I am looking at two populations on which I have measured 4 independent variables ($X_1$, $X_2$, $X_3$, $X_4$) and one dependent variable ($Y$) along with each measurement or observation. I suspect that the two populations are different in the sense that the second population's $Y$ shows a dependence on an additional non-considered factor (I expect $Y$ to be systematically lower, in fact). Considering that:
- the dependent variables are highly correlated;
- the dependence of $Y$ on the $X$'s is unknown and arguably non-parametric;
- the number of observables/measurements is small (~100 for the first group, ~30 for the second).
I feel that multi linear regression would assume some kind of underlying structure and would bias my analysis, so I would like to avoid it. I tried to use PCA on both and compare the PC's: nothing significant comes out in the sense of dimensionality. Could you suggest a test that would check if the two populations are really different in respect to $Y$ while keeping at a minimum the number of assumptions on its functional dependence?
Thank you very much,