Is using a 2 way MANOVA to check whether height and weight differ across age groups and gender, the same as using a 2 way ANOVA to check whether BMI (wt in kg/ht in m$^2$) differ across age groups and gender?
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No. The manova tests the bivariate effects, and is based only on linear functions thereof; whereas the BMI measure is a nonlinear function of those two responses. Even if BMI were linear, you'd be restricting the comparison to a 1-dimensional subspace of the two dimensions in your data.