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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?

Thank you!

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No, there's no simple way. It depends on effects of your variable of interest both on the outcome as well as your other covariates (age, family income, etc.).

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  • $\begingroup$ Do you have any guidance on how one would conduct a "power analysis" for effects like this? $\endgroup$
    – ila
    May 30, 2021 at 14:49
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    $\begingroup$ You can try a simulation approach where you model the data generating process. But, you'll have to make a number of assumptions on how the variables are related to each other. $\endgroup$
    – parasu
    May 30, 2021 at 17:18
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    $\begingroup$ Take a look at this article: psycnet.apa.org/record/2000-16737-004 But that still requires the covariance matrix for all your variables $\endgroup$
    – parasu
    May 30, 2021 at 17:26
  • $\begingroup$ Thank you for the article! And yes, I was thinking about a simulation approach. On the whole it seems like there's no simple way to approach this, as you say, but I appreciate the suggestions $\endgroup$
    – ila
    May 30, 2021 at 20:08

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