Hello all,

I am running an ANCOVA in R (Anova function) to assess the results of a randomized experimental study. I have a 2x2 full factorial model that will control for three continuous and two categorical covariates (ethnicity and gender). The gender covariate is unbalanced with a breakdown is roughly 2/3 women, 1/3 men, with about 5-10 participants of another gender identity. I am debating what kind of coding to use for gender. My options I see are to use dummy codes, unweighted effects codes, or weighted effects codes. My questions are the following:

1) The gender coding scheme makes no difference to the main and interactive effects of the experimental conditions. However, the decision of course effects the intercept value. I see multiple studies were people say they dummy coded categorical covariates. However, I know in ANCOVA you generally center continuous covariates to make the intercept at the mean of all covariates. Extending that logic, I would think I should use weighted effects coding for gender if I am going to plot interaction effects and adjusted means. But seeing that others seem not to do this when using categorical covariates, I am wondering if I am not understanding something correctly. Will the adjusted means be the same if I use dummy codes for gender or should I use weighted effects codes?

2) I would rather not drop anyone from analyses but realize the 5-10 cases for those of other gender identity is very small. In a separate set of analyses I will be running a linear regression and dummy coding with women as the reference. The women-men comparison should have enough folks to be useful. I know the women-other gender identity comparison won't be very interpretable but the women-other gender comparison is not one of my main outcomes of interest and it keeps the folks in analyses. I wonder if people think those folks should be dropped from analyses or if it makes sense to keep them in as their other data will still be useful? I am leaning towards keeping them in and making a note that that one beta should be interpreted with extreme caution.

Thanks for any thoughts you have,