The Power Advantage of Within-Subjects Designs
In quantitative studies that involve comparisons of conditions or treatments, there are two basic types of designs to consider: between-subjects or within-subjects (also known as repeated-measures). In a between-subjects design, each participant receives only one condition or treatment, whereas in a within-subjects design each participant receives multiple conditions or treatments. Each design approach has its advantages and disadvantages. However, there is a particular statistical advantage that within-subjects designs generally hold over between-subjects designs.
Within-subjects designs have greater statistical power than between-subjects designs, meaning that you need fewer participants in your study in order to find statistically significant effects. For example, the between-subjects version of a standard t-test requires a sample size of 128 to achieve a power of .80, while the within-subjects version only requires a sample size of 34 to achieve the same power. This advantage of within-subjects designs may be well-known to some students, but many may not understand the reason behind it. The answer lies in how variance is divided up (or “partitioned”) in a within-subjects analysis.
Variance Partitioning in ANOVA
Consider the case analysis of variance (ANOVA) for example. In a between-subjects ANOVA, treatment variance and error variance comprise the total variance. You determine if there are differences between groups by examining the proportion of treatment variance to error variance. The error variance in this design can be attributable to individual differences between participants (e.g., demographic differences). In other words, you are trying to see through the “noise” of the variance caused by individual differences. This allows you to better isolate and understand the actual impact your treatment is having.
However, in a within-subjects ANOVA, we are able to divide up the variance even further. Specifically, we can partition the variance due to individual differences from the rest of the “error” variance. Thus, treatment variance, between-subjects variance (i.e., individual differences), and error variance comprise the total variance in the within-subjects ANOVA. We still determine the effect of the treatment by examining the proportion of treatment variance to error variance. By partitioning out the between-subjects variance, we reduce the amount of error variance in the equation. Thus reducing the “noise” we have to see through in order to see a significant treatment effect. Put another way, since differences between participants in a within-subjects design are not of interest, we can discard the between-subjects variance to gain a clearer understanding of the data.
Having a deeper understanding of the statistical advantages of intra-subjects designs may help you make more informed choices about your research design moving forward!
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