# Identifying a confounder

I'm trying to check whether a variable is a confounder or not. Specifically, for a randomized trial where I want to investigate the effects of a reduction in class size on student performance, would free lunch status be a confounder? According to this answer, a confounder must satisfy the following conditions:

1. Be independently associated with the outcome;
2. Be associated with the exposure
3. Must not lie on the causal pathway between exposure and outcome.

I have verified 1 and 3 but am confused about 2 because I perform a chi-square test and find that the Pearson chi2(2) = 1.6e+03 and its Pr = 0.000, which would indicate that it is independent of the exposure and thus lunch status is not a confounder. Intuitively, this doesn't make sense to me since in the study I'm trying to replicate, they condition on free lunch status, which would mean it is a confounder. Am I just being stubborn in believing that free lunch status must be a confounder that needs to be adjusted for or am I just wrong?

• Check the marital "satisfaction" example taken from Agresti here - $H_0: Independence$. You reject $H_0$. – Antoni Parellada Jan 26 '16 at 19:27