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I have seen posts that said ANOVA and multiple regression are theoretically the same. But if this is really the case, does anyone know why the G*Power (Linear multiple regression vs ANOVA) gives massively different sample sizes with the same/similar inputs (effect size, power & alpha)?

I have three independent variables (2 categorical IVs and 1 continuous IV), one dependent variable (continuous), and two control variables (age & gender). I will use a hierarchical regression analysis to examine the main & interaction effects. In G*Power, when I opt for the option "Linear multiple regression:Fixed model R^2 increase" (effect size = 0,15; alpha = 0,05, power = 0,8, #of tested predictors = 4 (three IVs + a three-way interaction), and total number of predictors = 6 (three IVs + a three way interaction + 2 control variables), then I get a sample size of 85.

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However, when I opt for "ANOVA: fixed effects, special, main effects and interaction effects" with effect size = 0,25 (medium as in the previous one), alpha = 0,05, power = 0,8, df = 1 (the categorical IVs are two-level factors + the continous IV which is treated as -1/+1 here), and the number of groups = 4 (2 x 2 categorical factors). Then I get a sample size of 128. Does anyone know why this is? Which one should I use? Or, if I am doing something wrong here, what would you suggest that I do?

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Welcome to CrossValidated.

Small, medium and large effects were defined by Cohen, based on what he had seen in papers and his experience of research.

A medium effect in a correlation (r = 0.3, R^2 = 0.09) is not a medium effect in regression (f^2 = 0.15, R^2 = 0.13).

Although both your effects were medium, they aren't the same, hence different results.

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  • $\begingroup$ thank you for your reply - yes, I am aware of that, but even when I put the same effect size (0,25 for instance), I am afraid I still get different results!! $\endgroup$ – user240313 Mar 9 at 22:47
  • $\begingroup$ Actually, I think I now see what you mean; my input was indeed wrong - thank you for the help! $\endgroup$ – user240313 Mar 10 at 10:17

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