Dear Lorren,
When adding covariates to a second-level design there's an option to center the values ("Centering"), thus it is going to depend on the combination of values and settings for centering. When going with "overall mean" it won't matter how you code sex (1, -1 or 0, 1).
Whether to mean center or not is going to depend on your hypotheses, see http://mumford.fmripower.org/mean_centering/ . For mean activity for "mean sex" you would go with no centering and values of e.g. 1 and -1, as you might have different no. of males and females. In contrast, [1 0] in combination with a mean-centered covariate corresponds to the mean activity across subjects, not across sex. Only if you have equal no. of males and females the two are going to be identical.
In case of binary variables you could also go with an extra between-subject factor.
Best
Helmut
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