Say I am predicting happiness in a sample of college students and my predictors are age, family income, gender, and ethnicity. For my categorical variables (gender and ethnicity), I want to specify ahead of time the minimum number of respondents in a level (e.g., ethnicity = Asian) for me to report that coefficient. For example, if I have an overall sample of 300 respondents and only 2 are Asian, I don't think that dummy variable's coefficient would be reliable and I wouldn't want to report it. If 100 of my 300 respondents were Asian, I'd feel comfortable reporting that coefficient. But where is the cut-off?
Is this something that could be solved with a standard power analysis? For example, if I expect the effect of being Asian vs. my reference group is d = .2, would I need n = __ Asian students to report on that level?