In a study, I have measured two dependent variables. They are closely correlated, both theoretically and mathematically (r = 0.9).
As an example, think of body height and foot size as dependent variables and age as the independent variable. Certainly not every small person has small feet, but the correlation is so strong as to render measuring both variables unnecessary if I conceptualize both body height and foot size as indicators for "physical growth", and the result (that age is a good predictor for growth) will be the same, using either or both of these variables.
But an ANOVA using either of these variables returns differing levels of insignificance (p = .17 vs p = .60). If they are so highly correlated, why are not similarly insignificant?
So, from a theoretical perspective, should I analyze my data using only one of these variables? Or do two univariate ANOVAS? Or should I do a multivariate MANOVA and test the effect between the variables?
What confuses me here is that I already know that the two variables are highly interdependent (and, unlike age on body height, both are not significantly predicted by my independent variable), so it seems to me that I should have measured, analyzed and reported only one.