related to sample means and population means:  Directional Research Hypotheses and Non-Directional Research Hypotheses

Directional Research Hypothesis

If we expect our obtained sample mean to be above or below the other group's mean (the population mean, for example), we have a directional hypothesis. There are two options:

• Symbol:       \( \displaystyle \bar{X} > \mu \)
• (The mean of the sample is greater than than the mean of the population.)
• Symbol:     \( \displaystyle \bar{X} < \mu \)
• (The mean of the sample is less than than mean of the population.)

Example \(\PageIndex{1}\)

A study by Blackwell, Trzesniewski, and Dweck (2007) measured growth mindset and how long the junior high student participants spent on their math homework.  What’s a directional hypothesis for how scoring higher on growth mindset (compared to the population of junior high students) would be related to how long students spent on their homework?  Write this out in words and symbols.

Answer in Words:            Students who scored high on growth mindset would spend more time on their homework than the population of junior high students.

Answer in Symbols:         \( \displaystyle \bar{X} > \mu \) 

Non-Directional Research Hypothesis

A non-directional hypothesis states that the means will be different, but does not specify which will be higher.  In reality, there is rarely a situation in which we actually don't want one group to be higher than the other, so we will focus on directional research hypotheses.  There is only one option for a non-directional research hypothesis: "The sample mean differs from the population mean."  These types of research hypotheses don’t give a direction, the hypothesis doesn’t say which will be higher or lower.

A non-directional research hypothesis in symbols should look like this:    \( \displaystyle \bar{X} \neq \mu \) (The mean of the sample is not equal to the mean of the population).

Exercise \(\PageIndex{1}\)

What’s a non-directional hypothesis for how scoring higher on growth mindset higher on growth mindset (compared to the population of junior high students) would be related to how long students spent on their homework (Blackwell, Trzesniewski, & Dweck, 2007)?  Write this out in words and symbols.

Answer in Words:            Students who scored high on growth mindset would spend a different amount of time on their homework than the population of junior high students.

Answer in Symbols:        \( \displaystyle \bar{X} \neq \mu \) 

See how a non-directional research hypothesis doesn't really make sense?  The big issue is not if the two groups differ, but if one group seems to improve what was measured (if having a growth mindset leads to more time spent on math homework).  This textbook will only use directional research hypotheses because researchers almost always have a predicted direction (meaning that we almost always know which group we think will score higher).

The Null Hypothesis

The hypothesis that an apparent effect is due to chance is called the null hypothesis, written \(H_0\) (“H-naught”). We usually test this through comparing an experimental group to a comparison (control) group.  This null hypothesis can be written as:

\[\mathrm{H}_{0}: \bar{X} = \mu \nonumber \]

For most of this textbook, the null hypothesis is that the means of the two groups are similar.  Much later, the null hypothesis will be that there is no relationship between the two groups.  Either way, remember that a null hypothesis is always saying that nothing is different.  

This is where descriptive statistics diverge from inferential statistics.  We know what the value of \(\overline{\mathrm{X}}\) is – it’s not a mystery or a question, it is what we observed from the sample.  What we are using inferential statistics to do is infer whether this sample's descriptive statistics probably represents the population's descriptive statistics.  This is the null hypothesis, that the two groups are similar.  

Keep in mind that the null hypothesis is typically the opposite of the research hypothesis. A research hypothesis for the ESP example is that those in my sample who say that they have ESP would get more correct answers than the population would get correct, while the null hypothesis is that the average number correct for the two groups will be similar. 

In general, the null hypothesis is the idea that nothing is going on: there is no effect of our treatment, no relation between our variables, and no difference in our sample mean from what we expected about the population mean. This is always our baseline starting assumption, and it is what we seek to reject. If we are trying to treat depression, we want to find a difference in average symptoms between our treatment and control groups. If we are trying to predict job performance, we want to find a relation between conscientiousness and evaluation scores. However, until we have evidence against it, we must use the null hypothesis as our starting point.

In sum, the null hypothesis is always : There is no difference between the groups’ means OR There is no relationship between the variables .

In the next chapter, the null hypothesis is that there’s no difference between the sample mean   and population mean.  In other words:

• There is no mean difference between the sample and population.
• The mean of the sample is the same as the mean of a specific population.
• \(\mathrm{H}_{0}: \bar{X} = \mu \nonumber \)
• We expect our sample’s mean to be same as the population mean.

Exercise \(\PageIndex{2}\)

A study by Blackwell, Trzesniewski, and Dweck (2007) measured growth mindset and how long the junior high student participants spent on their math homework.  What’s the null hypothesis for scoring higher on growth mindset (compared to the population of junior high students) and how long students spent on their homework?  Write this out in words and symbols.

Answer in Words:            Students who scored high on growth mindset would spend a similar amount of time on their homework as the population of junior high students.

Answer in Symbols:    \( \bar{X} = \mu \)

Contributors and Attributions

Foster et al.  (University of Missouri-St. Louis, Rice University, & University of Houston, Downtown Campus)

Dr. MO ( Taft College )

• Open access
• Published: 13 May 2024

SCIPAC: quantitative estimation of cell-phenotype associations

• Dailin Gan 1 ,
• Yini Zhu 2 ,
• Xin Lu 2 , 3 &
• Jun Li   ORCID: orcid.org/0000-0003-4353-5761 1  

Genome Biology volume  25 , Article number:  119 ( 2024 ) Cite this article

374 Accesses

2 Altmetric

Metrics details

Numerous algorithms have been proposed to identify cell types in single-cell RNA sequencing data, yet a fundamental problem remains: determining associations between cells and phenotypes such as cancer. We develop SCIPAC, the first algorithm that quantitatively estimates the association between each cell in single-cell data and a phenotype. SCIPAC also provides a p -value for each association and applies to data with virtually any type of phenotype. We demonstrate SCIPAC’s accuracy in simulated data. On four real cancerous or noncancerous datasets, insights from SCIPAC help interpret the data and generate new hypotheses. SCIPAC requires minimum tuning and is computationally very fast.

Single-cell RNA sequencing (scRNA-seq) technologies are revolutionizing biomedical research by providing comprehensive characterizations of diverse cell populations in heterogeneous tissues [ 1 , 2 ]. Unlike bulk RNA sequencing (RNA-seq), which measures the average expression profile of the whole tissue, scRNA-seq gives the expression profiles of thousands of individual cells in the tissue [ 3 , 4 , 5 , 6 , 7 ]. Based on this rich data, cell types may be discovered/determined in an unsupervised (e.g., [ 8 , 9 ]), semi-supervised (e.g., [ 10 , 11 , 12 , 13 ]), or supervised manner (e.g., [ 14 , 15 , 16 ]). Despite the fast development, there are still limitations with scRNA-seq technologies. Notably, the cost for each scRNA-seq experiment is still high; as a result, most scRNA-seq data are from a single or a few biological samples/tissues. Very few datasets consist of large numbers of samples with different phenotypes, e.g., cancer vs. normal. This places great difficulties in determining how a cell type contributes to a phenotype based on single-cell studies (especially if the cell type is discovered in a completely unsupervised manner or if people have limited knowledge of this cell type). For example, without having single-cell data from multiple cancer patients and multiple normal controls, it could be hard to computationally infer whether a cell type may promote or inhibit cancer development. However, such association can be critical for cancer research [ 17 ], disease diagnosis [ 18 ], cell-type targeted therapy development [ 19 ], etc.

Fortunately, this difficulty may be overcome by borrowing information from bulk RNA-seq data. Over the past decade, a considerable amount of bulk RNA-seq data from a large number of samples with different phenotypes have been accumulated and made available through databases like The Cancer Genome Atlas (TCGA) [ 20 ] and cBioPortal [ 21 , 22 ]. Data in these databases often contain comprehensive patient phenotype information, such as cancer status, cancer stages, survival status and time, and tumor metastasis. Combining single-cell data from a single or a few individuals and bulk data from a relatively large number of individuals regarding a particular phenotype can be a cost-effective way to determine how a cell type contributes to the phenotype. A recent method Scissor [ 23 ] took an essential step in this direction. It uses single-cell and bulk RNA-seq data with phenotype information to classify the cells into three discrete categories: Scissor+, Scissor−, and null cells, corresponding to cells that are positively associated, negatively associated, and not associated with the phenotype.

Here, we present a method that takes another big step in this direction, which is called Single-Cell and bulk data-based Identifier for Phenotype Associated Cells or SCIPAC for short. SCIPAC enables quantitative estimation of the strength of association between each cell in a scRNA-seq data and a phenotype, with the help of bulk RNA-seq data with phenotype information. Moreover, SCIPAC also enables the estimation of the statistical significance of the association. That is, it gives a p -value for the association between each cell and the phenotype. Furthermore, SCIPAC enables the estimation of association between cells and an ordinal phenotype (e.g., different stages of cancer), which could be informative as people may not only be interested in the emergence/existence of cancer (cancer vs. healthy, a binary problem) but also in the progression of cancer (different stages of cancer, an ordinal problem).

To study the performance of SCIPAC, we first apply SCIPAC to simulated data under three schemes. SCIPAC shows high accuracy with low false positive rates. We further show the broad applicability of SCIPAC on real datasets across various diseases, including prostate cancer, breast cancer, lung cancer, and muscular dystrophy. The association inferred by SCIPAC is highly informative. In real datasets, some cell types have definite and well-studied functions, while others are less well-understood: their functions may be disease-dependent or tissue-dependent, and they may contain different sub-types with distinct functions. In the former case, SCIPAC’s results agree with current biological knowledge. In the latter case, SCIPAC’s discoveries inspire the generation of new hypotheses regarding the roles and functions of cells under different conditions.

An overview of the SCIPAC algorithm

SCIPAC is a computational method that identifies cells in single-cell data that are associated with a given phenotype. This phenotype can be binary (e.g., cancer vs. normal), ordinal (e.g., cancer stage), continuous (e.g., quantitative traits), or survival (i.e., survival time and status). SCIPAC uses input data consisting of three parts: single-cell RNA-seq data that measures the expression of p genes in m cells, bulk RNA-seq data that measures the expression of the same set of p genes in n samples/tissues, and the statuses/values of the phenotype of the n bulk samples/tissues. The output of SCIPAC is the strength and the p -value of the association between each cell and the phenotype.

SCIPAC proposes the following definition of “association” between a cell and a phenotype: A group of cells that are likely to play a similar role in the phenotype (such as cells of a specific cell type or sub-type, cells in a particular state, cells in a cluster, cells with similar expression profiles, or cells with similar functions) is considered to be positively/negatively associated with a phenotype if an increase in their proportion within the tissue likely indicates an increased/decreased probability of the phenotype’s presence. SCIPAC assigns the same association to all cells within such a group. Taking cancer as the phenotype as an example, if increasing the proportion of a cell type indicates a higher chance of having cancer (binary), having a higher cancer stage (ordinal), or a higher hazard rate (survival), all cells in this cell type is positively associated with cancer.

The algorithm of SCIPAC follows the following four steps. First, the cells in the single-cell data are grouped into clusters according to their expression profiles. The Louvain algorithm from the Seurat package [ 24 , 25 ] is used as the default clustering algorithm, but the user may choose any clustering algorithm they prefer. Or if information of the cell types or other groupings of cells is available a priori, it may be supplied to SCIPAC as the cell clusters, and this clustering step can be skipped. In the second step, a regression model is learned from bulk gene expression data with the phenotype. Depending on the type of the phenotype, this model can be logistic regression, ordinary linear regression, proportional odds model, or Cox proportional hazards model. To achieve a higher prediction power with less variance, by default, the elastic net (a blender of Lasso and ridge regression [ 26 ]) is used to fit the model. In the third step, SCIPAC computes the association strength \(\Lambda\) between each cell cluster and the phenotype based on a mathematical formula that we derive. Finally, the p -values are computed. The association strength and its p -value between a cell cluster and the phenotype are given to all cells in the cluster.

SCIPAC requires minimum tuning. When the cell-type information is given in step 1, SCIPAC does not have any (hyper)parameter. Otherwise, the Louvain algorithm used in step 1 has a “resolution” parameter that controls the number of cell clusters: a larger resolution results in more clusters. SCIPAC inherits this parameter as its only parameter. Since SCIPAC gives the same association strength and p -value to cells from the same cluster, this parameter also determines the resolution of results provided by SCIPAC. Thus, we still call it “resolution” in SCIPAC. Because of its meaning, we recommend setting it so that the number of cell clusters given by the clustering algorithm is comparable to, or reasonably larger than, the number of cell types (or sub-types) in the data. We will see that the performance of SCIPAC is insensitive to this resolution parameter, and the default value 2.0 typically works well.

The details of the SCIPAC algorithm are given in the “ Methods ” section.

Performance in simulated data

We assess the performance of SCIPAC in simulated data under three different schemes. The first scheme is simple and consists of only three cell types. The second scheme is more complicated and consists of seven cell types, which better imitates actual scRNA-seq data. In the third scheme, we simulate cells under different cell development stages to test the performance of SCIPAC under an ordinal phenotype. Details of the simulation are given in Additional file 1.

Simulation scheme I

Under this scheme, the single-cell data consists of three cell types: one is positively associated with the phenotype, one is negatively associated, and the third is not associated (we call it “null”). Figure 1 a gives the UMAP [ 27 ] plot of the three cell types, and Fig. 1 b gives the true associations of these three cell types with the phenotype, with red, blue, and light gray denoting positive, negative, and null associations.

UMAP visualization and numeric measures of the simulated data under scheme I. All the plots in a–e  are scatterplots of the two dimensional single-cell data given by UMAP. The x and y axes represent the two dimensions, and their scales are not shown as their specific values are not directly relevant. Points in the plots represents single cells, and they are colored differently in each subplot to reflect different information/results. a  Cell types. b  True associations. The association between cell types 1, 2, and 3 and the phenotype are positive, negative, and null, respectively. c  Association strengths \(\Lambda\) given by SCIPAC under different resolutions. Red/blue represents the sign of \(\Lambda\) , and the shade gives the absolute value of \(\Lambda\) . Every cell is colored red or blue since no \(\Lambda\) is exactly zero. Below each subplot, Res stands for resolution, and K stands for the number of cell clusters given by this resolution. d   p -values given by SCIPAC. Only cells with p -value \(< 0.05\) are colored red (positive association) or blue (negative association); others are colored white. e  Results given by Scissor under different \(\alpha\) values. Red, blue, and light gray stands for Scissor+, Scissor−, and background (i.e., null) cells. f  F1 scores and g  FSC for SCIPAC and Scissor under different parameter values. For SCIPAC, each bar is the value under a resolution/number of clusters. For Scissor, each bar is the value under an \(\alpha\)

We apply SCIPAC to the simulated data. For the resolution parameter (see the “ Methods ” section), values 0.5, 1.0, and 1.5 give 3, 4, and 4 clusters, respectively, close to the actual number of cell types. They are good choices based on the guidance for choosing this parameter. To show how SCIPAC behaves under parameter misspecification, we also set the resolution up to 4.0, which gives a whopping 61 clusters. Figure 1 c and d give the association strengths \(\Lambda\) and the p -values given by four different resolutions (results under other resolutions are provided in Additional file 1: Fig. S1 and S2). In Fig. 1 c, red and blue denote positive and negative associations, respectively, and the shade of the color represents the strength of the association, i.e., the absolute value of \(\Lambda\) . Every cell is colored blue or red, as none of \(\Lambda\) is exactly zero. In Fig. 1 d, red and blue denote positive and negative associations that are statistically significant ( p -value \(< 0.05\) ). Cells whose associations are not statistically significant ( p -value \(\ge 0.05\) ) are shown in white. To avoid confusion, it is worth repeating that cells that are colored in red/blue in Fig. 1 c are shown in red/blue in Fig. 1 d only if they are statistically significant; otherwise, they are colored white in Fig. 1 d.

From Fig. 1 c, d (as well as Additional file 1: Fig. S1 and S2), it is clear that the results of SCIPAC are highly consistent under different resolution values, including both the estimated association strengths and the p -values. It is also clear that SCIPAC is highly accurate: most truly associated cells are identified as significant, and most, if not all, truly null cells are identified as null.

As the first algorithm that quantitatively estimates the association strength and the first algorithm that gives the p -value of the association, SCIPAC does not have a real competitor. A previous algorithm, Scissor, is able to classify cells into three discrete categories according to their associations with the phenotype. So, we compare SCIPAC with Scissor in respect of the ability to differentiate positively associated, negatively associated, and null cells.

Running Scissor requires tuning a parameter called \(\alpha\) , which is a number between 0 and 1 that balances the amount of regularization for the smoothness and for the sparsity of the associations. The Scissor R package does not provide a default value for this \(\alpha\) or a function to help select this value. The Scissor paper suggests the following criterion: “the number of Scissor-selected cells should not exceed a certain percentage of total cells (default 20%) in the single-cell data. In each experiment, a search on the above searching list is performed from the smallest to the largest until a value of \(\alpha\) meets the above criteria.” In practice, we have found that this criterion does not often work properly, as the truly associated cells may not compose 20% of all cells in actual data. Therefore, instead of setting \(\alpha\) to any particular value, we set \(\alpha\) values that span the whole range of \(\alpha\) to see the best possible performance of Scissor.

The performance of Scissor in our simulation data under four different \(\alpha\) values are shown in Fig. 1 e, and results under more \(\alpha\) values are shown in Additional file 1: Fig. S3. In the figures, red, blue, and light gray denote Scissor+, Scissor−, and null (called “background” in Scissor) cells, respectively. The results of Scissor have several characteristics different from SCIPAC. First, Scissor does not give the strength or statistical significance of the association, and thus the colors of the cells in the figures do not have different shades. Second, different \(\alpha\) values give very different results. Greater \(\alpha\) values generally give fewer Scissor+ and Scissor− cells, but there are additional complexities. One complexity is that the Scissor+ (or Scissor−) cells under a greater \(\alpha\) value are not a strict subset of Scissor+ (or Scissor−) cells under a smaller \(\alpha\) value. For example, the number of truly negatively associated cells detected as Scissor− increases when \(\alpha\) increases from 0.01 to 0.30. Another complexity is that the direction of the association may flip as \(\alpha\) increases. For example, most cells of cell type 2 are identified as Scissor+ under \(\alpha =0.01\) , but many of them are identified as Scissor− under larger \(\alpha\) values. Third, Scissor does not achieve high power and low false-positive rate at the same time under any \(\alpha\) . No matter what the \(\alpha\) value is, there is only a small proportion of cells from cell type 2 that are correctly identified as negatively associated, and there is always a non-negligible proportion of null cells (i.e., cells from cell type 3) that are incorrectly identified as positively or negatively associated. Fourth, Scissor+ and Scissor− cells can be close to each other in the figure, even under a large \(\alpha\) value. This means that cells with nearly identical expression profiles are detected to be associated with the phenotype in opposite directions, which can place difficulties in interpreting the results.

SCIPAC overcomes the difficulties of Scissor and gives results that are more informative (quantitative strengths with p -values), more accurate (both high power and low false-positive rate), less sensitive to the tuning parameter, and easier to interpret (cells with similar expression typically have similar associations to the phenotype).

SCIPAC’s higher accuracy in differentiating positively associated, negatively associated, and null cells than Scissors can also be measured numerically using the F1 score and the fraction of sign correctness (FSC). F1, which is the harmonic mean of precision and recall, is a commonly used measure of calling accuracy. Note that precision and recall are only defined for two-class problems, which try to classify desired signals/discoveries (so-called “positives”) against noises/trivial results (so-called “negatives”). Our case, on the other hand, is a three-class problem: positive association, negative association, and null. To compute F1, we combine the positive and negative associations and treat them as “positives,” and treat null as “negatives.” This F1 score ignores the direction of the association; thus, it alone is not enough to describe the performance of an association-detection algorithm. For example, an algorithm may have a perfect F1 score even if it incorrectly calls all negative associations positive. To measure an algorithm’s ability to determine the direction of the association, we propose a statistic called FSC, defined as the fraction of true discoveries that also have the correct direction of the association. The F1 score and FSC are numbers between 0 and 1, and higher values are preferred. A mathematical definition of these two measures is given in Additional file 1.

Figure 1 f, g show the F1 score and FSC of SCIPAC and Scissor under different values of tuning parameters. The F1 score of Scissor is between 0.2 and 0.7 under different \(\alpha\) ’s. The FSC of Scissor increases from around 0.5 to nearly 1 as \(\alpha\) increases, but Scissor does not achieve high F1 and FSC scores at the same time under any \(\alpha\) . On the other hand, the F1 score of SCIPAC is close to perfection when the resolution parameter is properly set, and it is still above 0.90 even if the resolution parameter is set too large. The FSC of SCIPAC is always above 0.96 under different resolutions. That is, SCIPAC achieves high F1 and FSC scores simultaneously under a wide range of resolutions, representing a much higher accuracy than Scissor.

Simulation scheme II

This more complicated simulation scheme has seven cell types, which are shown in Fig. 2 a. As shown in Fig. 2 b, cell types 1 and 3 are negatively associated (colored blue), 2 and 4 are positively associated (colored red), and 5, 6, and 7 are not associated (colored light gray).

UMAP visualization of the simulated data under a–g  scheme II and h–k  scheme III. a  Cell types. b  True associations. c , d  Association strengths \(\Lambda\) and p -values given by SCIPAC under the default resolution. e  Results given by Scissor under different \(\alpha\) values. f  F1 scores and g  FSC for SCIPAC and Scissor under different parameter values. h  Cell differentiation paths. The four paths have the same starting location, which is in the center, but different ending locations. This can be considered as a progenitor cell type differentiating into four specialized cell types. i  Cell differentiation steps. These steps are used to create four stages, each containing 500 steps. Thus, this plot of differentiation steps can also be viewed as the plot of true association strengths. j , k  Association strengths \(\Lambda\) and p -values given by SCIPAC under the default resolution

The association strengths and p -values given by SCIPAC under the default resolution are illustrated in Fig. 2 c, d, respectively. Results under several other resolutions are given in Additional file 1: Fig. S4 and S5. Again, we find that SCIPAC gives highly consistent results under different resolutions. SCIPAC successfully identifies three out of the four truly associated cell types. For the other truly associated cell type, cell type 1, SCIPAC correctly recognizes its association with the phenotype as negative, although the p -values are not significant enough. The F1 score is 0.85, and the FSC is greater than 0.99, as shown in Fig. 2 f, g.

The results of Scissor under four different \(\alpha\) values are given in Fig. 2 e. (More shown in Additional file 1: Fig. S6.) Under this highly challenging simulation scheme, Scissor can only identify one out of four truly associated cell types. Its F1 score is below 0.4.

Simulation scheme III

This simulation scheme is to assess the performance of SCIPAC for ordinal phenotypes. We simulate cells along four cell-differentiation paths with the same starting location but different ending locations, as shown in Fig. 2 h. These cells can be considered as a progenitor cell population differentiating into four specialized cell types. In Fig. 2 i, the “step” reflects their position in the differentiation path, with step 0 meaning the start and step 2000 meaning the end of the differentiation. Then, the “stage” is generated according to the step: cells in steps 0 \(\sim\) 500, 501 \(\sim\) 1000, 1001 \(\sim\) 1500, and 1501 \(\sim\) 2000 are assigned to stages I, II, III, and IV, respectively. This stage is treated as the ordinal phenotype. Under this simulation scheme, Fig. 2 i also gives the actual associations, and all cells are associated with the phenotype.

The results of SCIPAC under the default resolution are shown in Fig. 2 j, k. Clearly, the associations SCIPAC identifies are highly consistent with the truth. Particularly, it successfully identifies the cells in the center as early-stage cells and most cells at the end of branches as last-stage cells. The results of SCIPAC under other resolutions are given in Additional file 1: Fig. S7 and S8, which are highly consistent. Scissor does not work with ordinal phenotypes; thus, no results are reported here.

Performance in real data

We consider four real datasets: a prostate cancer dataset, a breast cancer dataset, a lung cancer dataset, and a muscular dystrophy dataset. The bulk RNA-seq data of the three cancer datasets are obtained from the TCGA database, and that of the muscular dystrophy dataset is obtained from a published paper [ 28 ]. A detailed description of these datasets is given in Additional file 1. We will use these datasets to assess the performance of SCIPAC on different types of phenotypes. The cell type information (i.e., which cell belongs to which cell type) is available for the first three datasets, but we ignore this information so that we can make a fair comparison with Scissor, which cannot utilize this information.

Prostate cancer data with a binary phenotype

We use the single-cell expression of 8,700 cells from prostate-cancer tumors sequenced by [ 29 ]. The cell types of these cells are known and given in Fig. 3 a. The bulk data comprises 550 TCGA-PRAD (prostate adenocarcinoma) samples with phenotype (cancer vs. normal) information. Here the phenotype is cancer, and it is binary: present or absent.

UMAP visualization of the prostate cancer data, with a zoom-in view for the red-circled region (cell type MNP). a  True cell types. BE, HE, and CE stand for basal, hillock, club epithelial cells, LE-KLK3 and LE-KLK4 stand for luminal epithelial cells with high levels of kallikrein related peptidase 3 and 4, and MNP stands for mononuclear phagocytes. In the zoom-in view, the sub-types of MNP cells are given. b  Association strengths \(\Lambda\) given by SCIPAC under the default resolution. The cyan-circled cells are B cells, which are estimated by SCIPAC as negatively associated with cancer but estimated by Scissor as Scissor+ or null. c   p -values given by SCIPAC. The MNP cell type, which is red-circled in the plot, is estimated by SCIPAC to be strongly negatively associated with cancer but estimated by Scissor to be positively associated with cancer. d  Results given by Scissor under different \(\alpha\) values

Results from SCIPAC with the default resolution are shown in Fig. 3 b, c (results with other resolutions, given in Additional file 1: Fig. S9 and S10, are highly consistent with results here.) Compared with results from Scissor, shown in Fig. 3 d, results from SCIPAC again show three advantages. First, results from SCIPAC are richer and more comprehensive. SCIPAC gives estimated associations and the corresponding p -values, and the estimated associations are quantitative (shown in Fig. 3 b as different shades to the red or blue color) instead of discrete (shown in Fig. 3 d as a uniform shade to the red, blue, or light gray color). Second, SCIPAC’s results can be easier to interpret as the red and blue colors are more block-wise instead of scattered. Third, unlike Scissor, which produces multiple sets of results varying based on the parameter \(\alpha\) —a parameter without a default value or tuning guidance—typically, a single set of results from SCIPAC under its default settings suffices.

Comparing the results from our SCIPAC method with those from Scissor is non-trivial, as the latter’s outcomes are scattered and include multiple sets. We propose the following solutions to summarize the inferred association of a known cell type with the phenotype using a specific method (Scissor under a specific \(\alpha\) value, or SCIPAC with the default setting). We first calculate the proportion of cells in this cell type identified as Scissor+ (by Scissor at a specific \(\alpha\) value) or as significantly positively associated (by SCIPAC), denoted by \(p_{+}\) . We also calculate the proportion of all cells, encompassing any cell type, which are identified as Scissor+ or significantly positively associated, serving as the average background strength, denoted by \(p_{a}\) . Then, we compute the log odds ratio for this cell type to be positively associated with the phenotype compared to the background, represented as:

Similarly, the log odds ratio for the cell type to be negatively associated with the phenotype, \(\rho _-\) , is computed in a parallel manner.

For SCIPAC, a cell type is summarized as positively associated with the phenotype if \(\rho _+ \ge 1\) and \(\rho _- < 1\)  and negatively associated if \(\rho _- \ge 1\) and \(\rho _+ < 1\) . If neither condition is met, the association is inconclusive. For Scissor, we apply it under six different \(\alpha\) values: 0.01, 0.05, 0.10, 0.15, 0.20, and 0.25. A cell type is summarized as positively associated with the phenotype if \(\rho _+ \ge 1\) and \(\rho _- < 1\) in at least four of these \(\alpha\) values and negatively associated if \(\rho _- \ge 1\) and \(\rho _+ < 1\) in at least four \(\alpha\) values. If these criteria are not met, the association is deemed inconclusive. The above computation of log odds ratios and the determination of associations are performed only on cell types that each compose at least 1% of the cell population, to ensure adequate power.

For the prostate cancer data, the log odds ratios for each cell type using each method are presented in Tables S1 and S2. The final associations determined for each cell type are summarized in Table S3. In the last column of this table, we also indicate whether the conclusions drawn from SCIPAC and Scissor are consistent or not.

We find that SCIPAC’s results agree with Scissor on most cell types. However, there are three exceptions: mononuclear phagocytes (MNPs), B cells, and LE-KLK4.

MNPs are red-circled and zoomed in in each sub-figure of Fig. 3 . Most cells in this cell type are colored red in Fig. 3 d but colored dark blue in Fig. 3 b. In other words, while Scissor determines that this cell type is Scissor+, SCIPAC makes the opposite inference. Moreover, SCIPAC is confident about its judgment by giving small p -values, as shown in Fig. 3 c. To see which inference is closer to the biological fact is not easy, as biologically MNPs contain a number of sub-types that each have different functions [ 30 , 31 ]. Fortunately, this cell population has been studied in detail in the original paper that generated this dataset [ 29 ], and the sub-type information of each cell is provided there: this MNP population contains six sub-types, which are dendritic cells (DC), M1 macrophages (Mac1), metallothionein-expressing macrophages (Mac-MT), M2 macrophages (Mac2), proliferating macrophages (Mac-cycling), and monocytes (Mono), as shown in the zoom-in view of Fig. 3 a. Among these six sub-types, DC, Mac1, and Mac-MT are believed to inhibit cancer development and can serve as targets in cancer immunotherapy [ 29 ]; they compose more than 60% of all MNP cells in this dataset. SCIPAC makes the correct inference on this majority of MNP cells. Another cell type, Mac2, is reported to promote tumor development [ 32 ], but it only composes less than \(15\%\) of the MNPs. How the other two cell types, Mac-cycling and Mono, are associated with cancer is less studied. Overall, the results given by SCIPAC are more consistent with the current biological knowledge.

B cells are cyan-circled in Fig. 3 b. B cells are generally believed to have anti-tumor activity by producing tumor-reactive antibodies and forming tertiary lymphoid structures [ 29 , 33 ]. This means that B cells are likely to be negatively associated with cancer. SCIPAC successfully identifies this negative association, while Scissor fails.

LE-KLK4, a subtype of cancer cells, is thought to be positively associated with the tumor phenotype [ 29 ]. SCIPAC successfully identified this positive association, in contrast to Scissor, which failed to do so (in the figure, a proportion of LE-KLK4 cells are identified as Scissor+, especially under the smallest \(\alpha\) value; however, this proportion is not significantly higher than the background Scissor+ level under the majority of \(\alpha\) values).

In summary, across all three cell types, the results from SCIPAC appear to be more consistent with current biological knowledge. For more discussions regarding this dataset, refer to Additional file 1.

Breast cancer data with an ordinal phenotype

The scRNA-seq data for breast cancer are from [ 34 ], and we use the 19,311 cells from the five HER2+ tumor tissues. The true cell types are shown in Fig. 4 a. The bulk data include 1215 TCGA-BRCA samples with information on the cancer stage (I, II, III, or IV), which is treated as an ordinal phenotype.

UMAP visualization of the breast cancer data. a  True cell types. CAFs stand for cancer-associated fibroblasts, PB stands for plasmablasts and PVL stands for perivascular-like cells. b , c  Association strengths \(\Lambda\) and p -values given by SCIPAC under the default resolution. Cyan-circled are a group of T cells that are estimated by SCIPAC to be most significantly associated with the cancer stage in the negative direction, and orange-circled are a group of T cells that are estimated by SCIPAC to be significantly positively associated with the cancer stage. d  DE analysis of the cyan-circled T cells vs. all the other T cells. e  DE analysis of the cyan-circled T cells vs. all the other cells. f  Expression of CD8+ T cell marker genes in the cyan-circled cells and all the other cells. g  DE analysis of the orange-circled T cells vs. all the other cells. h  Expression of regulatory T cell marker genes in the orange-circled cells and all the other cells

Association strengths and p -values given by SCIPAC under the default resolution are shown in Fig. 4 b, c. Results under other resolutions are given in Additional file 1: Fig. S11 and S12, and again they are highly consistent with results under the default resolution. We do not present the results from Scissor, as Scissor does not take ordinal phenotypes.

In the SCIPAC results, cells that are most strongly and statistically significantly associated with the phenotype in the positive direction are the cancer-associated fibroblasts (CAFs). This finding agrees with the literature: CAFs contribute to therapy resistance and metastasis of cancer cells via the production of secreted factors and direct interaction with cancer cells [ 35 ], and they are also active players in breast cancer initiation and progression [ 36 , 37 , 38 , 39 ]. Another large group of cells identified as positively associated with the phenotype is the cancer epithelial cells. They are malignant cells in breast cancer tissues and are thus expected to be associated with severe cancer stages.

Of the cells identified as negatively associated with severe cancer stages, a large portion of T cells is the most noticeable. Biologically, T cells contain many sub-types, including CD4+, CD8+, regulatory T cells, and more, and their functions are diverse in the tumor microenvironment [ 40 ]. To explore SCIPAC’s discoveries, we compare T cells that are identified as most statistically significant, with p -values \(< 10^{-6}\) and circled in Fig. 4 d, with the other T cells. Differential expression (DE) analysis (details about DE analysis and other analyses are given in Additional file 1) identifies seven genes upregulated in these most significant T cells. Of these seven genes, at least five are supported by the literature: CCL4, XCL1, IFNG, and GZMB are associated with CD8+ T cell infiltration; they have been shown to have anti-tumor functions and are involved in cancer immunotherapy [ 41 , 42 , 43 ]. Also, IL2 has been shown to serve an important role in combination therapies for autoimmunity and cancer [ 44 ]. We also perform an enrichment analysis [ 45 ], in which a pathway called Myc stands out with a \(\textit{p}\text{-value}<10^{-7}\) , much smaller than all other pathways. Myc is downregulated in the T cells that are identified as most negatively associated with cancer stage progress. This agrees with current biological knowledge about this pathway: Myc is known to contribute to malignant cell transformation and tumor metastasis [ 46 , 47 , 48 ].

On the above, we have compared T cells that are most significantly associated with cancer stages in the negative direction with the other T cells using DE and pathway analysis, and the results could suggest that these cells are tumor-infiltrated CD8+ T cells with tumor-inhibition functions. To check this hypothesis, we perform DE analysis of these cells against all other cells (i.e., the other T cells and all the other cell types). The DE genes are shown in Fig. 4 e. It can be noted that CD8+ T cell marker genes such as CD8A, CD8B, and GZMK are upregulated. We further obtain CD8+ T cell marker genes from CellMarker [ 49 ] and check their expression, as illustrated in Fig. 4 f. Marker genes CD8A, CD8B, CD3D, GZMK, and CD7 show significantly higher expression in these T cells. This again supports our hypothesis that these cells are tumor-infiltrated CD8+ T cells that have anti-tumor functions.

Interestingly, not all T cells are identified as negatively associated with severe cancer stages; a group of T cells is identified as positively associated, as circled in Fig. 4 c. To explore the function of this group of T cells, we perform DE analysis of these T cells against the other T cells. The DE genes are shown in Fig. 4 g. Based on the literature, six out of eight over-expressed genes are associated with cancer development. The high expression of NUSAP1 gene is associated with poor patient overall survival, and this gene also serves as a prognostic factor in breast cancer [ 50 , 51 , 52 ]. Gene MKI67 has been treated as a candidate prognostic prediction for cancer proliferation [ 53 , 54 ]. The over-expression of RRM2 has been linked to higher proliferation and invasiveness of malignant cells [ 55 , 56 ], and the upregulation of RRM2 in breast cancer suggests it to be a possible prognostic indicator [ 57 , 58 , 59 , 60 , 61 , 62 ]. The high expression of UBE2C gene always occurs in cancers with a high degree of malignancy, low differentiation, and high metastatic tendency [ 63 ]. For gene TOP2A, it has been proposed that the HER2 amplification in HER2 breast cancers may be a direct result of the frequent co-amplification of TOP2A [ 64 , 65 , 66 ], and there is a high correlation between the high expressions of TOP2A and the oncogene HER2 [ 67 , 68 ]. Gene CENPF is a cell cycle-associated gene, and it has been identified as a marker of cell proliferation in breast cancers [ 69 ]. The over-expression of these genes strongly supports the correctness of the association identified by SCIPAC. To further validate this positive association, we perform DE analysis of these cells against all the other cells. We find that the top marker genes obtained from CellMarker [ 49 ] for the regulatory T cells, which are known to be immunosuppressive and promote cancer progression [ 70 ], are over-expressed with statistical significance, as shown in Fig. 4 h. This finding again provides strong evidence that the positive association identified by SCIPAC for this group of T cells is correct.

Lung cancer data with survival information

The scRNA-seq data for lung cancer are from [ 71 ], and we use two lung adenocarcinoma (LUAD) patients’ data with 29,888 cells. The true cell types are shown in Fig. 5 a. The bulk data consist of 576 TCGA-LUAD samples with survival status and time.

UMAP visualization of a–d  the lung cancer data and e–g  the muscular dystrophy data. a  True cell types. b , c  Association strengths \(\Lambda\) and p -values given by SCIPAC under the default resolution. d  Results given by Scissor under different \(\alpha\) values. e , f  Association strengths \(\Lambda\) and p -values given by SCIPAC under the default resolution. Circled are a group of cells that are identified by SCIPAC as significantly positively associated with the disease but identified by Scissor as null. g  Results given by Scissor under different \(\alpha\) values

Association strengths and p -values given by SCIPAC are given in Fig. 5 b, c (results under other resolutions are given in Additional file 1: Fig. S13 and S14). In Fig. 5 c, most cells with statistically significant associations are CD4+ T cells or B cells. These associations are negative, meaning that the abundance of these cells is associated with a reduced death rate, i.e., longer survival time. This agrees with the literature: CD4+ T cells primarily mediate anti-tumor immunity and are associated with favorable prognosis in lung cancer patients [ 72 , 73 , 74 ]; B cells also show anti-tumor functions in all stages of human lung cancer development and play an essential role in anti-tumor responses [ 75 , 76 ].

The results by Scissor under different \(\alpha\) values are shown in Fig. 5 d. The highly scattered Scissor+ and Scissor− cells make identifying and interpreting meaningful phenotype-associated cell groups difficult.

Muscular dystrophy data with a binary phenotype

This dataset contains cells from four facioscapulohumeral muscular dystrophy (FSHD) samples and two control samples [ 77 ]. We pool all the 7047 cells from these six samples together. The true cell types of these cells are unknown. The bulk data consists of 27 FSHD patients and eight controls from [ 28 ]. Here the phenotype is FSHD, and it is binary: present or absent.

The results of SCIPAC with the default resolution are given in Fig. 5 e, f. Results under other resolutions are highly similar (shown in Additional file 1: Fig. S15 and S16). For comparison, results given by Scissor under different \(\alpha\) values are presented in Fig. 5 g. The agreements between the results of SCIPAC and Scissor are clear. For example, both methods identify cells located at the top and lower left part of UMAP plots to be negatively associated with FSHD, and cells located at the center and right parts of UMAP plots to be positively associated. However, the discrepancies in their results are also evident. The most pronounced one is a large group of cells (circled in Fig. 5 f) that are identified by SCIPAC as significantly positively associated but are completely ignored by Scissor. Checking into this group of cells, we find that over 90% (424 out of 469) come from the FSHD patients, and less than 10% come from the control samples. However, cells from FSHD patients only compose 73% (5133) of all the 7047 cells. This statistically significant ( p -value \(<10^{-15}\) , Fisher’s exact test) over-representation (odds ratio = 3.51) suggests that the positive association identified SCIPAC is likely to be correct.

SCIPAC is computationally highly efficient. On an 8-core machine with 2.50 GHz CPU and 16 GB RAM, SCIPAC takes 7, 24, and 2 s to finish all the computation and give the estimated association strengths and p -values on the prostate cancer, lung cancer, and muscular dystrophy datasets, respectively. As a reference, Scissor takes 314, 539, and 171 seconds, respectively.

SCIPAC works with various phenotype types, including binary, continuous, survival, and ordinal. It can easily accommodate other types by using a proper regression model with a systematic component in the form of Eq. 3 (see the “ Methods ” section). For example, a Poisson or negative binomial log-linear model can be used if the phenotype is a count (i.e., non-negative integer).

In SCIPAC’s definition of association, a cell type is associated with the phenotype if increasing the proportion of this cell type leads to a change of probability of the phenotype occurring. The strength of association represents the extent of the increase or decrease in this probability. In the case of binary-response, this change is measured by the log odds ratio. For example, if the association strength of cell type A is twice that of cell type B, increasing cell type A by a certain proportion leads to twice the amount of change in the log odds ratio of having the phenotype compared to increasing cell type B by the same proportion. The association strength under other types of phenotypes can be interpreted similarly, with the major difference lying in the measure of change in probability. For quantitative, ordinal, and survival outcomes, the difference in the quantitative outcome, log odds ratio of the right-tail probability, and log hazard ratio respectively are used. Despite the differences in the exact form of the association strength under different types of phenotypes, the underlying concept remains the same: a larger (absolute value of) association strength indicates that the same increase/decrease in a cell type leads to a larger change in the occurrence of the phenotype.

As SCIPAC utilizes both bulk RNA-seq data with phenotype and single-cell RNA-seq data, the estimated associations for the cells are influenced by the choice of the bulk data. Although different bulk data can yield varying estimations of the association for the same single cells, the estimated associations appear to be reasonably robust even when minor changes are made to the bulk data. See Additional file 1 for further discussions.

When using the Louvain algorithm in the Seurat package to cluster cells, SCIPAC’s default resolution is 2.0, larger than the default setting of Seurat. This allows for the identification of potential subtypes within the major cell type and enables the estimation of individual association strengths. Consequently, a more detailed and comprehensive description of the association between single cells and the phenotype can be obtained by SCIPAC.

When applying SCIPAC to real datasets, we made a deliberate choice to disregard the cell annotation provided by the original publications and instead relied on the inferred cell clusters produced by the Louvain algorithm. We made this decision for several reasons. Firstly, we aimed to ensure a fair comparison with Scissor, as it does not utilize cell-type annotations. Secondly, the original annotation might not be sufficiently comprehensive or detailed. Presumed cell types could potentially encompass multiple subtypes, each of which may exhibit distinct associations with the phenotype under investigation. In such cases, employing the Louvain algorithm with a relatively high resolution, which is the default setting in SCIPAC, enables us to differentiate between these subtypes and allows SCIPAC to assign varying association strengths to each subtype.

SCIPAC fits the regression model using the elastic net, a machine-learning algorithm that maximizes a penalized version of the likelihood. The elastic net can be replaced by other penalized estimates of regression models, such as SCAD [ 78 ], without altering the rest of the SCIPAC algorithm. The combination of a regression model and a penalized estimation algorithm such as the elastic net has shown comparable or higher prediction power than other sophisticated methods such as random forests, boosting, or neural networks in numerous applications, especially for gene expression data [ 79 ]. However, there can still be datasets where other models have higher prediction power. It will be future work to incorporate these models into SCIPAC.

The use of metacells is becoming an efficient way to handle large single-cell datasets [ 80 , 81 , 82 , 83 ]. Conceptually, SCIPAC can incorporate metacells and their representatives as an alternative to its default setting of using cell clusters/types and their centroids. We have explored this aspect using metacells provided by SEACells [ 81 ]. Details are given in Additional file 1. Our comparative analysis reveals that combining SCIPAC with SEACells results in significantly reduced performance compared to using SCIPAC directly on original single-cell data. The primary reason for this appears to be the subpar performance of SEACells in cell grouping, especially when contrasted with the Louvain algorithm. Given these findings, we do not suggest using metacells provided by SEACells for SCIPAC applications in the current stage.

Conclusions

SCIPAC is a novel algorithm for studying the associations between cells and phenotypes. Compared to the previous algorithm, SCIPAC gives a much more detailed and comprehensive description of the associations by enabling a quantitative estimation of the association strength and by providing a quality control—the p -value. Underlying SCIPAC are a general statistical model that accommodates virtually all types of phenotypes, including ordinal (and potentially count) phenotypes that have never been considered before, and a concise and closed-form mathematical formula that quantifies the association, which minimizes the computational load. The mathematical conciseness also largely frees SCIPAC from parameter tuning. The only parameter (i.e., the resolution) barely changes the results given by SCIPAC. Overall, compared with its predecessor, SCIPAC represents a substantially more capable software by being much more informative, versatile, robust, and user-friendly.

The improvement in accuracy is also remarkable. In simulated data, SCIPAC achieves high power and low false positives, which is evident from the UMAP plot, F1 score, and FSC score. In real data, SCIPAC gives results that are consistent with current biological knowledge for cell types whose functions are well understood. For cell types whose functions are less studied or more multifaceted, SCIPAC gives support to certain biological hypotheses or helps identify/discover cell sub-types.

SCIPAC’s identification of cell-phenotype associations closely follows its definition of association: when increasing the fraction of a cell type increases (or decreases) the probability for a phenotype to be present, this cell type is positively (or negatively) associated with the phenotype.

The increase of the fraction of a cell type

For a bulk sample, let vector \(\varvec{G} \in \mathbb {R}^p\) be its expression profile, that is, its expression on the p genes. Suppose there are K cell types in the tissue, and let \(\varvec{g}_{k}\) be the representative expression of the k ’th cell type. Usually, people assume that \(\varvec{G}\) can be decomposed by

where \(\gamma _{k}\) is the proportion of cell type k in the bulk tissue, with \(\sum _{k = 1}^{K}\gamma _{k} = 1\) . This equation links the bulk and single-cell expression data.

Now consider increasing cells from cell type k by \(\Delta \gamma\) proportion of the original number of cells. Then, the new proportion of cell type k becomes \(\frac{\gamma _{k} + \Delta \gamma }{1 + \Delta \gamma }\) , and the new proportion of cell type \(j \ne k\) becomes \(\frac{\gamma _{j}}{1 + \Delta \gamma }\)  (note that the new proportions of all cell types should still add up to 1). Thus, the bulk expression profile with the increase of cell type k becomes

Plugging Eq. 1 , we get

Interestingly, this expression of \(\varvec{G}^*\) does not include \(\gamma _{1}, \ldots , \gamma _{K}\) . This means that there is no need actually to compute \(\gamma _{1}, \ldots , \gamma _{K}\) in Eq. 1 , which could otherwise be done using a cell-type-decomposition software, but an accurate and robust decomposition is non-trivial [ 84 , 85 , 86 ]. See Additional file 1 for a more in-depth discussion on the connections of SCIPAC with decomposition/deconvolution.

The change in chance of a phenotype

In this section, we consider how the increase in the fraction of a cell type will change the chance for a binary phenotype such as cancer to occur. Other types of phenotypes will be considered in the next section.

Let \(\pi (\varvec{G})\) be the chance of an individual with gene expression profile \(\varvec{G}\) for this phenotype to occur. We assume a logistic regression model to describe the relationship between \(\pi (\varvec{G})\) and \(\varvec{G}\) :

here the left-hand side is the log odds of \(\pi (\varvec{G})\) , \(\beta _{0}\) is the intercept, and \(\varvec{\beta }\) is a length- p vector of coefficients. In the section after the next, we will describe how we obtain \(\beta _{0}\) and \(\varvec{\beta }\) from the data.

When increasing cells from cell type k by \(\Delta \gamma\) , \(\varvec{G}\) becomes \(\varvec{G}^*\) in Eq. 3 . Plugging Eq. 2 , we get

We further take the difference between Eqs. 4 and 3 and get

The left-hand side of this equation is the log odds ratio (i.e., the change of log odds). On the right-hand side, \(\frac{\Delta \gamma }{1 + \Delta \gamma }\) is an increasing function with respect to \(\Delta \gamma\) , and \(\varvec{\beta }^T(\varvec{g}_{k} - \varvec{G})\) is independent of \(\Delta \gamma\) . This indicates that given any specific \(\Delta \gamma\) , the log odds ratio under over-representation of cell type k is proportional to

\(\lambda _k\) describes the strength of the effect of increasing cell type k to a bulk sample with expression profile \(\varvec{G}\) . Given the presence of numerous bulk samples, employing multiple \(\lambda _k\) ’s could be cumbersome and obscure the overall effect of a particular cell type. To concisely summarize the association of cell type k , we propose averaging their effects. The average effect on all bulk samples can be obtained by

where \(\bar{\varvec{G}}\) is the average expression profile of all bulk samples.

\(\Lambda _k\) gives an overall impression of how strong the effect is when cell type k over-represents to the probability for the phenotype to be present. Its sign represents the direction of the change: a positive value means an increase in probability, and a negative value means a decrease in probability. Its absolute value represents the strength of the effect. In SCIPAC, we call \(\Lambda _k\) the association strength of cell type k and the phenotype.

Note that this derivation does not involve likelihood, although the computation of \(\varvec{\beta }\) does. Here, it serves more as a definitional approach.

Definition of the association strength for other types of phenotype

Our definition of \(\Lambda _k\) relies on vector \(\varvec{\beta }\) . In the case of a binary phenotype, \(\varvec{\beta }\) are the coefficients of a logistic regression that describes a linear relationship between the expression profile and the log odds of having the phenotype, as shown in Eq. 3 . For other types of phenotype, \(\varvec{\beta }\) can be defined/computed similarly.

For a quantitative (i.e., continuous) phenotype, an ordinary linear regression can be used, and the left-hand side of Eq. 3 is changed to the quantitative value of the phenotype.

For a survival phenotype, a Cox proportional hazards model can be used, and the left-hand side of Eq. 3 is changed to the log hazard ratio.

For an ordinal phenotype, we use a proportional odds model

where \(j \in \{1, 2, ..., (J - 1)\}\) and J is the number of ordinal levels. It should be noted that here we use the right-tail probability \(\Pr (Y_{i} \ge j + 1 | X)\) instead of the commonly used cumulative probability (left-tail probability) \(\Pr (Y_{i} \le j | X)\) . Such a change makes the interpretation consistent with other types of phenotypes: in our model, a larger value on the right-hand side indicates a larger chance for \(Y_{i}\) to have a higher level, which in turn guarantees that the sign of the association strength defined according to this \(\varvec{\beta }\) has the usual meaning: a positive \(\Lambda _k\) value means a positive association with the phenotype-using the cancer stage as an example. A positive \(\Lambda _k\) means the over-representation of cell type k increases the chance of a higher cancer stage. In contrast, using the commonly used cumulative probability leads to a counter-intuitive, reversed interpretation.

Computation of the association strength in practice

In practice, \(\varvec{\beta }\) in Eq. 3 needs to be learned from the bulk data. By default, SCIPAC uses the elastic net, a popular and powerful penalized regression method:

In this model, \(l(\beta _{0}, \varvec{\beta })\) is a log-likelihood of the linear model (i.e., logistic regression for a binary phenotype, ordinary linear regression for a quantitative phenotype, Cox proportional odds model for a survival phenotype, and proportional odds model for an ordinal phenotype). \(\alpha\) is a number between 0 and 1, denoting a combination of \(\ell _1\) and \(\ell _2\) penalties, and \(\lambda\) is the penalty strength. SCIPAC fixes \(\alpha\) to be 0.4 (see Additional file 1 for discussions on this choice) and uses 10-fold cross-validation to decide \(\lambda\) automatically. This way, they do not become hyperparameters.

In SCIPAC, the fitting and cross-validation of the elastic net are done by calling the ordinalNet [ 87 ] R package for the ordinal phenotype and by calling the glmnet R package [ 88 , 89 , 90 , 91 ] for other types of phenotypes.

The computation of the association strength, as defined by Eq. 7 , does not only require \(\varvec{\beta }\) , but also \(\varvec{g}_k\) and \(\bar{\varvec{G}}\) . \(\bar{\varvec{G}}\) is simply the average expression profile of all bulk samples. On the other hand, \(\varvec{g}_k\) requires knowing the cell type of each cell. By default, SCIPAC does not assume this information to be given, and it uses the Louvain clustering implemented in the Seurat [ 24 , 25 ] R package to infer it. This clustering algorithm has one tuning parameter called “resolution.” SCIPAC sets its default value as 2.0, and the user can use other values. With the inferred or given cell types, \(\varvec{g}_k\) is computed as the centroid (i.e., the mean expression profile) of cells in cluster k .

Given \(\varvec{\beta }\) , \(\bar{\varvec{G}}\) , and \(\varvec{g}_k\) , the association strength can be computed using Eq. 7 . Knowing the association strength for each cell type and the cell-type label for each cell, we also know the association strength for every single cell. In practice, we standardize the association strengths for all cells. That is, we compute the mean and standard deviation of the association strengths of all cells and use them to centralize and scale the association strength, respectively. We have found such standardization makes SCIPAC more robust to the possible unbalance in sample size of bulk data in different phenotype groups.

Computation of the p -value

SCIPAC uses non-parametric bootstrap [ 92 ] to compute the standard deviation and hence the p -value of the association. Fifty bootstrap samples, which are believed to be enough to compute the standard error of most statistics [ 93 ], are generated for the bulk expression data, and each is used to compute (standardized) \(\Lambda\) values for all the cells. For cell i , let its original \(\Lambda\) values be \(\Lambda _i\) , and the bootstrapped values be \(\Lambda _i^{(1)}, \ldots , \Lambda _i^{(50)}\) . A z -score is then computed using

and then the p -value is computed according to the cumulative distribution function of the standard Gaussian distribution. See Additional file 1 for more discussions on the calculation of p -value.

Availability of data and materials

The simulated datasets [ 94 ] under three schemes are available at Zenodo with DOI 10.5281/zenodo.11013320 [ 95 ]. The SCIPAC package is available at GitHub website https://github.com/RavenGan/SCIPAC under the MIT license [ 96 ]. The source code of SCIPAC is also deposited at Zenodo with DOI 10.5281/zenodo.11013696 [ 97 ]. A vignette of the R package is available on the GitHub page and in the Additional file 2. The prostate cancer scRNA-seq data is obtained from the Prostate Cell Atlas https://www.prostatecellatlas.org [ 29 ]; the scRNA-seq data for the breast cancer are from the Gene Expression Omnibus (GEO) under accession number GSE176078 [ 34 , 98 ]; the scRNA-seq data for the lung cancer are from E-MTAB-6149 [ 99 ] and E-MTAB-6653 [ 71 , 100 ]; the scRNA-seq data for facioscapulohumeral muscular dystrophy data are from the GEO under accession number GSE122873 [ 101 ]. The bulk RNA-seq data are obtained from the TCGA database via TCGAbiolinks (ver. 2.25.2) R package [ 102 ]. More details about the simulated and real scRNA-seq and bulk RNA-seq data can be found in the Additional file 1.

Yofe I, Dahan R, Amit I. Single-cell genomic approaches for developing the next generation of immunotherapies. Nat Med. 2020;26(2):171–7.

Article   CAS   PubMed   Google Scholar  

Zhang Q, He Y, Luo N, Patel SJ, Han Y, Gao R, et al. Landscape and dynamics of single immune cells in hepatocellular carcinoma. Cell. 2019;179(4):829–45.

Fan J, Slowikowski K, Zhang F. Single-cell transcriptomics in cancer: computational challenges and opportunities. Exp Mol Med. 2020;52(9):1452–65.

Article   CAS   PubMed   PubMed Central   Google Scholar  

Klein AM, Mazutis L, Akartuna I, Tallapragada N, Veres A, Li V, et al. Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells. Cell. 2015;161(5):1187–201.

Macosko EZ, Basu A, Satija R, Nemesh J, Shekhar K, Goldman M, et al. Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets. Cell. 2015;161(5):1202–14.

Rosenberg AB, Roco CM, Muscat RA, Kuchina A, Sample P, Yao Z, et al. Single-cell profiling of the developing mouse brain and spinal cord with split-pool barcoding. Science. 2018;360(6385):176–82.

Zheng GX, Terry JM, Belgrader P, Ryvkin P, Bent ZW, Wilson R, et al. Massively parallel digital transcriptional profiling of single cells. Nat Commun. 2017;8(1):1–12.

Article   Google Scholar  

Abdelaal T, Michielsen L, Cats D, Hoogduin D, Mei H, Reinders MJ, et al. A comparison of automatic cell identification methods for single-cell RNA sequencing data. Genome Biol. 2019;20(1):1–19.

Article   CAS   Google Scholar  

Luecken MD, Theis FJ. Current best practices in single-cell RNA-seq analysis: a tutorial. Mol Syst Biol. 2019;15(6):e8746.

Article   PubMed   PubMed Central   Google Scholar  

Guo H, Li J. scSorter: assigning cells to known cell types according to marker genes. Genome Biol. 2021;22(1):1–18.

Pliner HA, Shendure J, Trapnell C. Supervised classification enables rapid annotation of cell atlases. Nat Methods. 2019;16(10):983–6.

Zhang AW, O’Flanagan C, Chavez EA, Lim JL, Ceglia N, McPherson A, et al. Probabilistic cell-type assignment of single-cell RNA-seq for tumor microenvironment profiling. Nat Methods. 2019;16(10):1007–15.

Zhang Z, Luo D, Zhong X, Choi JH, Ma Y, Wang S, et al. SCINA: a semi-supervised subtyping algorithm of single cells and bulk samples. Genes. 2019;10(7):531.

Johnson TS, Wang T, Huang Z, Yu CY, Wu Y, Han Y, et al. LAmbDA: label ambiguous domain adaptation dataset integration reduces batch effects and improves subtype detection. Bioinformatics. 2019;35(22):4696–706.

Ma F, Pellegrini M. ACTINN: automated identification of cell types in single cell RNA sequencing. Bioinformatics. 2020;36(2):533–8.

Tan Y, Cahan P. SingleCellNet: a computational tool to classify single cell RNA-Seq data across platforms and across species. Cell Syst. 2019;9(2):207–13.

Salcher S, Sturm G, Horvath L, Untergasser G, Kuempers C, Fotakis G, et al. High-resolution single-cell atlas reveals diversity and plasticity of tissue-resident neutrophils in non-small cell lung cancer. Cancer Cell. 2022;40(12):1503–20.

Good Z, Sarno J, Jager A, Samusik N, Aghaeepour N, Simonds EF, et al. Single-cell developmental classification of B cell precursor acute lymphoblastic leukemia at diagnosis reveals predictors of relapse. Nat Med. 2018;24(4):474–83.

Wagner J, Rapsomaniki MA, Chevrier S, Anzeneder T, Langwieder C, Dykgers A, et al. A single-cell atlas of the tumor and immune ecosystem of human breast cancer. Cell. 2019;177(5):1330–45.

Weinstein JN, Collisson EA, Mills GB, Shaw KR, Ozenberger BA, Ellrott K, et al. The cancer genome atlas pan-cancer analysis project. Nat Genet. 2013;45(10):1113–20.

Cerami E, Gao J, Dogrusoz U, Gross BE, Sumer SO, Aksoy BA, et al. The cBio cancer genomics portal: an open platform for exploring multidimensional cancer genomics data. Cancer Disc. 2012;2(5):401–4.

Gao J, Aksoy BA, Dogrusoz U, Dresdner G, Gross B, Sumer SO, et al. Integrative analysis of complex cancer genomics and clinical profiles using the cBioPortal. Sci Signal. 2013;6(269):1.

Sun D, Guan X, Moran AE, Wu LY, Qian DZ, Schedin P, et al. Identifying phenotype-associated subpopulations by integrating bulk and single-cell sequencing data. Nat Biotechnol. 2022;40(4):527–38.

Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E. Fast unfolding of communities in large networks. J Stat Mech Theory Exp. 2008;2008(10):P10008.

Stuart T, Butler A, Hoffman P, Hafemeister C, Papalexi E, Mauck WM III, et al. Comprehensive integration of single-cell data. Cell. 2019;177(7):1888–902.

Zou H, Hastie T. Regularization and variable selection via the elastic net. J R Stat Soc Ser B Stat Methodol. 2005;67(2):301–20.

McInnes L, Healy J, Melville J. UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction. 2018. arXiv preprint arXiv:1802.03426 .

Wong CJ, Wang LH, Friedman SD, Shaw D, Campbell AE, Budech CB, et al. Longitudinal measures of RNA expression and disease activity in FSHD muscle biopsies. Hum Mol Genet. 2020;29(6):1030–43.

Tuong ZK, Loudon KW, Berry B, Richoz N, Jones J, Tan X, et al. Resolving the immune landscape of human prostate at a single-cell level in health and cancer. Cell Rep. 2021;37(12):110132.

Hume DA. The mononuclear phagocyte system. Curr Opin Immunol. 2006;18(1):49–53.

Hume DA, Ross IL, Himes SR, Sasmono RT, Wells CA, Ravasi T. The mononuclear phagocyte system revisited. J Leukoc Biol. 2002;72(4):621–7.

Raggi F, Bosco MC. Targeting mononuclear phagocyte receptors in cancer immunotherapy: new perspectives of the triggering receptor expressed on myeloid cells (TREM-1). Cancers. 2020;12(5):1337.

Largeot A, Pagano G, Gonder S, Moussay E, Paggetti J. The B-side of cancer immunity: the underrated tune. Cells. 2019;8(5):449.

Wu SZ, Al-Eryani G, Roden DL, Junankar S, Harvey K, Andersson A, et al. A single-cell and spatially resolved atlas of human breast cancers. Nat Genet. 2021;53(9):1334–47.

Fernández-Nogueira P, Fuster G, Gutierrez-Uzquiza Á, Gascón P, Carbó N, Bragado P. Cancer-associated fibroblasts in breast cancer treatment response and metastasis. Cancers. 2021;13(13):3146.

Ao Z, Shah SH, Machlin LM, Parajuli R, Miller PC, Rawal S, et al. Identification of cancer-associated fibroblasts in circulating blood from patients with metastatic breast cancer. Identification of cCAFs from metastatic cancer patients. Cancer Res. 2015;75(22):4681–7.

Arcucci A, Ruocco MR, Granato G, Sacco AM, Montagnani S. Cancer: an oxidative crosstalk between solid tumor cells and cancer associated fibroblasts. BioMed Res Int. 2016;2016.  https://pubmed.ncbi.nlm.nih.gov/27595103/ .

Buchsbaum RJ, Oh SY. Breast cancer-associated fibroblasts: where we are and where we need to go. Cancers. 2016;8(2):19.

Ruocco MR, Avagliano A, Granato G, Imparato V, Masone S, Masullo M, et al. Involvement of breast cancer-associated fibroblasts in tumor development, therapy resistance and evaluation of potential therapeutic strategies. Curr Med Chem. 2018;25(29):3414–34.

Savas P, Virassamy B, Ye C, Salim A, Mintoff CP, Caramia F, et al. Single-cell profiling of breast cancer T cells reveals a tissue-resident memory subset associated with improved prognosis. Nat Med. 2018;24(7):986–93.

Bassez A, Vos H, Van Dyck L, Floris G, Arijs I, Desmedt C, et al. A single-cell map of intratumoral changes during anti-PD1 treatment of patients with breast cancer. Nat Med. 2021;27(5):820–32.

Romero JM, Grünwald B, Jang GH, Bavi PP, Jhaveri A, Masoomian M, et al. A four-chemokine signature is associated with a T-cell-inflamed phenotype in primary and metastatic pancreatic cancer. Chemokines in Pancreatic Cancer. Clin Cancer Res. 2020;26(8):1997–2010.

Tamura R, Yoshihara K, Nakaoka H, Yachida N, Yamaguchi M, Suda K, et al. XCL1 expression correlates with CD8-positive T cells infiltration and PD-L1 expression in squamous cell carcinoma arising from mature cystic teratoma of the ovary. Oncogene. 2020;39(17):3541–54.

Hernandez R, Põder J, LaPorte KM, Malek TR. Engineering IL-2 for immunotherapy of autoimmunity and cancer. Nat Rev Immunol. 2022:22:1–15.  https://pubmed.ncbi.nlm.nih.gov/35217787/ .

Korotkevich G, Sukhov V, Budin N, Shpak B, Artyomov MN, Sergushichev A. Fast gene set enrichment analysis. BioRxiv. 2016:060012.  https://www.biorxiv.org/content/10.1101/060012v3.abstract .

Dang CV. MYC on the path to cancer. Cell. 2012;149(1):22–35.

Gnanaprakasam JR, Wang R. MYC in regulating immunity: metabolism and beyond. Genes. 2017;8(3):88.

Oshi M, Takahashi H, Tokumaru Y, Yan L, Rashid OM, Matsuyama R, et al. G2M cell cycle pathway score as a prognostic biomarker of metastasis in estrogen receptor (ER)-positive breast cancer. Int J Mol Sci. 2020;21(8):2921.

Zhang X, Lan Y, Xu J, Quan F, Zhao E, Deng C, et al. Cell Marker: a manually curated resource of cell markers in human and mouse. Nucleic Acids Res. 2019;47(D1):D721–8.

Chen L, Yang L, Qiao F, Hu X, Li S, Yao L, et al. High levels of nucleolar spindle-associated protein and reduced levels of BRCA1 expression predict poor prognosis in triple-negative breast cancer. PLoS ONE. 2015;10(10):e0140572.

Li M, Yang B. Prognostic value of NUSAP1 and its correlation with immune infiltrates in human breast cancer. Crit Rev TM Eukaryot Gene Expr. 2022;32(3).  https://pubmed.ncbi.nlm.nih.gov/35695609/ .

Zhang X, Pan Y, Fu H, Zhang J. Nucleolar and spindle associated protein 1 (NUSAP1) inhibits cell proliferation and enhances susceptibility to epirubicin in invasive breast cancer cells by regulating cyclin D kinase (CDK1) and DLGAP5 expression. Med Sci Monit: Int Med J Exp Clin Res. 2018;24:8553.

Geyer FC, Rodrigues DN, Weigelt B, Reis-Filho JS. Molecular classification of estrogen receptor-positive/luminal breast cancers. Adv Anat Pathol. 2012;19(1):39–53.

Karamitopoulou E, Perentes E, Tolnay M, Probst A. Prognostic significance of MIB-1, p53, and bcl-2 immunoreactivity in meningiomas. Hum Pathol. 1998;29(2):140–5.

Duxbury MS, Whang EE. RRM2 induces NF- \(\kappa\) B-dependent MMP-9 activation and enhances cellular invasiveness. Biochem Biophys Res Commun. 2007;354(1):190–6.

Zhou BS, Tsai P, Ker R, Tsai J, Ho R, Yu J, et al. Overexpression of transfected human ribonucleotide reductase M2 subunit in human cancer cells enhances their invasive potential. Clin Exp Metastasis. 1998;16(1):43–9.

Zhang H, Liu X, Warden CD, Huang Y, Loera S, Xue L, et al. Prognostic and therapeutic significance of ribonucleotide reductase small subunit M2 in estrogen-negative breast cancers. BMC Cancer. 2014;14(1):1–16.

Putluri N, Maity S, Kommagani R, Creighton CJ, Putluri V, Chen F, et al. Pathway-centric integrative analysis identifies RRM2 as a prognostic marker in breast cancer associated with poor survival and tamoxifen resistance. Neoplasia. 2014;16(5):390–402.

Koleck TA, Conley YP. Identification and prioritization of candidate genes for symptom variability in breast cancer survivors based on disease characteristics at the cellular level. Breast Cancer Targets Ther. 2016;8:29.

Li Jp, Zhang Xm, Zhang Z, Zheng Lh, Jindal S, Liu Yj. Association of p53 expression with poor prognosis in patients with triple-negative breast invasive ductal carcinoma. Medicine. 2019;98(18).  https://pubmed.ncbi.nlm.nih.gov/31045815/ .

Gong MT, Ye SD, Lv WW, He K, Li WX. Comprehensive integrated analysis of gene expression datasets identifies key anti-cancer targets in different stages of breast cancer. Exp Ther Med. 2018;16(2):802–10.

PubMed   PubMed Central   Google Scholar  

Chen Wx, Yang Lg, Xu Ly, Cheng L, Qian Q, Sun L, et al. Bioinformatics analysis revealing prognostic significance of RRM2 gene in breast cancer. Biosci Rep. 2019;39(4).  https://pubmed.ncbi.nlm.nih.gov/30898978/ .

Hao Z, Zhang H, Cowell J. Ubiquitin-conjugating enzyme UBE2C: molecular biology, role in tumorigenesis, and potential as a biomarker. Tumor Biol. 2012;33(3):723–30.

Arriola E, Rodriguez-Pinilla SM, Lambros MB, Jones RL, James M, Savage K, et al. Topoisomerase II alpha amplification may predict benefit from adjuvant anthracyclines in HER2 positive early breast cancer. Breast Cancer Res Treat. 2007;106(2):181–9.

Knoop AS, Knudsen H, Balslev E, Rasmussen BB, Overgaard J, Nielsen KV, et al. Retrospective analysis of topoisomerase IIa amplifications and deletions as predictive markers in primary breast cancer patients randomly assigned to cyclophosphamide, methotrexate, and fluorouracil or cyclophosphamide, epirubicin, and fluorouracil: Danish Breast Cancer Cooperative Group. J Clin Oncol. 2005;23(30):7483–90.

Tanner M, Isola J, Wiklund T, Erikstein B, Kellokumpu-Lehtinen P, Malmstrom P, et al. Topoisomerase II \(\alpha\) gene amplification predicts favorable treatment response to tailored and dose-escalated anthracycline-based adjuvant chemotherapy in HER-2/neu-amplified breast cancer: Scandinavian Breast Group Trial 9401. J Clin Oncol. 2006;24(16):2428–36.

Arriola E, Moreno A, Varela M, Serra JM, Falo C, Benito E, et al. Predictive value of HER-2 and topoisomerase II \(\alpha\) in response to primary doxorubicin in breast cancer. Eur J Cancer. 2006;42(17):2954–60.

Järvinen TA, Tanner M, Bärlund M, Borg Å, Isola J. Characterization of topoisomerase II \(\alpha\) gene amplification and deletion in breast cancer. Gene Chromosome Cancer. 1999;26(2):142–50.

Landberg G, Erlanson M, Roos G, Tan EM, Casiano CA. Nuclear autoantigen p330d/CENP-F: a marker for cell proliferation in human malignancies. Cytom J Int Soc Anal Cytol. 1996;25(1):90–8.

CAS   Google Scholar  

Bettelli E, Carrier Y, Gao W, Korn T, Strom TB, Oukka M, et al. Reciprocal developmental pathways for the generation of pathogenic effector TH17 and regulatory T cells. Nature. 2006;441(7090):235–8.

Lambrechts D, Wauters E, Boeckx B, Aibar S, Nittner D, Burton O, et al. Phenotype molding of stromal cells in the lung tumor microenvironment. Nat Med. 2018;24(8):1277–89.

Bremnes RM, Busund LT, Kilvær TL, Andersen S, Richardsen E, Paulsen EE, et al. The role of tumor-infiltrating lymphocytes in development, progression, and prognosis of non-small cell lung cancer. J Thorac Oncol. 2016;11(6):789–800.

Article   PubMed   Google Scholar  

Schalper KA, Brown J, Carvajal-Hausdorf D, McLaughlin J, Velcheti V, Syrigos KN, et al. Objective measurement and clinical significance of TILs in non–small cell lung cancer. J Natl Cancer Inst. 2015;107(3):dju435.

Tay RE, Richardson EK, Toh HC. Revisiting the role of CD4+ T cells in cancer immunotherapy—new insights into old paradigms. Cancer Gene Ther. 2021;28(1):5–17.

Dieu-Nosjean MC, Goc J, Giraldo NA, Sautès-Fridman C, Fridman WH. Tertiary lymphoid structures in cancer and beyond. Trends Immunol. 2014;35(11):571–80.

Wang Ss, Liu W, Ly D, Xu H, Qu L, Zhang L. Tumor-infiltrating B cells: their role and application in anti-tumor immunity in lung cancer. Cell Mol Immunol. 2019;16(1):6–18.

van den Heuvel A, Mahfouz A, Kloet SL, Balog J, van Engelen BG, Tawil R, et al. Single-cell RNA sequencing in facioscapulohumeral muscular dystrophy disease etiology and development. Hum Mol Genet. 2019;28(7):1064–75.

Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc. 2001;96(456):1348–60.

Hastie T, Tibshirani R, Friedman JH, Friedman JH. The elements of statistical learning: data mining, inference, and prediction, vol. 2. New York: Springer; 2009.

Book   Google Scholar  

Baran Y, Bercovich A, Sebe-Pedros A, Lubling Y, Giladi A, Chomsky E, et al. MetaCell: analysis of single-cell RNA-seq data using K-nn graph partitions. Genome Biol. 2019;20(1):1–19.

Persad S, Choo ZN, Dien C, Sohail N, Masilionis I, Chaligné R, et al. SEACells infers transcriptional and epigenomic cellular states from single-cell genomics data. Nat Biotechnol. 2023;41:1–12.  https://pubmed.ncbi.nlm.nih.gov/36973557/ .

Ben-Kiki O, Bercovich A, Lifshitz A, Tanay A. Metacell-2: a divide-and-conquer metacell algorithm for scalable scRNA-seq analysis. Genome Biol. 2022;23(1):100.

Bilous M, Tran L, Cianciaruso C, Gabriel A, Michel H, Carmona SJ, et al. Metacells untangle large and complex single-cell transcriptome networks. BMC Bioinformatics. 2022;23(1):336.

Avila Cobos F, Alquicira-Hernandez J, Powell JE, Mestdagh P, De Preter K. Benchmarking of cell type deconvolution pipelines for transcriptomics data. Nat Commun. 2020;11(1):1–14.

Jin H, Liu Z. A benchmark for RNA-seq deconvolution analysis under dynamic testing environments. Genome Biol. 2021;22(1):1–23.

Wang X, Park J, Susztak K, Zhang NR, Li M. Bulk tissue cell type deconvolution with multi-subject single-cell expression reference. Nat Commun. 2019;10(1):380.

Wurm MJ, Rathouz PJ, Hanlon BM. Regularized ordinal regression and the ordinalNet R package. 2017. arXiv preprint arXiv:1706.05003 .

Friedman J, Hastie T, Tibshirani R. Regularization paths for generalized linear models via coordinate descent. J Stat Softw. 2010;33(1):1.

Simon N, Friedman J, Hastie T. A blockwise descent algorithm for group-penalized multiresponse and multinomial regression. 2013. arXiv preprint arXiv:1311.6529 .

Simon N, Friedman J, Hastie T, Tibshirani R. Regularization paths for Cox’s proportional hazards model via coordinate descent. J Stat Softw. 2011;39(5):1.

Tibshirani R, Bien J, Friedman J, Hastie T, Simon N, Taylor J, et al. Strong rules for discarding predictors in lasso-type problems. J R Stat Soc Ser B Stat Methodol. 2012;74(2):245–66.

Efron B. Bootstrap methods: another look at the jackknife. In: Breakthroughs in statistics. New York: Springer; 1992. pp. 569–593.

Efron B, Tibshirani RJ. An introduction to the bootstrap. London: CRC Press; 1994.

Zappia L, Phipson B, Oshlack A. Splatter: simulation of single-cell RNA sequencing data. Genome Biol. 2017;18(1):174.

Gan D, Zhu Y, Lu X, Li J. Simulated datasets used in SCIPAC analysis. Zenodo. 2024. https://doi.org/10.5281/zenodo.11013320 .

Gan D, Zhu Y, Lu X, Li J. SCIPAC R package. GitHub. 2024. https://github.com/RavenGan/SCIPAC . Accessed 24 Apr 2024.

Gan D, Zhu Y, Lu X, Li J. SCIPAC source code. Zenodo. 2024. https://doi.org/10.5281/zenodo.11013696 .

Wu SZ, Al-Eryani G, Roden DL, Junankar S, Harvey K, Andersson A, et al. A single-cell and spatially resolved atlas of human breast cancers. Datasets. 2021. https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE176078 . Gene Expression Omnibus. Accessed 1 Oct 2022.

Lambrechts D, Wauters E, Boeckx B, Aibar S, Nittner D, Burton O, et al. Phenotype molding of stromal cells in the lung tumor microenvironment. Datasets. 2018. https://www.ebi.ac.uk/biostudies/arrayexpress/studies/E-MTAB-6149 . ArrayExpress. Accessed 24 July 2022.

Lambrechts D, Wauters E, Boeckx B, Aibar S, Nittner D, Burton O, et al. Phenotype molding of stromal cells in the lung tumor microenvironment. Datasets. 2018. https://www.ebi.ac.uk/biostudies/arrayexpress/studies/E-MTAB-6653 . ArrayExpress. Accessed 24 July 2022.

van den Heuvel A, Mahfouz A, Kloet SL, Balog J, van Engelen BG, Tawil R, et al. Single-cell RNA sequencing in facioscapulohumeral muscular dystrophy disease etiology and development. Datasets. 2019. https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE122873 . Gene Expression Omnibus. Accessed 13 Aug 2022.

Colaprico A, Silva TC, Olsen C, Garofano L, Cava C, Garolini D, et al. TCGAbiolinks: an R/Bioconductor package for integrative analysis of TCGA data. Nucleic Acids Res. 2016;44(8):e71.

Download references

Review history

The review history is available as Additional file 3.

Peer review information

Veronique van den Berghe was the primary editor of this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

This work is supported by the National Institutes of Health (R01CA280097 to X.L. and J.L, R01CA252878 to J.L.) and the DOD BCRP Breakthrough Award, Level 2 (W81XWH2110432 to J.L.).

Author information

Authors and affiliations.

Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, 46556, IN, USA

Dailin Gan & Jun Li

Department of Biological Sciences, Boler-Parseghian Center for Rare and Neglected Diseases, Harper Cancer Research Institute, Integrated Biomedical Sciences Graduate Program, University of Notre Dame, Notre Dame, 46556, IN, USA

Yini Zhu & Xin Lu

Tumor Microenvironment and Metastasis Program, Indiana University Melvin and Bren Simon Comprehensive Cancer Center, Indianapolis, 46202, IN, USA

You can also search for this author in PubMed   Google Scholar

Contributions

J.L. conceived and supervised the study. J.L. and D.G. proposed the methods. D.G. implemented the methods and analyzed the data. D.G. and J.L. drafted the paper. D.G., Y.Z., X.L., and J.L. interpreted the results and revised the paper.

Corresponding author

Correspondence to Jun Li .

Ethics declarations

Ethics approval and consent to participate.

Not applicable.

Consent for publication

Competing interests.

The authors declare that they have no competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Additional file 1. supplementary materials that include additional results and plots., additional file 2. a vignette of the scipac package., additional file 3. review history., rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/ ) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Reprints and permissions

About this article

Cite this article.

Gan, D., Zhu, Y., Lu, X. et al. SCIPAC: quantitative estimation of cell-phenotype associations. Genome Biol 25 , 119 (2024). https://doi.org/10.1186/s13059-024-03263-1

Download citation

Received : 30 January 2023

Accepted : 30 April 2024

Published : 13 May 2024

DOI : https://doi.org/10.1186/s13059-024-03263-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Phenotype association
• Single cell
• RNA sequencing
• Cancer research

Genome Biology

ISSN: 1474-760X

• Submission enquiries: [email protected]
• General enquiries: [email protected]