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I have a mixed-ANOVA design: 2 groups (experimental & control) x 4 time points (pre, post, post2, post3), and am using G*Power to calculate the required sample size.

My understanding is that the "ANOVA Repeated measures, between factors" should be used if I am interested in the sample size required to detect the main effect of the group factor, and that the "ANOVA Repeated measures, within-between interaction" should be used if I am interested in the sample size required to detect the interaction effect (group*time).

However, the sample size required when I used "ANOVA Repeated measures, within-between interaction" is lower than the sample size required when using "ANOVA Repeated measures, between factors", which is weird as we generally require larger sample size to detect an interaction effect.

Am I missing something here?

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  • $\begingroup$ Can you give details on what parameters you're using for these power analyses? $\endgroup$
    – David B
    Mar 1, 2023 at 13:31
  • $\begingroup$ Hi @David, I'm using effect size f: 0.25, alpha of .05, power of .80, 2 groups, 4 measurements, and the corr among rep measures as 0.5. This leads to a total sample size of 82 if I selected "ANOVA: Repeated measures, between factors", but a total sample size of 24 if I selected "ANOVA: Repeated measures, within-between interaction". $\endgroup$
    – user381122
    Mar 1, 2023 at 13:57

1 Answer 1

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Based on your comment, it seems your running a power analysis using the default GPower values (except for Power parameter). This is not recommended. Instead, I would look into the literature to determine what effect sizes are reasonable for the kind of data I'm working with. You might also want to think about determining what your smallest effect size of interest is before running the power analysis.

Now, you mentioned that interactions often require larger samples. This is not because interactions are special statistically (they are just variables in a regression model after all), rather in practice interactions tend to be very small across fields and domains. So the standard is to plan on a small effect size for an interaction.

In your case, you have specified the same effect size for two parameters in a regression model, yet you get different estimates of the necessary sample size. Why is this? The key is understanding how power analyses in GPower work (and why I hate GPower for complex models). In essence, GPower assumes that all other effects are null except when the model implies that they are not - it has no way of specifying how much variance is explained by other parameters in your model. You're getting a smaller N in the second model because the way GPower runs these analyses implies the presence of large effects (outside of your control) that are independent of your effects of interest.

For your interaction, try to imagine a situation where there is no main effect of group, there is no main effect of your repeated measurement, but there is an interaction and the repeated measurements are highly correlated within-subjects. The only way this could happen is if there's a large within-subject effect of the repeated measurement that is independent of all other effects in the model (i.e., the random slope explains a lot of variance). BUT, this isn't the case in your between-factor model. So, more variance is explained by terms independent of your variable of interest in the second than the first model. That's why the N is lower.

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