This may be a basic econometrics question but I cannot find an answer. I know under what conditions a parametric test is preferable, but shouldn't the two techniques still give at least somewhat similar results?

In my study I have 500 subjects who took part in a decision-making experiments where they choose to "give" or "not give" in a set of scenarios. Thus, my dependent variable is binary and I am interested to see whether in scenario B more people gave compared to scenario A.

In scenario A, 84.8% of people gave; in scenario B, 85.4% of people gave. Yet, a tab chi2 tells me that the difference is significant [Pearson chi2(1) = 54.3799; n = 500]. However, if I run a xtreg fixed effects the coefficient for scenario B is obviously not significant.

I am asked to report both results, but don't understand how to reconcile them, or explain why reporting both wouldn't make sense.

Thanks!