I'm estimating the appropriate sample size for a RCT study, 3 groups, 3 measurements, power=90%, medium effect size (F=0.25), p=0.01 - anova repeated measures, within-between interaction.

When doing this in R, I get a total sample size of 335 participants:

wp.rmanova(n = NULL, ng = 3, nm = 3, f = 0.25, nscor = 1,

  • alpha = 0.01, power = 0.9, type = 2)

Repeated-measures ANOVA analysis

n f ng nm nscor alpha power

335.1259 0.25 3 3 1 0.01 0.9

However, in G*Power - the sample size calculated with the same numbers/parameters as above, is only 60 participants in total.

Can anyone explain this (huge) difference in sample sizes?


1 Answer 1


As you can see, this can be a very good idea to compare the output of different statistical software.

By default, G*Power uses a different effect size than the R library you use (webpower). Webpower uses the Jacob Cohen's definition of effect size. This is why you get different results. If you want more details about the effect size G*Power uses by default, this is addressed in this other answer.

Now, to reconcile the two, go in the options of G*Power (this is a button available at the bottom of the window, when you selected "Anova repeated measures"). Choose "as in Cohen (1988) - recommended" in "effect size specification", and re-run your calculation. You'll get a sample size of 336.

  • 1
    $\begingroup$ As a side note, it baffles me that the recommended configuration is not the default in G*Power. Hopefully the developers will correct it in a future version. $\endgroup$
    – J-J-J
    Jul 5, 2023 at 8:01
  • $\begingroup$ Thank you for a very clarifying answer. I guess, after reading all you links/attachments, that the default effect size specification in GPower should be avoided, and that one instead should use "as in spss" or "as in cohen". The default "As in GPower 3.0" seems to underestimate the required sample sizes to a very large extent. $\endgroup$ Jul 5, 2023 at 18:20
  • $\begingroup$ @Per-OlaRike It depends on the type of effect size and test you plan to use once you collected your data. The important thing is to stick to the same type of effect size at each stage of the study. But in general I'd say it's probably a better idea to stick to the commonly used Cohen's definition of effect size. $\endgroup$
    – J-J-J
    Jul 6, 2023 at 14:44

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