# The Power Advantage of Within-Subjects Designs

Sample Size

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.

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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, whereas the within-subjects version only requires a sample size of 34 to achieve the same power. This advantage of within-subjects designs might be common knowledge for some students, but many students may not know why this is the case. The answer lies in how variance is divided up (or “partitioned”) in a within-subjects analysis.

Take an analysis of variance (ANOVA) for example. In a between-subjects ANOVA, the total variance is comprised of treatment variance and error 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 due to individual differences to see what 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, the total variance in the within-subjects ANOVA is comprised of treatment variance, between-subjects variance (i.e., individual differences), and error variance. 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 we are not interested in differences between participants in a within-subjects design, we can throw out the between-subjects variance to get a clearer picture of what is going on in the data.