# Hypothesis testing on values that are functions of multiple distributions

I have a hypothetical experiment where I am comparing scores on some measure at 1 year to scores on the measure at 4 years. I use a non-paired t-test to see if there is a significant difference between the two. Then, I do:

(4 year mean) - (1 year mean)


Now, I want to take that value, a function of two different distributions that have different n and SD, and compare it to another value that was obtained in the same way from two similar distributions (1st & 4th year but under a different independent variable). How can I do this? And is it valid do 4yrMean - 1yrMean to obtain the value, or should I do p-value4 - p-value1 or something?

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