# How to test if the change in difference between 2 distributions is significant?

I have 2 different conditions of 'behaviour state' and 2 different people. I'm trying to find a way to test if the difference in distributions (which I'm assuming are approximately normal) changes significantly between these conditions, and cannot for the life of me figure out how to do this (particularly in MATLAB). Each person has a different number of observations, so I can't simply act as if they were matched pairs and subtract.

Or in other words, if the difference $\Delta_1$ between people $X_1$ and $Y_1$ differs significantly between the difference $\Delta_2$ between people $X_2$ and $Y_2$.

If Δ1 and Δ2 can be viewed as two separate samples, you could use a two-sample Kolmogorov-Smirnov test to see if they have different distributions (kstest2 function). Or there are different functions to see if they have different means or medians or whatever.