Measuring effect magnitude in repeated measures ANOVA designs: implications for gerontological research

Many methodologists advocate reporting effect size (ES) measures to assess the importance of observed differences. Unlike significance levels, these measures are independent of sample size. A second use of ES measures, particularly relevant to gerontological research, is to assert the null hypothesis by demonstrating the smallness of an effect. However, ES estimation is problematic in many commonly-used repeated measures ANOVA designs: If the additivity assumption is invalid and the design includes a fixed within-subject factor, the sample estimates of ES will be biased negatively. Our paper offers an alternative estimation procedure that can compensate for that bias. We define the lower and upper bounds of an interval within which lies the unbiased ES estimate. Further, we assert that for most design situations violation of the additivity assumption has a relatively small effect on the ES estimate. In addition, we provide a detailed, concrete example that should facilitate calculation of ES in repeated measures designs.