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.
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?