random assignment to groups is a critical part of the methodology

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Establishing Equivalence: Methodological Progress in Group-Matching Design and Analysis

Sara t. kover.

University of Wisconsin-Madison, Waisman Center, 1500 Highland Avenue, Madison, WI 53705

Amy K. Atwood

University of Wisconsin-Madison

This methodological review draws attention to the challenges faced by intellectual and developmental disabilities researchers in the appropriate design and analysis of group comparison studies. We provide a brief overview of matching methodologies in the field, emphasizing group-matching designs utilized in behavioral research on cognition and language in neurodevelopmental disorders, including autism spectrum disorder, fragile X syndrome, Down syndrome, and Williams syndrome. The limitations of relying on p -values to establish group equivalence are discussed in the context of other existing methods: equivalence tests, propensity scores, and regression-based analyses. Our primary recommendation for advancing research on intellectual and developmental disabilities is the use of descriptive indices of adequate group matching: effect sizes (i.e., standardized mean differences) and variance ratios.

With the ultimate goal of understanding their causal effects on development, much of behavioral research on intellectual and developmental disabilities (IDDs) is designed to (1) characterize phenotypic strengths and weaknesses in behavior and cognition and/or (2) identify syndrome-specific aspects of these profiles. Such aims are often addressed with group-matching designs, in which statistical comparisons between nonrandomized groups (e.g., autism spectrum disorder [ASD] versus typical development) provide the basis for conclusions. Despite the considerable attention matching has received ( Abbeduto, 2010 ; Burack, 2004 ), methodological issues in group matching remain at the forefront of concerns regarding the progress of behavioral research on neurodevelopmental disorders ( Beeghly, 2006 ; Eigsti, de Marchena, Schuh, & Kelley, 2011 ).

The purpose of this article is to introduce methodological improvements to group-matching designs frequently used in IDD research. To that end, we discuss the pitfalls of common group-matching strategies and suggest metrics for establishing adequate group equivalence that are not novel, but are new to the field: effect sizes and variance ratios. Because our primary goal is to provide a foundation from which informed decisions on research design, analysis, and interpretation can be made, we highlight several other study designs worthy of consideration. We conclude by emphasizing the need for thoughtful research questions and responsible use of equivalence thresholds.

Challenges of Group Matching in IDD Research

Frameworks for causality.

The ability to draw conclusions about causality has traditionally hinged upon random assignment of participants to the target group (e.g., treatment, intervention, diagnosis—in our case) and comparison group. Properly implemented, random assignment allows estimation of causal effects because it ensures, in the long run, that any differences between the target and comparison groups (i.e., bias or selection bias) aside from group assignment prior to the study are due to chance. One approach to causality, the Rubin Causal Model, defines the causal effect—that is, the effect of a manipulable treatment—in terms of potential outcomes: what the outcome would have been for participants in the comparison group had they received the treatment and what the outcome would have been for those in the treatment group had they not received it ( Holland, 1986 ; Rubin, 1974 ). In quasi-experimental designs (e.g., regression discontinuity, interrupted time series), it is possible to test hypotheses about the effects of causes without random assignment. A nonequivalent control group design is one that seeks to remove the bias associated with nonrandom assignment by matching the target and comparison groups to establish equivalence, or balance ( Shadish, Cook, & Campbell, 2002 ).

Methods in IDD Research

Although IDDs are attributable to neurodevelopmental disorders, those disorders can scarcely be considered manipulable causes. Research on IDDs is further constrained by ethical parameters (e.g., inability to randomly assign the circumstances that lead to a diagnosis of fetal alcohol spectrum disorder) and relatively small samples due to low prevalence. As such, the use of more desirable techniques, such as random assignment or sophisticated matching that relies on large datasets, is precluded. Instead, in the simplest and perhaps most common group-matching design in the field, two groups composed of participants with preexisting diagnoses are matched on a single variable, such as nonverbal cognitive ability, and then compared on some dependent variable of interest, such as vocabulary ability. These groups are selected in such a manner as to presume they are equivalent on a dimension of ability thought to be relevant to the dependent variable of interest. Differences between groups on the dependent variable are taken to indicate strengths or weaknesses on the construct of interest relative to the matching construct. How to select constructs and variables on which to match is discussed elsewhere and is beyond the current scope (see Burack, Iarocci, Bowler, & Mottron, 2002 ; Mervis & Klein-Tasman, 2004 ; Mervis & Robinson, 1999 ; Strauss, 2001 ). We focus here on a specific aspect of matching: establishing when groups are equivalent.

A customary group-matching procedure is to iteratively exclude participants from one or both groups until an independent samples t -test of the group mean difference on the matching variable yields a sufficiently high p -value, showing that the groups do not significantly differ. This process is achieved by first testing the difference between the groups on the matching variable. For example, a hypothetical target group of 30 participants with a mean score of 60.10 on the matching variable would not be considered matched to a comparison group of 30 participants with a mean score of 71.70 because the p -value for the t -test on the matching variable is less than .05 (hypothetical data are given in the Appendix ). Two matched groups might be attained by next removing all participants outside of the overlapping range of the groups or according to some other criterion, and then testing the group difference again, usually yielding iteratively higher p -values ( Mervis & John, 2008 ). This procedure might be repeated an unreported number of times by a researcher and usually yields higher p -values as participants are removed.

P -value Thresholds

The most persuasive standard in the field for group matching has been generated by Mervis and colleagues ( Mervis & Klein-Tasman, 2004 , Mervis & Robinson, 1999 ), who drew important attention to the matching procedures used to study individuals with IDDs. Mervis and colleagues highlighted that accepting groups as matched when a t -test on the matching variable yields a p -value greater than .05 is not sufficient ( Mervis & Klein-Tasman, 2004 ; Mervis & Robinson, 1999 ). As such, they substantially improved upon the common practice of accepting the null hypothesis that population means are equal given any nonsignficant p -value. Mervis and Klein-Tasman (2004) suggested that when considering a p -value threshold for matching groups, “…it is important to show that the group distributions on the matching variable overlap strongly, as evidenced, we suggest, by a p -level of at least .50 on the test of mean differences for the control variable(s),” (p. 9). While p -values below .05 are taken as clear indication of a group difference, Mervis and colleagues (2004 , 1999 ) proposed that p -values between .20 and .50 are ambiguous; p -values of .50 and above are sufficient evidence of equivalence. The .50 p -value threshold was based on Frick’s (1995) “good-effort criterion” for accepting the null hypothesis, which included p -value thresholds in combination with a small effect.

According to Mervis’ guideline, groups might be considered matched on a measure of cognitive ability only when the p -value for the test of the group difference on the matching variable is greater than or equal to .50. In our hypothetical example, a subset of participants ( n = 20 from each group) could be selected to improve the overlap of the groups on the matching variable by removing the lowest scoring participants of the target group and the highest scoring participants of the comparison group, yielding a mean of 68.10 for the target group and a mean of 67.10 for the comparison group. The t -test on the matching variable for these subgroups is not significant, but instead gives a p -value of .55, which is a value that might be taken as evidence that the groups are matched.

The Trouble with P -value Thresholds

Mervis and colleagues (2004 , 1999 ) were correct in emphasizing that groups ought not be considered matched solely on the basis of a p -value greater than .05. Most importantly, their recommendations increased awareness in the field that some p -values should lead to a conclusion of failing to reject the null hypothesis that the population means are equal. Nonetheless the p -value threshold proposed by Mervis et al. (2004 , 1999 ) and Frick (1995) is not without limitations ( Edgell, 1995 ; Imai, King, & Stuart, 2008 ). Difficulties hinge around the interpretation of p -values and the role of power in hypothesis testing.

Interpretation of a P -value

A p -value is defined as the probability of observing the sampled data or data more extreme, given that the null hypothesis is true. The hypotheses in question in the traditional matching procedure are H 0 : Δ = 0 and H 1 : Δ ≠ 0, where Δ is the population mean difference on the matching variable. The p -value represents the probability of observing the sample mean difference (or one more extreme) when the population mean difference is zero. When there is no difference in the population on the matching variable, one would expect a p -value to be less than or equal to .05 exactly 5% of the time. As such, using p > .05 as a threshold for declaring groups to be matched will result in groups being considered matched 95% of the time when there is no true population mean difference. This can be seen in the first panel of Figure 1 . Likewise, one would expect a p -value to be less than or equal to .20 exactly 20% of the time; a p -value of less than or equal to .50 would be expected 50% of the time when the populations are equivalent. Thus, using a matching threshold of p ≥ .50, one would conclude that the group samples are matched just 50% of the time on average when the groups are truly matched in the population.

Proportion of samples considered to be adequately matched according to p -value thresholds by sample size and population effect size (Cohen’s d ).

Failure to reject H 0 :Δ = 0 does not allow one to conclude that the groups come from populations with the same mean because a p -value denotes nothing about the probability of the truth of H 0 given the observed data ( Schervish, 1996 ). Null hypothesis significance testing allows for rejecting or failing to reject the null hypothesis; the option of accepting the null hypothesis simply does not exist. Thus, observing a p -value of .50 leads only to a conclusion that the groups are not significantly different (i.e., a failure to reject the null hypothesis).

Power and P -values

It is possible to observe a large p -value due to a lack of effect, due to a small effect, and/or due to the lack of power to detect that effect because of a small sample size. Eliminating participants until a test of the mean difference results in a large enough p -value may decrease the difference between the observed sample means for the matching variable, but also decreases the power (due to the decreasing sample size) to detect any effect at all, including on the dependent variable of interest. In other words, increasing p -values on the matching variable may have less to do with achieving equivalence between groups and more to do with a reduction in power, particularly when sample sizes are initially small. Mervis and John (2008) provide a substantive example of this for a sample of participants with Williams syndrome.

Impact of sample size on p -value threshold matching

To further illustrate these difficulties, we simulated the process of sampling groups of various sizes from populations with known mean differences in a Monte Carlo simulation using R version 2.10.1 ( R Development Core Team, 2010 ). Over 10,000 iterations, we tracked the frequency with which various p -value matching thresholds resulted in concluding that the groups were matched. We defined groups to be matched when a t -test comparing group means on the matching variable resulted in a p -value greater than p -value thresholds of .05, .20, and .50. We based the matching variable on a standardized assessment of cognitive ability, such as IQ ( M = 100, SD = 15), because it is often used in this context and is readily interpretable. The true difference in populations was calculated in terms of the standardized mean difference effect size, ranging from 0 (i.e., no difference) to 0.5 (i.e., a medium effect size using Cohen's [1988] guidelines).

The impact of sample size on the p -value threshold method for determining when groups are matched becomes apparent when the population mean difference is truly greater than zero. As seen in Figure 1 , when the population mean difference is a medium effect of d = 0.50, using a threshold of p ≥ .50, one concludes that the groups are matched between 5% and 35% of the time across sample sizes of 10 to 50. This notable discrepancy in rate of meeting the p -value threshold and concluding that the groups are matched is due to variability in sample size alone.

Inferential statistics should not be used in isolation for establishing equivalence because the results of a t -test hinge on both the observed mean difference between groups and the statistical power of the test, which has a direct relation to sample sizes—dropping participants reduces power and increases a p -value without respect to the mean difference ( Imai et al., 2008 ).

Improved Equivalence Thresholds: Recommendations

Descriptive statistics for group matching.

Contemporary reviews of matching methodologies highlight descriptive statistics pre- and post-matching as an alternative to inferential statistics for determining the adequacy of group equivalence ( Steiner & Cook, 2012 ; Stuart, 2010 ). As the basis for equivalence thresholds—a term from Stegner et al. (1996) —for IDD research, we suggest two descriptive metrics: effect sizes (i.e., standardized mean differences) and variance ratios. These metrics are used widely in quasi-experimental designs with propensity score analysis, which we describe below. Importantly, effect sizes and variance ratios yield interpretable estimates of group matching adequacy and reduce the influence of sample size ( Breaugh & Arnold, 2007 ; Imai et al., 2008 ).

Sometimes referred to as standardized bias, standardized mean differences are a simple and effective index of matching ( Rosenbaum & Rubin, 1985 ; Rubin, 2001 ). Where x ̄ t and x ̄ c are the means of the target and comparison groups on the matching variable, respectively, and s 2 is the corresponding variance, Cohen’s d should be calculated as ( x t ¯ − x c ¯ ) / s t 2 + s c 2 / 2 , when population variances are assumed equal a priori and sample sizes are equal. Note that Cohen’s d is calculated as ( x t ¯ − x c ¯ ) / [ ( n t − 1 ) s t 2 + ( n c − 1 ) s c 2 ] / [ n t + n c − 2 ] for equal or unequal sample sizes, but the formula simplifies as above when sample sizes are equal. When variances are not assumed equal and/or interpreting the mean difference with respect to the variance of the comparison group is preferred, Cohen’s d can be calculated as ( x t ¯ − x c ¯ ) / s c 2 . For our hypothetical example of the n = 20 groups (see Appendix ), Cohen’s d is: ( 68.10 − 67.10 ) / ( 36 + 20 ) / 2 = .19 . Effect sizes should be reported as best practice for tests of the dependent variable ( American Psychological Association, 2010 ; Bakeman, 2006 ), but also reporting standardized mean differences alongside p -values on the matching variable provides context to the comparison of groups. The strategy of reporting effect sizes has been utilized in investigations of language and cognitive abilities in boys with ASD to aid the reader in interpreting the equivalence between the target and comparison samples ( Brown, Aczel, Jimenez, Kaufman, & Grant, 2010 ; Kover, McDuffie, Hagerman, & Abbeduto, under revision ).

The weaknesses of matching groups on just one aspect of their distributions (i.e., means) has been noted ( Facon, Magis, & Belmont, 2011 ); however, using p -value threshold tests on variance, skewness, and kurtosis may exacerbate the issues associated with using p -value thresholds for means alone. We do not recommend p -value threshold matching for variances in addition to means. Rather, we favor Rubin’s (2001) guideline, which avoids use of an inferential statistic: reporting the ratio of the variance of the target group to the variance of the comparison group. The variance ratio should be calculated as: s t 2 / s c 2 . For our hypothetical example of the n = 20 groups, the variance ratio is: 36.00/20.20 = 1.78.

Thresholds for Effects Sizes and Variance Ratios

Of course, the issue of where to set the equivalence thresholds for effect sizes and variance ratios remains ( Shadish & Steiner, 2010 ). Researchers will need to decide on meaningful thresholds based on seminal substantive studies because general guidelines are not universally applicable and should be used only when other references are not available ( Cohen, 1988 ):

"The terms 'small,' 'medium,' and 'large' are relative, not only to each other, but to the area of behavioral science or even more particularly to the specific content and research method being employed in any given investigation…In the face of this relativity, there is a certain risk inherent in offering conventional operational definitions for these terms for use in power analysis in as diverse a field of inquiry as behavioral science. This risk is nevertheless accepted in the belief that more is to be gained than lost by supplying a common conventional frame of reference which is recommended for use only when no better bases for estimating the ES [effect size] index is available" (p. 25).

An adequately small effect size for matched groups might be defined as the smallest value at which a difference in groups would be clinically meaningful ( Piaggio et al., 2006 ). Rubin (2001) proposed that the standardized mean difference be close to zero (less than half a standard deviation apart; d ≤ .5) and that the ratio of variances be near 1 (0.5 and 2 serve as endpoints that indicate very poor variance matches). Others have been more specific in defining equivalence as a standardized mean difference near zero such that it is within .1 standard deviation and a variance ratio greater than .8 and less than 1.25 ( Steiner, Cook, Shadish, & Clark, 2010 ). In research on ASD, a Cohen’s d of less than .20 has been described as trivial, but this threshold has yet to be evaluated in terms of group-matching adequacy ( Cicchetti et al., 2011 ). Steiner and Cook (2012) point out that a given effect size on the matching variable must be interpreted together with the expected effect size of the variable of interest (e.g., a Cohen’s d of 0.15 on the matching variable would not be sufficiently small if the effect of interest was expected to be 0.20).

We suggest that groups be considered adequately matched when they fall within the field’s standards for both the absolute value of Cohen’s d and the variance ratio. Table 1 lists a variety of effect sizes and variance ratios with illustrative corresponding means and variances on a matching variable for two groups. A Cohen’s d of 0.00 reflects well-matched group means; a Cohen’s d of 1.00 reflects poorly matched groups. A variance ratio of 1 indicates no difference in variances; a ratio of 2 reflects an unacceptable magnitude of difference in the spread of the distributions. For our hypothetical example, the effect size of .19 might be sufficiently small in some contexts for some researchers to conclude that the groups are matched, but taken together with the variance ratio of 1.78, it is unlikely that these two groups should be considered matched in most fields of study.

Example Standardized Mean Differences (Cohen’s d ) and Variance Ratios as Thresholds

Note . Matched-group adequacy should be evaluated with respect to both means (i.e., absolute value of the effect size) and variances. We emphasize that decisions regarding the adequacy of group matches must be reached through consensus within individual fields; we merely provide starting points based on Rubin (2001) and Steiner and Cook (2012) . Sample statistics reflect a matching variable with M = 100 and SD = 15.

Although negotiating appropriate equivalence thresholds will be far from a trivial feat, these descriptive indices of group matching have several strengths. First, effect sizes are less directly affected by sample size than are p -values. Second, effect sizes and variance ratios can be used in combination with other metrics of equivalence, including visual inspection of plots and p -values from the t -test on the matching variable. Furthermore, because means and standard deviations are usually reported for matching variables in published studies, an interested reader can calculate effect sizes and variance ratios to aid in interpreting extant findings. In Table 2 , we summarize the strengths and weaknesses of the indices of equivalence discussed, as well as the methods described in the next section.

Brief Summary of Strengths and Weaknesses of Methodologies for IDD Research

Existing Methodologies Applied to IDD Research

Simple group-matching designs are ubiquitous in research on IDDs; however, other methodological options are available. We briefly describe three classes of methodologies with strengths and weaknesses that may be unfamiliar to the reader: equivalence tests, propensity score matching, and regression-based techniques.

Equivalence Tests

Often used in medical studies to demonstrate that the difference between two treatments does not exceed some clinically meaningful equivalence threshold, equivalence tests can also be applied to behavioral research ( Rogers, Howard, & Vessey, 1993 ; Serlin & Lapsley, 1985 ; Stegner et al., 1996 ). Schuirmann (1987) suggested a “two one-sided tests” procedure wherein one may conclude that Δ lies within the equivalence bounds (−Δ B , Δ B ) by simultaneously rejecting both H 0 : Δ ≥ −Δ B and H 0 : Δ ≤ Δ B . For Westlake’s (1979) confidence interval method, equivalence is established if the confidence interval (constructed in the usual manner, but with coverage of 0.90) for Δ ̂ , the observed mean difference, falls entirely within the equivalence bounds (−Δ B , Δ B ). Finally, the range equivalence confidence intervals proposed by Serlin and Lapsley (1985 ; 1993 ) stem from a good-enough principle and provide an additional alternative to "strawman" point null hypothesis testing. It is important to note that limited sample sizes may prevent equivalence methods from having the necessary power to detect a truly ‘trivial’ effect, or else triviality may need to be set at a higher magnitude than would be desired. For example, Brown et al. (2010) concluded based on equivalence testing that implicit learning is unimpaired in individuals with ASD relative to typical development, though their choice of threshold value may have been unusually large.

Propensity Scores

The state-of-the-art for matching nonequivalent control groups in quasi-experimental design is propensity score analysis. With the goal of removing selection bias by modeling the probability of being in the target group, propensity scores are aggregated variables that predict group membership using logistic regression ( Fraser & Guo, 2009 ; Shadish et al., 2002 ). Propensity score analysis involves creating a single score from many variables that could be related to group membership and then matching the groups on those propensity scores ( Fraser & Guo, 2009 ). The nonequivalent control groups are often matched utilizing algorithms that, for example, select comparison participants who have scores within a defined absolute difference from a given target participant (i.e., caliper matching) or minimize the total difference between pairs of target and comparison participants (i.e., optimal matching; Rosenbaum, 1989 ).

Propensity scores are best suited to the analysis of large datasets in which it is reasonable to assume that all variables relevant to group membership have been measured and those with complete overlap between the groups on the range of propensity scores ( Shadish et al., 2002 ). In addition, propensity score analysis may be no better than regression techniques unless the primary concern is the large number of matching variables included in the analysis ( Shadish & Steiner, 2010 ). Despite the fact that these conditions are rarely met in IDD research, there are cases in which propensity score matching has been applied. For example, Blackford (2009) used propensity score matching for data from State of Tennessee administrative databases to test whether infants with Down syndrome have lower birth weight than those without. Unfortunately, such large databases are yet unavailable to answer many research questions relevant to neurodevelopmental disorders.

Importantly, matching groups on propensity scores escapes neither the problem of having a satisfactory way to determine when groups are adequately matched nor other problems associated with matching groups on a single variable. Even when using large samples and sophisticated matching algorithms, matching can be problematic when the populations of interest do not completely overlap in range. As such, group-matching procedures can lead researchers to analyze data from samples of participants that are not representative of the populations from which they are drawn or to which the researcher wishes to generalize ( Shadish et al., 2002 ). Furthermore, when participants are chosen from the ends of their distributions due to matching criteria and when matching variables are measured with error, regression to the mean is of concern because participants selected for their extreme, apparently nonrepresentative scores are likely to have less extreme scores on the dependent variable and/or over time ( Breaugh & Arnold, 2007 ; Marsh, 1998 ; Shadish et al., 2002 ). Thus, propensity scores are not a panacea for researchers interested in a single matching construct or those with limited resources to collect large samples with all measurable variables relevant to group membership.

Regression-based Methods

Analysis of covariance (ANCOVA) is sometimes used as an alternative to group matching. ANCOVA is ideal for reducing sampling bias due to variability between groups in experimental designs when unbalance occurs due to chance. Assumptions of ANCOVA include: group membership independent of the covariate, linearly related predictor and outcome, and identical slopes for the groups between the covariate and the dependent variable. When used with preexisting groups, a researcher can expect difficult interpretation, at best, and spurious findings, at worst, because ANCOVA attempts to adjust or control for part of what the group effect is thought to be ( Brock, Jarrold, Farran, Laws, & Riby, 2007 ; Miller & Chapman, 2001 ). For neurodevelopmental disorders, the “selection bias” being removed is often integrally related to the causal effect of interest (e.g., background genes, maternal interaction styles, family stress, world experiences; see Newcombe, 2003 for an example related to children's socioemotional adjustment). In these cases, statistical adjustments between groups diminish true population differences that are attributes of the disorder, yielding uninterpretable results ( Dennis et al., 2009 ; Miller & Chapman, 2001 ; Tupper & Rosenblood, 1984 ). A strong argument has been made in particular against the use of IQ as a covariate in studies of neurodevelopmental disorders because it is inseparable from the disorder itself ( Dennis et al., 2009 ).

More generally, the process of choosing a matching variable or covariate should be deliberate. Preliminary tests of significance—including tests on the matching variable to decide whether it should be used as a covariate—are not recommended ( Atwood, Swoboda, & Serlin, 2010 ; Zimmerman, 2004 ). Above all, the choice of covariate or matching variable is likely to have a greater impact on the conclusions drawn than the choice of analytic method and, thus, should be carefully theoretically justified ( Breaugh & Arnold, 2007 ; Steiner et al., 2010 ).

Developmental trajectories and residuals

Distinct from ANCOVA, Thomas and colleagues (2009) have put forth a regression-based approach, termed cross-sectional developmental trajectories analysis, that allows testing within-group slope differences with respect to theoretically motivated predictors. From this perspective, trajectories are estimated for the dependent variable of interest relative to age and other predictors, such as nonverbal cognitive ability, and these trajectories are compared between a target group and a large comparison group. Conclusions can be drawn about group differences in intercepts (i.e., level of ability) and slopes (i.e., the relationship between a given predictor and the variable of interest). This approach has been applied to aspects of cognitive development in individuals with Williams syndrome ( Karmiloff-Smith et al., 2004 ) and vocabulary ability in individuals with ASD ( Kover et al., under revision ). We refer the interested reader to the detailed substantive examples and thorough characterization of the approach provided by Thomas et al. (2009) , which includes an online worksheet that walks through trajectory analyses step-by-step.

A special case of this type of analysis involves standardizing the performance of the target group based on the residual score (the difference between observed and predicted) from the trajectory of the comparison group ( Jarrold & Brock, 2004 ). The z -scores (or alternatively, scores divided by the standard error of the regression estimate) of these residuals can be used to assess relative deficits on multiple tasks of interest that have been standardized using the same predictor ( Jarrold, Baddeley, & Phillips, 2007 ; Jarrold & Brock, 2004 ). For example, Jarrold and colleagues (2007) examined the performance of individuals with Down syndrome and Williams syndrome on memory tasks with respect to multiple control variables (e.g., age, vocabulary ability), standardized against the performance of 110 typically developing children. By standardizing performance relative to these constructs, Jarrold et al. (2007) identified distinct relationships among abilities relative to the comparison group and differentiated the nature of the deficits in long-term memory in individuals with Down syndrome from those with Williams syndrome.

The developmental trajectories method carries fewer assumptions than ANCOVA because the regression with the matching variable is done for the comparison group alone, avoiding the potential to violate the assumption of independence between the covariate and group ( Brock et al., 2007 ). While allowing simultaneous analysis and “comparison” of disparate participant groups, this procedure is not without limitations. First, a very large comparison group is required. Second, transformations of matching and dependent variables limit the extent to which results can be transparently interpreted. Finally, like other methods, this technique still requires linearity and complete overlap between the groups on the matching variable. As data sharing and access to national datasets (e.g., the National Database for Autism Research; NDAR) become more common, analytic techniques like the developmental trajectories approach will only become more valuable because of the availability of larger samples.

Summary of Recommendations for Researchers

Having brought attention to some of the methodological challenges in research on IDDs, we close with comments on the relationship between research questions and design, and on the responsible use of effect sizes and variance ratios as descriptive equivalence thresholds.

Choose Productive Research Questions

Thoughtful research questions that yield interpretable results should drive study design. We have focused on the simplest type of group-matching design (i.e., two groups and one matching variable); however, many research questions call for other applications of nonequivalent comparison designs. For example, pair-wise matching on one or more control variables might ensure more closely matched groups, but it might also call into question the generalizability of the findings ( Mervis & Robinson, 1999 ). In some cases, studies might be strengthened by including multiple comparison groups ( Burack et al., 2002 ; Eigsti et al., 2011 ) or by matching that is conducted on control tasks that very closely align with the skill of interest ( Jarrold & Brock, 2004 ). Another alternative is creating individual profiles of ability (e.g., case-study analysis), rather than group-level profiles that might fail to represent any individuals from the population from which the sample was drawn ( Mervis & Robinson, 1999 ; Towgood, Meuwese, Gilbert, Turner, & Burgess, 2009 ). Regardless of the research question, reporting results based on multiple matching and analysis techniques will leave the reader informed and free to draw conclusions based on maximal information ( Breaugh & Arnold, 2007 ; Brock et al., 2007 ; Kover et al., under revision ; Mervis & John, 2008 ).

Shifting focus towards understanding individual variability avoids some difficulties associated with group matching, while also leading researchers closer to understanding the sources of difficulty that result in phenotypic strengths and weaknesses. Comparing unrepresentative samples provides little advantage over studying the entire range of variability within a given phenotype and identifying foundational cognitive skills that account for individual variation ( Beeghly, 2006 ; Eigsti et al., 2011 ). Adopting an individual differences approach can highlight phenotypic variability and emphasizes the prerequisite skills necessary for development, ultimately supporting research that emphasizes learning mechanisms rather than outcomes. Of course, some research questions will nonetheless necessitate group comparisons.

Use Effect Sizes and Variance Ratios for Equivalence Thresholds

Group-matching studies that appropriately compare groups presumed to be equivalent on a single matching variable have the potential to provide the groundwork for stronger, well-controlled studies of greater scope. Researchers will benefit from including as many sources of information as possible for establishing group equivalence: plots of the distributions, effect sizes, variance ratios, etc. Given the complexities faced by IDD researchers, our recommendation is that groups be considered adequately matched when both the effect size (e.g., Cohen’s d ) and variance ratio fall within acceptable ranges for a particular area of research. We have provided a table of effect sizes and variance ratios that demonstrates how this technique can be applied to decision making regarding group matching adequacy; however, this table is meant to be thought-provoking, not prescriptive. In published reports, best practice would be to report effect sizes and variance ratios in all cases—for the matching variable and the dependent variable of interest—to allow the reader to interpret where meaningful differences exist.

Conclusions and Future Directions

We have discussed the limitations of p -value thresholds and ways in which using descriptive diagnostics (effect sizes and variance ratios) as equivalence thresholds will benefit research on neurodevelopmental disorders. Drawing the interest of methodological specialists to the study of IDDs will also be key to advancing the field. Open dialogue concerning current practices, paired with the development of improved methods for defining and testing meaningful differences, will significantly improve the design and implementation of research on IDDs.

Acknowledgments

This work was supported in part by NIH P30 HD03352 to the Waisman Center and NIH T32 DC05359. We thank Peter Steiner for his comments on an earlier draft. Following Strauss (2001), we chose to maintain a methodological focus and avoided citing substantive studies as examples, with the exception of those that have utilized methodologies likely to be lesser known to the reader.

Hypothetical Scores on a Matching Variable from Two Groups

Note . The shaded cells show the subset of 20 participants in each group who remained in the analysis during the process of obtaining a higher p -value. They were chosen simply to demonstrate the calculation of effect size and variance ratio, not to demonstrate adequate equivalence.

A preliminary paper was presented at the 2011 annual meeting of the American Educational Research Association in New Orleans.

Contributor Information

Sara T. Kover, University of Wisconsin-Madison, Waisman Center, 1500 Highland Avenue, Madison, WI 53705.

Amy K. Atwood, University of Wisconsin-Madison.

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Frequently asked questions

What is random assignment.

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

Frequently asked questions: Methodology

Attrition refers to participants leaving a study. It always happens to some extent—for example, in randomized controlled trials for medical research.

Differential attrition occurs when attrition or dropout rates differ systematically between the intervention and the control group . As a result, the characteristics of the participants who drop out differ from the characteristics of those who stay in the study. Because of this, study results may be biased .

Action research is conducted in order to solve a particular issue immediately, while case studies are often conducted over a longer period of time and focus more on observing and analyzing a particular ongoing phenomenon.

Action research is focused on solving a problem or informing individual and community-based knowledge in a way that impacts teaching, learning, and other related processes. It is less focused on contributing theoretical input, instead producing actionable input.

Action research is particularly popular with educators as a form of systematic inquiry because it prioritizes reflection and bridges the gap between theory and practice. Educators are able to simultaneously investigate an issue as they solve it, and the method is very iterative and flexible.

A cycle of inquiry is another name for action research . It is usually visualized in a spiral shape following a series of steps, such as “planning → acting → observing → reflecting.”

To make quantitative observations , you need to use instruments that are capable of measuring the quantity you want to observe. For example, you might use a ruler to measure the length of an object or a thermometer to measure its temperature.

Criterion validity and construct validity are both types of measurement validity . In other words, they both show you how accurately a method measures something.

While construct validity is the degree to which a test or other measurement method measures what it claims to measure, criterion validity is the degree to which a test can predictively (in the future) or concurrently (in the present) measure something.

Construct validity is often considered the overarching type of measurement validity . You need to have face validity , content validity , and criterion validity in order to achieve construct validity.

Convergent validity and discriminant validity are both subtypes of construct validity . Together, they help you evaluate whether a test measures the concept it was designed to measure.

• Convergent validity indicates whether a test that is designed to measure a particular construct correlates with other tests that assess the same or similar construct.
• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related. This type of validity is also called divergent validity .

You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.

• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related

Content validity shows you how accurately a test or other measurement method taps  into the various aspects of the specific construct you are researching.

In other words, it helps you answer the question: “does the test measure all aspects of the construct I want to measure?” If it does, then the test has high content validity.

The higher the content validity, the more accurate the measurement of the construct.

If the test fails to include parts of the construct, or irrelevant parts are included, the validity of the instrument is threatened, which brings your results into question.

Face validity and content validity are similar in that they both evaluate how suitable the content of a test is. The difference is that face validity is subjective, and assesses content at surface level.

When a test has strong face validity, anyone would agree that the test’s questions appear to measure what they are intended to measure.

For example, looking at a 4th grade math test consisting of problems in which students have to add and multiply, most people would agree that it has strong face validity (i.e., it looks like a math test).

On the other hand, content validity evaluates how well a test represents all the aspects of a topic. Assessing content validity is more systematic and relies on expert evaluation. of each question, analyzing whether each one covers the aspects that the test was designed to cover.

A 4th grade math test would have high content validity if it covered all the skills taught in that grade. Experts(in this case, math teachers), would have to evaluate the content validity by comparing the test to the learning objectives.

Snowball sampling is a non-probability sampling method . Unlike probability sampling (which involves some form of random selection ), the initial individuals selected to be studied are the ones who recruit new participants.

Because not every member of the target population has an equal chance of being recruited into the sample, selection in snowball sampling is non-random.

Snowball sampling is a non-probability sampling method , where there is not an equal chance for every member of the population to be included in the sample .

This means that you cannot use inferential statistics and make generalizations —often the goal of quantitative research . As such, a snowball sample is not representative of the target population and is usually a better fit for qualitative research .

Snowball sampling relies on the use of referrals. Here, the researcher recruits one or more initial participants, who then recruit the next ones.

Participants share similar characteristics and/or know each other. Because of this, not every member of the population has an equal chance of being included in the sample, giving rise to sampling bias .

Snowball sampling is best used in the following cases:

• If there is no sampling frame available (e.g., people with a rare disease)
• If the population of interest is hard to access or locate (e.g., people experiencing homelessness)
• If the research focuses on a sensitive topic (e.g., extramarital affairs)

The reproducibility and replicability of a study can be ensured by writing a transparent, detailed method section and using clear, unambiguous language.

Reproducibility and replicability are related terms.

• Reproducing research entails reanalyzing the existing data in the same manner.
• Replicating (or repeating ) the research entails reconducting the entire analysis, including the collection of new data . 
• A successful reproduction shows that the data analyses were conducted in a fair and honest manner.
• A successful replication shows that the reliability of the results is high.

Stratified sampling and quota sampling both involve dividing the population into subgroups and selecting units from each subgroup. The purpose in both cases is to select a representative sample and/or to allow comparisons between subgroups.

The main difference is that in stratified sampling, you draw a random sample from each subgroup ( probability sampling ). In quota sampling you select a predetermined number or proportion of units, in a non-random manner ( non-probability sampling ).

Purposive and convenience sampling are both sampling methods that are typically used in qualitative data collection.

A convenience sample is drawn from a source that is conveniently accessible to the researcher. Convenience sampling does not distinguish characteristics among the participants. On the other hand, purposive sampling focuses on selecting participants possessing characteristics associated with the research study.

The findings of studies based on either convenience or purposive sampling can only be generalized to the (sub)population from which the sample is drawn, and not to the entire population.

Random sampling or probability sampling is based on random selection. This means that each unit has an equal chance (i.e., equal probability) of being included in the sample.

On the other hand, convenience sampling involves stopping people at random, which means that not everyone has an equal chance of being selected depending on the place, time, or day you are collecting your data.

Convenience sampling and quota sampling are both non-probability sampling methods. They both use non-random criteria like availability, geographical proximity, or expert knowledge to recruit study participants.

However, in convenience sampling, you continue to sample units or cases until you reach the required sample size.

In quota sampling, you first need to divide your population of interest into subgroups (strata) and estimate their proportions (quota) in the population. Then you can start your data collection, using convenience sampling to recruit participants, until the proportions in each subgroup coincide with the estimated proportions in the population.

A sampling frame is a list of every member in the entire population . It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.

Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous , so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous , as units share characteristics.

Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population .

A systematic review is secondary research because it uses existing research. You don’t collect new data yourself.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

An observational study is a great choice for you if your research question is based purely on observations. If there are ethical, logistical, or practical concerns that prevent you from conducting a traditional experiment , an observational study may be a good choice. In an observational study, there is no interference or manipulation of the research subjects, as well as no control or treatment groups .

It’s often best to ask a variety of people to review your measurements. You can ask experts, such as other researchers, or laypeople, such as potential participants, to judge the face validity of tests.

While experts have a deep understanding of research methods , the people you’re studying can provide you with valuable insights you may have missed otherwise.

Face validity is important because it’s a simple first step to measuring the overall validity of a test or technique. It’s a relatively intuitive, quick, and easy way to start checking whether a new measure seems useful at first glance.

Good face validity means that anyone who reviews your measure says that it seems to be measuring what it’s supposed to. With poor face validity, someone reviewing your measure may be left confused about what you’re measuring and why you’re using this method.

Face validity is about whether a test appears to measure what it’s supposed to measure. This type of validity is concerned with whether a measure seems relevant and appropriate for what it’s assessing only on the surface.

Statistical analyses are often applied to test validity with data from your measures. You test convergent validity and discriminant validity with correlations to see if results from your test are positively or negatively related to those of other established tests.

You can also use regression analyses to assess whether your measure is actually predictive of outcomes that you expect it to predict theoretically. A regression analysis that supports your expectations strengthens your claim of construct validity .

When designing or evaluating a measure, construct validity helps you ensure you’re actually measuring the construct you’re interested in. If you don’t have construct validity, you may inadvertently measure unrelated or distinct constructs and lose precision in your research.

Construct validity is often considered the overarching type of measurement validity ,  because it covers all of the other types. You need to have face validity , content validity , and criterion validity to achieve construct validity.

Construct validity is about how well a test measures the concept it was designed to evaluate. It’s one of four types of measurement validity , which includes construct validity, face validity , and criterion validity.

There are two subtypes of construct validity.

• Convergent validity : The extent to which your measure corresponds to measures of related constructs
• Discriminant validity : The extent to which your measure is unrelated or negatively related to measures of distinct constructs

Naturalistic observation is a valuable tool because of its flexibility, external validity , and suitability for topics that can’t be studied in a lab setting.

The downsides of naturalistic observation include its lack of scientific control , ethical considerations , and potential for bias from observers and subjects.

Naturalistic observation is a qualitative research method where you record the behaviors of your research subjects in real world settings. You avoid interfering or influencing anything in a naturalistic observation.

You can think of naturalistic observation as “people watching” with a purpose.

A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it “depends” on your independent variable.

In statistics, dependent variables are also called:

• Response variables (they respond to a change in another variable)
• Outcome variables (they represent the outcome you want to measure)
• Left-hand-side variables (they appear on the left-hand side of a regression equation)

An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.

Independent variables are also called:

• Explanatory variables (they explain an event or outcome)
• Predictor variables (they can be used to predict the value of a dependent variable)
• Right-hand-side variables (they appear on the right-hand side of a regression equation).

As a rule of thumb, questions related to thoughts, beliefs, and feelings work well in focus groups. Take your time formulating strong questions, paying special attention to phrasing. Be careful to avoid leading questions , which can bias your responses.

Overall, your focus group questions should be:

• Open-ended and flexible
• Impossible to answer with “yes” or “no” (questions that start with “why” or “how” are often best)
• Unambiguous, getting straight to the point while still stimulating discussion
• Unbiased and neutral

A structured interview is a data collection method that relies on asking questions in a set order to collect data on a topic. They are often quantitative in nature. Structured interviews are best used when: 

• You already have a very clear understanding of your topic. Perhaps significant research has already been conducted, or you have done some prior research yourself, but you already possess a baseline for designing strong structured questions.
• You are constrained in terms of time or resources and need to analyze your data quickly and efficiently.
• Your research question depends on strong parity between participants, with environmental conditions held constant.

More flexible interview options include semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias is the tendency for interview participants to give responses that will be viewed favorably by the interviewer or other participants. It occurs in all types of interviews and surveys , but is most common in semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias can be mitigated by ensuring participants feel at ease and comfortable sharing their views. Make sure to pay attention to your own body language and any physical or verbal cues, such as nodding or widening your eyes.

This type of bias can also occur in observations if the participants know they’re being observed. They might alter their behavior accordingly.

The interviewer effect is a type of bias that emerges when a characteristic of an interviewer (race, age, gender identity, etc.) influences the responses given by the interviewee.

There is a risk of an interviewer effect in all types of interviews , but it can be mitigated by writing really high-quality interview questions.

A semi-structured interview is a blend of structured and unstructured types of interviews. Semi-structured interviews are best used when:

• You have prior interview experience. Spontaneous questions are deceptively challenging, and it’s easy to accidentally ask a leading question or make a participant uncomfortable.
• Your research question is exploratory in nature. Participant answers can guide future research questions and help you develop a more robust knowledge base for future research.

An unstructured interview is the most flexible type of interview, but it is not always the best fit for your research topic.

Unstructured interviews are best used when:

• You are an experienced interviewer and have a very strong background in your research topic, since it is challenging to ask spontaneous, colloquial questions.
• Your research question is exploratory in nature. While you may have developed hypotheses, you are open to discovering new or shifting viewpoints through the interview process.
• You are seeking descriptive data, and are ready to ask questions that will deepen and contextualize your initial thoughts and hypotheses.
• Your research depends on forming connections with your participants and making them feel comfortable revealing deeper emotions, lived experiences, or thoughts.

The four most common types of interviews are:

• Structured interviews : The questions are predetermined in both topic and order. 
• Semi-structured interviews : A few questions are predetermined, but other questions aren’t planned.
• Unstructured interviews : None of the questions are predetermined.
• Focus group interviews : The questions are presented to a group instead of one individual.

Deductive reasoning is commonly used in scientific research, and it’s especially associated with quantitative research .

In research, you might have come across something called the hypothetico-deductive method . It’s the scientific method of testing hypotheses to check whether your predictions are substantiated by real-world data.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

There are many different types of inductive reasoning that people use formally or informally.

Here are a few common types:

• Inductive generalization : You use observations about a sample to come to a conclusion about the population it came from.
• Statistical generalization: You use specific numbers about samples to make statements about populations.
• Causal reasoning: You make cause-and-effect links between different things.
• Sign reasoning: You make a conclusion about a correlational relationship between different things.
• Analogical reasoning: You make a conclusion about something based on its similarities to something else.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Triangulation can help:

• Reduce research bias that comes from using a single method, theory, or investigator
• Enhance validity by approaching the same topic with different tools
• Establish credibility by giving you a complete picture of the research problem

But triangulation can also pose problems:

• It’s time-consuming and labor-intensive, often involving an interdisciplinary team.
• Your results may be inconsistent or even contradictory.

There are four main types of triangulation :

• Data triangulation : Using data from different times, spaces, and people
• Investigator triangulation : Involving multiple researchers in collecting or analyzing data
• Theory triangulation : Using varying theoretical perspectives in your research
• Methodological triangulation : Using different methodologies to approach the same topic

Many academic fields use peer review , largely to determine whether a manuscript is suitable for publication. Peer review enhances the credibility of the published manuscript.

However, peer review is also common in non-academic settings. The United Nations, the European Union, and many individual nations use peer review to evaluate grant applications. It is also widely used in medical and health-related fields as a teaching or quality-of-care measure. 

Peer assessment is often used in the classroom as a pedagogical tool. Both receiving feedback and providing it are thought to enhance the learning process, helping students think critically and collaboratively.

Peer review can stop obviously problematic, falsified, or otherwise untrustworthy research from being published. It also represents an excellent opportunity to get feedback from renowned experts in your field. It acts as a first defense, helping you ensure your argument is clear and that there are no gaps, vague terms, or unanswered questions for readers who weren’t involved in the research process.

Peer-reviewed articles are considered a highly credible source due to this stringent process they go through before publication.

In general, the peer review process follows the following steps: 

• First, the author submits the manuscript to the editor.
• Reject the manuscript and send it back to author, or 
• Send it onward to the selected peer reviewer(s) 
• Next, the peer review process occurs. The reviewer provides feedback, addressing any major or minor issues with the manuscript, and gives their advice regarding what edits should be made. 
• Lastly, the edited manuscript is sent back to the author. They input the edits, and resubmit it to the editor for publication.

Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.

You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.

Exploratory research is a methodology approach that explores research questions that have not previously been studied in depth. It is often used when the issue you’re studying is new, or the data collection process is challenging in some way.

Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.

Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.

Explanatory research is a research method used to investigate how or why something occurs when only a small amount of information is available pertaining to that topic. It can help you increase your understanding of a given topic.

Clean data are valid, accurate, complete, consistent, unique, and uniform. Dirty data include inconsistencies and errors.

Dirty data can come from any part of the research process, including poor research design , inappropriate measurement materials, or flawed data entry.

Data cleaning takes place between data collection and data analyses. But you can use some methods even before collecting data.

For clean data, you should start by designing measures that collect valid data. Data validation at the time of data entry or collection helps you minimize the amount of data cleaning you’ll need to do.

After data collection, you can use data standardization and data transformation to clean your data. You’ll also deal with any missing values, outliers, and duplicate values.

Every dataset requires different techniques to clean dirty data , but you need to address these issues in a systematic way. You focus on finding and resolving data points that don’t agree or fit with the rest of your dataset.

These data might be missing values, outliers, duplicate values, incorrectly formatted, or irrelevant. You’ll start with screening and diagnosing your data. Then, you’ll often standardize and accept or remove data to make your dataset consistent and valid.

Data cleaning is necessary for valid and appropriate analyses. Dirty data contain inconsistencies or errors , but cleaning your data helps you minimize or resolve these.

Without data cleaning, you could end up with a Type I or II error in your conclusion. These types of erroneous conclusions can be practically significant with important consequences, because they lead to misplaced investments or missed opportunities.

Data cleaning involves spotting and resolving potential data inconsistencies or errors to improve your data quality. An error is any value (e.g., recorded weight) that doesn’t reflect the true value (e.g., actual weight) of something that’s being measured.

In this process, you review, analyze, detect, modify, or remove “dirty” data to make your dataset “clean.” Data cleaning is also called data cleansing or data scrubbing.

Research misconduct means making up or falsifying data, manipulating data analyses, or misrepresenting results in research reports. It’s a form of academic fraud.

These actions are committed intentionally and can have serious consequences; research misconduct is not a simple mistake or a point of disagreement but a serious ethical failure.

Anonymity means you don’t know who the participants are, while confidentiality means you know who they are but remove identifying information from your research report. Both are important ethical considerations .

You can only guarantee anonymity by not collecting any personally identifying information—for example, names, phone numbers, email addresses, IP addresses, physical characteristics, photos, or videos.

You can keep data confidential by using aggregate information in your research report, so that you only refer to groups of participants rather than individuals.

Research ethics matter for scientific integrity, human rights and dignity, and collaboration between science and society. These principles make sure that participation in studies is voluntary, informed, and safe.

Ethical considerations in research are a set of principles that guide your research designs and practices. These principles include voluntary participation, informed consent, anonymity, confidentiality, potential for harm, and results communication.

Scientists and researchers must always adhere to a certain code of conduct when collecting data from others .

These considerations protect the rights of research participants, enhance research validity , and maintain scientific integrity.

In multistage sampling , you can use probability or non-probability sampling methods .

For a probability sample, you have to conduct probability sampling at every stage.

You can mix it up by using simple random sampling , systematic sampling , or stratified sampling to select units at different stages, depending on what is applicable and relevant to your study.

Multistage sampling can simplify data collection when you have large, geographically spread samples, and you can obtain a probability sample without a complete sampling frame.

But multistage sampling may not lead to a representative sample, and larger samples are needed for multistage samples to achieve the statistical properties of simple random samples .

These are four of the most common mixed methods designs :

• Convergent parallel: Quantitative and qualitative data are collected at the same time and analyzed separately. After both analyses are complete, compare your results to draw overall conclusions. 
• Embedded: Quantitative and qualitative data are collected at the same time, but within a larger quantitative or qualitative design. One type of data is secondary to the other.
• Explanatory sequential: Quantitative data is collected and analyzed first, followed by qualitative data. You can use this design if you think your qualitative data will explain and contextualize your quantitative findings.
• Exploratory sequential: Qualitative data is collected and analyzed first, followed by quantitative data. You can use this design if you think the quantitative data will confirm or validate your qualitative findings.

Triangulation in research means using multiple datasets, methods, theories and/or investigators to address a research question. It’s a research strategy that can help you enhance the validity and credibility of your findings.

Triangulation is mainly used in qualitative research , but it’s also commonly applied in quantitative research . Mixed methods research always uses triangulation.

In multistage sampling , or multistage cluster sampling, you draw a sample from a population using smaller and smaller groups at each stage.

This method is often used to collect data from a large, geographically spread group of people in national surveys, for example. You take advantage of hierarchical groupings (e.g., from state to city to neighborhood) to create a sample that’s less expensive and time-consuming to collect data from.

No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.

To find the slope of the line, you’ll need to perform a regression analysis .

Correlation coefficients always range between -1 and 1.

The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.

The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.

These are the assumptions your data must meet if you want to use Pearson’s r :

• Both variables are on an interval or ratio level of measurement
• Data from both variables follow normal distributions
• Your data have no outliers
• Your data is from a random or representative sample
• You expect a linear relationship between the two variables

Quantitative research designs can be divided into two main categories:

• Correlational and descriptive designs are used to investigate characteristics, averages, trends, and associations between variables.
• Experimental and quasi-experimental designs are used to test causal relationships .

Qualitative research designs tend to be more flexible. Common types of qualitative design include case study , ethnography , and grounded theory designs.

A well-planned research design helps ensure that your methods match your research aims, that you collect high-quality data, and that you use the right kind of analysis to answer your questions, utilizing credible sources . This allows you to draw valid , trustworthy conclusions.

The priorities of a research design can vary depending on the field, but you usually have to specify:

• Your research questions and/or hypotheses
• Your overall approach (e.g., qualitative or quantitative )
• The type of design you’re using (e.g., a survey , experiment , or case study )
• Your sampling methods or criteria for selecting subjects
• Your data collection methods (e.g., questionnaires , observations)
• Your data collection procedures (e.g., operationalization , timing and data management)
• Your data analysis methods (e.g., statistical tests  or thematic analysis )

A research design is a strategy for answering your   research question . It defines your overall approach and determines how you will collect and analyze data.

Questionnaires can be self-administered or researcher-administered.

Self-administered questionnaires can be delivered online or in paper-and-pen formats, in person or through mail. All questions are standardized so that all respondents receive the same questions with identical wording.

Researcher-administered questionnaires are interviews that take place by phone, in-person, or online between researchers and respondents. You can gain deeper insights by clarifying questions for respondents or asking follow-up questions.

You can organize the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias. Randomization can minimize the bias from order effects.

Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly.

Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.

A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.

The third variable and directionality problems are two main reasons why correlation isn’t causation .

The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.

The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.

Correlation describes an association between variables : when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables.

Causation means that changes in one variable brings about changes in the other (i.e., there is a cause-and-effect relationship between variables). The two variables are correlated with each other, and there’s also a causal link between them.

While causation and correlation can exist simultaneously, correlation does not imply causation. In other words, correlation is simply a relationship where A relates to B—but A doesn’t necessarily cause B to happen (or vice versa). Mistaking correlation for causation is a common error and can lead to false cause fallacy .

Controlled experiments establish causality, whereas correlational studies only show associations between variables.

• In an experimental design , you manipulate an independent variable and measure its effect on a dependent variable. Other variables are controlled so they can’t impact the results.
• In a correlational design , you measure variables without manipulating any of them. You can test whether your variables change together, but you can’t be sure that one variable caused a change in another.

In general, correlational research is high in external validity while experimental research is high in internal validity .

A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.

A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.

Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.

A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research .

A correlation reflects the strength and/or direction of the association between two or more variables.

• A positive correlation means that both variables change in the same direction.
• A negative correlation means that the variables change in opposite directions.
• A zero correlation means there’s no relationship between the variables.

Random error  is almost always present in scientific studies, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error by taking repeated measurements, using a large sample, and controlling extraneous variables .

You can avoid systematic error through careful design of your sampling , data collection , and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment ; and apply masking (blinding) where possible.

Systematic error is generally a bigger problem in research.

With random error, multiple measurements will tend to cluster around the true value. When you’re collecting data from a large sample , the errors in different directions will cancel each other out.

Systematic errors are much more problematic because they can skew your data away from the true value. This can lead you to false conclusions ( Type I and II errors ) about the relationship between the variables you’re studying.

Random and systematic error are two types of measurement error.

Random error is a chance difference between the observed and true values of something (e.g., a researcher misreading a weighing scale records an incorrect measurement).

Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently records weights as higher than they actually are).

On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis.

• If you have quantitative variables , use a scatterplot or a line graph.
• If your response variable is categorical, use a scatterplot or a line graph.
• If your explanatory variable is categorical, use a bar graph.

The term “ explanatory variable ” is sometimes preferred over “ independent variable ” because, in real world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.

Multiple independent variables may also be correlated with each other, so “explanatory variables” is a more appropriate term.

The difference between explanatory and response variables is simple:

• An explanatory variable is the expected cause, and it explains the results.
• A response variable is the expected effect, and it responds to other variables.

In a controlled experiment , all extraneous variables are held constant so that they can’t influence the results. Controlled experiments require:

• A control group that receives a standard treatment, a fake treatment, or no treatment.
• Random assignment of participants to ensure the groups are equivalent.

Depending on your study topic, there are various other methods of controlling variables .

There are 4 main types of extraneous variables :

• Demand characteristics : environmental cues that encourage participants to conform to researchers’ expectations.
• Experimenter effects : unintentional actions by researchers that influence study outcomes.
• Situational variables : environmental variables that alter participants’ behaviors.
• Participant variables : any characteristic or aspect of a participant’s background that could affect study results.

An extraneous variable is any variable that you’re not investigating that can potentially affect the dependent variable of your research study.

A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.

In a factorial design, multiple independent variables are tested.

If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions.

Within-subjects designs have many potential threats to internal validity , but they are also very statistically powerful .

Advantages:

• Only requires small samples
• Statistically powerful
• Removes the effects of individual differences on the outcomes

Disadvantages:

• Internal validity threats reduce the likelihood of establishing a direct relationship between variables
• Time-related effects, such as growth, can influence the outcomes
• Carryover effects mean that the specific order of different treatments affect the outcomes

While a between-subjects design has fewer threats to internal validity , it also requires more participants for high statistical power than a within-subjects design .

• Prevents carryover effects of learning and fatigue.
• Shorter study duration.
• Needs larger samples for high power.
• Uses more resources to recruit participants, administer sessions, cover costs, etc.
• Individual differences may be an alternative explanation for results.

Yes. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables (a factorial design). In a mixed factorial design, one variable is altered between subjects and another is altered within subjects.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.

In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.

To implement random assignment , assign a unique number to every member of your study’s sample .

Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.

Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.

In contrast, random assignment is a way of sorting the sample into control and experimental groups.

Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.

“Controlling for a variable” means measuring extraneous variables and accounting for them statistically to remove their effects on other variables.

Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs . That way, you can isolate the control variable’s effects from the relationship between the variables of interest.

Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity .

If you don’t control relevant extraneous variables , they may influence the outcomes of your study, and you may not be able to demonstrate that your results are really an effect of your independent variable .

A control variable is any variable that’s held constant in a research study. It’s not a variable of interest in the study, but it’s controlled because it could influence the outcomes.

Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.

Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds.

If something is a mediating variable :

• It’s caused by the independent variable .
• It influences the dependent variable
• When it’s taken into account, the statistical correlation between the independent and dependent variables is higher than when it isn’t considered.

A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related.

A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.

There are three key steps in systematic sampling :

• Define and list your population , ensuring that it is not ordered in a cyclical or periodic order.
• Decide on your sample size and calculate your interval, k , by dividing your population by your target sample size.
• Choose every k th member of the population as your sample.

Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling .

Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.

For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 x 5 = 15 subgroups.

You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.

Using stratified sampling will allow you to obtain more precise (with lower variance ) statistical estimates of whatever you are trying to measure.

For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.

In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).

Once divided, each subgroup is randomly sampled using another probability sampling method.

Cluster sampling is more time- and cost-efficient than other probability sampling methods , particularly when it comes to large samples spread across a wide geographical area.

However, it provides less statistical certainty than other methods, such as simple random sampling , because it is difficult to ensure that your clusters properly represent the population as a whole.

There are three types of cluster sampling : single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.

• In single-stage sampling , you collect data from every unit within the selected clusters.
• In double-stage sampling , you select a random sample of units from within the clusters.
• In multi-stage sampling , you repeat the procedure of randomly sampling elements from within the clusters until you have reached a manageable sample.

Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample.

The clusters should ideally each be mini-representations of the population as a whole.

If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,

If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.

The American Community Survey  is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.

Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .

Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity  as they can use real-world interventions instead of artificial laboratory settings.

A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.

Blinding is important to reduce research bias (e.g., observer bias , demand characteristics ) and ensure a study’s internal validity .

If participants know whether they are in a control or treatment group , they may adjust their behavior in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.

• In a single-blind study , only the participants are blinded.
• In a double-blind study , both participants and experimenters are blinded.
• In a triple-blind study , the assignment is hidden not only from participants and experimenters, but also from the researchers analyzing the data.

Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment .

A true experiment (a.k.a. a controlled experiment) always includes at least one control group that doesn’t receive the experimental treatment.

However, some experiments use a within-subjects design to test treatments without a control group. In these designs, you usually compare one group’s outcomes before and after a treatment (instead of comparing outcomes between different groups).

For strong internal validity , it’s usually best to include a control group if possible. Without a control group, it’s harder to be certain that the outcome was caused by the experimental treatment and not by other variables.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.

Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.

The type of data determines what statistical tests you should use to analyze your data.

A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.

To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.

In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).

The process of turning abstract concepts into measurable variables and indicators is called operationalization .

There are various approaches to qualitative data analysis , but they all share five steps in common:

• Prepare and organize your data.
• Review and explore your data.
• Develop a data coding system.
• Assign codes to the data.
• Identify recurring themes.

The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .

There are five common approaches to qualitative research :

• Grounded theory involves collecting data in order to develop new theories.
• Ethnography involves immersing yourself in a group or organization to understand its culture.
• Narrative research involves interpreting stories to understand how people make sense of their experiences and perceptions.
• Phenomenological research involves investigating phenomena through people’s lived experiences.
• Action research links theory and practice in several cycles to drive innovative changes.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Operationalization means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.

When conducting research, collecting original data has significant advantages:

• You can tailor data collection to your specific research aims (e.g. understanding the needs of your consumers or user testing your website)
• You can control and standardize the process for high reliability and validity (e.g. choosing appropriate measurements and sampling methods )

However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.

There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.

In restriction , you restrict your sample by only including certain subjects that have the same values of potential confounding variables.

In matching , you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable .

In statistical control , you include potential confounders as variables in your regression .

In randomization , you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.

A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.

Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.

To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables , or even find a causal relationship where none exists.

Yes, but including more than one of either type requires multiple research questions .

For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.

You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .

To ensure the internal validity of an experiment , you should only change one independent variable at a time.

No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!

You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment .

• The type of soda – diet or regular – is the independent variable .
• The level of blood sugar that you measure is the dependent variable – it changes depending on the type of soda.

Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.

In non-probability sampling , the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.

Common non-probability sampling methods include convenience sampling , voluntary response sampling, purposive sampling , snowball sampling, and quota sampling .

Probability sampling means that every member of the target population has a known chance of being included in the sample.

Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .

Using careful research design and sampling procedures can help you avoid sampling bias . Oversampling can be used to correct undercoverage bias .

Some common types of sampling bias include self-selection bias , nonresponse bias , undercoverage bias , survivorship bias , pre-screening or advertising bias, and healthy user bias.

Sampling bias is a threat to external validity – it limits the generalizability of your findings to a broader group of people.

A sampling error is the difference between a population parameter and a sample statistic .

A statistic refers to measures about the sample , while a parameter refers to measures about the population .

Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

There are seven threats to external validity : selection bias , history, experimenter effect, Hawthorne effect , testing effect, aptitude-treatment and situation effect.

The two types of external validity are population validity (whether you can generalize to other groups of people) and ecological validity (whether you can generalize to other situations and settings).

The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures.

Cross-sectional studies cannot establish a cause-and-effect relationship or analyze behavior over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study .

Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.

Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.

Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.

The 1970 British Cohort Study , which has collected data on the lives of 17,000 Brits since their births in 1970, is one well-known example of a longitudinal study .

Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.

Longitudinal studies and cross-sectional studies are two different types of research design . In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.

There are eight threats to internal validity : history, maturation, instrumentation, testing, selection bias , regression to the mean, social interaction and attrition .

Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts and meanings, use qualitative methods .
• If you want to analyze a large amount of readily-available data, use secondary data. If you want data specific to your purposes with control over how it is generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .

In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:

• The  independent variable  is the amount of nutrients added to the crop field.
• The  dependent variable is the biomass of the crops at harvest time.

Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

• A testable hypothesis
• At least one independent variable that can be precisely manipulated
• At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

• How you will manipulate the variable(s)
• How you will control for any potential confounding variables
• How many subjects or samples will be included in the study
• How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

I nternal validity is the degree of confidence that the causal relationship you are testing is not influenced by other factors or variables .

External validity is the extent to which your results can be generalized to other contexts.

The validity of your experiment depends on your experimental design .

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research, you also have to consider the internal and external validity of your experiment.

A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

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• Methodology
• Random Assignment in Experiments | Introduction & Examples

Random Assignment in Experiments | Introduction & Examples

Published on 6 May 2022 by Pritha Bhandari . Revised on 13 February 2023.

In experimental research, random assignment is a way of placing participants from your sample into different treatment groups using randomisation.

With simple random assignment, every member of the sample has a known or equal chance of being placed in a control group or an experimental group. Studies that use simple random assignment are also called completely randomised designs .

Random assignment is a key part of experimental design . It helps you ensure that all groups are comparable at the start of a study: any differences between them are due to random factors.

Table of contents

Why does random assignment matter, random sampling vs random assignment, how do you use random assignment, when is random assignment not used, frequently asked questions about random assignment.

Random assignment is an important part of control in experimental research, because it helps strengthen the internal validity of an experiment.

In experiments, researchers manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. To do so, they often use different levels of an independent variable for different groups of participants.

This is called a between-groups or independent measures design.

You use three groups of participants that are each given a different level of the independent variable:

• A control group that’s given a placebo (no dosage)
• An experimental group that’s given a low dosage
• A second experimental group that’s given a high dosage

Random assignment to helps you make sure that the treatment groups don’t differ in systematic or biased ways at the start of the experiment.

If you don’t use random assignment, you may not be able to rule out alternative explanations for your results.

• Participants recruited from pubs are placed in the control group
• Participants recruited from local community centres are placed in the low-dosage experimental group
• Participants recruited from gyms are placed in the high-dosage group

With this type of assignment, it’s hard to tell whether the participant characteristics are the same across all groups at the start of the study. Gym users may tend to engage in more healthy behaviours than people who frequent pubs or community centres, and this would introduce a healthy user bias in your study.

Although random assignment helps even out baseline differences between groups, it doesn’t always make them completely equivalent. There may still be extraneous variables that differ between groups, and there will always be some group differences that arise from chance.

Most of the time, the random variation between groups is low, and, therefore, it’s acceptable for further analysis. This is especially true when you have a large sample. In general, you should always use random assignment in experiments when it is ethically possible and makes sense for your study topic.

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Random sampling and random assignment are both important concepts in research, but it’s important to understand the difference between them.

Random sampling (also called probability sampling or random selection) is a way of selecting members of a population to be included in your study. In contrast, random assignment is a way of sorting the sample participants into control and experimental groups.

While random sampling is used in many types of studies, random assignment is only used in between-subjects experimental designs.

Some studies use both random sampling and random assignment, while others use only one or the other.

Random sampling enhances the external validity or generalisability of your results, because it helps to ensure that your sample is unbiased and representative of the whole population. This allows you to make stronger statistical inferences .

You use a simple random sample to collect data. Because you have access to the whole population (all employees), you can assign all 8,000 employees a number and use a random number generator to select 300 employees. These 300 employees are your full sample.

Random assignment enhances the internal validity of the study, because it ensures that there are no systematic differences between the participants in each group. This helps you conclude that the outcomes can be attributed to the independent variable .

• A control group that receives no intervention
• An experimental group that has a remote team-building intervention every week for a month

You use random assignment to place participants into the control or experimental group. To do so, you take your list of participants and assign each participant a number. Again, you use a random number generator to place each participant in one of the two groups.

To use simple random assignment, you start by giving every member of the sample a unique number. Then, you can use computer programs or manual methods to randomly assign each participant to a group.

• Random number generator: Use a computer program to generate random numbers from the list for each group.
• Lottery method: Place all numbers individually into a hat or a bucket, and draw numbers at random for each group.
• Flip a coin: When you only have two groups, for each number on the list, flip a coin to decide if they’ll be in the control or the experimental group.
• Use a dice: When you have three groups, for each number on the list, roll a die to decide which of the groups they will be in. For example, assume that rolling 1 or 2 lands them in a control group; 3 or 4 in an experimental group; and 5 or 6 in a second control or experimental group.

This type of random assignment is the most powerful method of placing participants in conditions, because each individual has an equal chance of being placed in any one of your treatment groups.

Random assignment in block designs

In more complicated experimental designs, random assignment is only used after participants are grouped into blocks based on some characteristic (e.g., test score or demographic variable). These groupings mean that you need a larger sample to achieve high statistical power .

For example, a randomised block design involves placing participants into blocks based on a shared characteristic (e.g., college students vs graduates), and then using random assignment within each block to assign participants to every treatment condition. This helps you assess whether the characteristic affects the outcomes of your treatment.

In an experimental matched design , you use blocking and then match up individual participants from each block based on specific characteristics. Within each matched pair or group, you randomly assign each participant to one of the conditions in the experiment and compare their outcomes.

Sometimes, it’s not relevant or ethical to use simple random assignment, so groups are assigned in a different way.

When comparing different groups

Sometimes, differences between participants are the main focus of a study, for example, when comparing children and adults or people with and without health conditions. Participants are not randomly assigned to different groups, but instead assigned based on their characteristics.

In this type of study, the characteristic of interest (e.g., gender) is an independent variable, and the groups differ based on the different levels (e.g., men, women). All participants are tested the same way, and then their group-level outcomes are compared.

When it’s not ethically permissible

When studying unhealthy or dangerous behaviours, it’s not possible to use random assignment. For example, if you’re studying heavy drinkers and social drinkers, it’s unethical to randomly assign participants to one of the two groups and ask them to drink large amounts of alcohol for your experiment.

When you can’t assign participants to groups, you can also conduct a quasi-experimental study . In a quasi-experiment, you study the outcomes of pre-existing groups who receive treatments that you may not have any control over (e.g., heavy drinkers and social drinkers).

These groups aren’t randomly assigned, but may be considered comparable when some other variables (e.g., age or socioeconomic status) are controlled for.

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomisation. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.

In contrast, random assignment is a way of sorting the sample into control and experimental groups.

Random sampling enhances the external validity or generalisability of your results, while random assignment improves the internal validity of your study.

Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.

In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.

To implement random assignment , assign a unique number to every member of your study’s sample .

Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a die to randomly assign participants to groups.

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Bhandari, P. (2023, February 13). Random Assignment in Experiments | Introduction & Examples. Scribbr. Retrieved 24 June 2024, from https://www.scribbr.co.uk/research-methods/random-assignment-experiments/

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Random Sampling vs. Random Assignment

Random sampling and random assignment are fundamental concepts in the realm of research methods and statistics. However, many students struggle to differentiate between these two concepts, and very often use these terms interchangeably. Here we will explain the distinction between random sampling and random assignment.

Random sampling refers to the method you use to select individuals from the population to participate in your study. In other words, random sampling means that you are randomly selecting individuals from the population to participate in your study. This type of sampling is typically done to help ensure the representativeness of the sample (i.e., external validity). It is worth noting that a sample is only truly random if all individuals in the population have an equal probability of being selected to participate in the study. In practice, very few research studies use “true” random sampling because it is usually not feasible to ensure that all individuals in the population have an equal chance of being selected. For this reason, it is especially important to avoid using the term “random sample” if your study uses a nonprobability sampling method (such as convenience sampling).

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Random assignment refers to the method you use to place participants into groups in an experimental study. For example, say you are conducting a study comparing the blood pressure of patients after taking aspirin or a placebo. You have two groups of patients to compare: patients who will take aspirin (the experimental group) and patients who will take the placebo (the control group). Ideally, you would want to randomly assign the participants to be in the experimental group or the control group, meaning that each participant has an equal probability of being placed in the experimental or control group. This helps ensure that there are no systematic differences between the groups before the treatment (e.g., the aspirin or placebo) is given to the participants. Random assignment is a fundamental part of a “true” experiment because it helps ensure that any differences found between the groups are attributable to the treatment, rather than a confounding variable.

So, to summarize, random sampling refers to how you select individuals from the population to participate in your study. Random assignment refers to how you place those participants into groups (such as experimental vs. control). Knowing this distinction will help you clearly and accurately describe the methods you use to collect your data and conduct your study.