Suppose I'm interested in regressing variable A on variable B. I have two cohorts and want to be sure that there is not an interaction between cohort and variable B, so I include that in the regression. Both variables are continuous and have been standardized across the entire sample. My question is, is it correct or incorrect to standardize variable A within each gender before doing this analysis? How would doing so within each gender versus within the total sample change the interpretation of the results?
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$\begingroup$ When you say two cohorts: do you mean the data is split in regards to gender or do you have another variable that divides your sample in two? Do you intend to compare between gender? In that case, standardizing each variable within each gender is not a good idea. Just think what happens to their averages in that case. $\endgroup$– Fato39Apr 16, 2015 at 8:16
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1$\begingroup$ Also, see my recent answer Homogeneity of variance is violated for z-scores but not for raw data? on how different ways of standardization affect the homogeneity of variances of different groups. $\endgroup$– Fato39Apr 16, 2015 at 8:16
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1$\begingroup$ Why standardize at all? $\endgroup$– DavidJun 21, 2019 at 11:06
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If you standardize within each gender first, then a value of 1 for variable A would mean the person's value of variable A is one gender-specific standard deviation above the gender-specific mean of variable A. If you standardize across everyone, then a value of 1 for variable A would mean the person's value of variable A is one standard deviation above the overall mean of variable A.
The interpretation for the regression coefficient for variable A would probably get a bit muddled if you standardize each gender separately, unless you include an interaction term of variable A with gender. Then you would have separate interpretable coefficients for variable A for each gender.
