Let's say I run an experiment where participants play a behavioral game with someone that is either their same gender, or not their own gender. The primary criteria of interest is a pre and post measure of some outcome (taken before and after the game), captured as a change-score.
My approach for modeling this looks like the following:
felm(change_score ~ my_gender + other_gender_pairing + my_gender:other_gender_pairing | team_id | 0 | 0)
other_gender_pairing is a dummy variable set to
1 if you're paired with someone of the opposite gender. Standard errors are clustered a the
team_id level, since all dyads will have correlated error terms.
I have already conducted a pilot of this experiment involving 80 participants in each "cluster." Where a
1 indicates whether somebody was paired with their same gender (M-M or F-F = 0) or opposite gender (M-F or F-M = 1)
0 1 Male 80 80 Female 80 80
I would like to conduct power analysis to figure out the size of the effects I can detect given some fixed sample size per cell, informed by the coefficients estimated in the pilot. Unfortunately, because this design is somewhat complicated by the interaction effect and clustered standard errors, I cannot find any useful guides.
Can somebody point me in the right direction?
For reference, here are the coefficients identified in the regression run on the pilot. I'd like to be able to incorporate these estimates for more accurate power analyses.
Coefficients: Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF (Intercept) -0.8254 1.169 -0.7061 0.4817274 -3.144 1.493 101 my_gender 3.1266 2.092 1.4947 0.1381022 -1.023 7.276 101 other_gender_pairing 11.6639 3.330 3.5023 0.0006886 5.057 18.270 101 my_gender:other_gender_pairing -5.0025 4.645 -1.0769 0.2840919 -14.218 4.213 101
I use post-estimation tools to estimate contrasts where I compare means of M:M to M:F and F:F to F:M. This results in the following:
contrast estimate SE df t.ratio p.value 0 - 1 -11.66 3.33 199 -3.502 0.0006 gender = Female: contrast estimate SE df t.ratio p.value 0 - 1 -6.66 3.27 199 -2.040 0.0427
I'd like to know how big of a sample size to have in each cell in order to detect effects for the interaction effect.
Edit: I should note that my preferred language is R. It would be very helpful to see some template code for how to deal with experimental designs like this.