Why does the sum of two metrics give us a p-value above significance level but each metric viewed separately has p-value below significance level? Suppose that we have an AB test in which the individuals have been evenly split. We are measuring many variables simultaneously for each one of the individuals of this test (for example, X and Y). All the variables only take values >= 0.
When doing a T-test on X values, we obtain a p-value = 0.02 and when doing T-test on Y values we obtain a p-value = 0.0001.
However, when taking the variable Z = X+Y (which has an important and relevant meaning in our particular experiment), the T-test gives us a p-value of 0.46.
Why is this happening? Obviously, the p-value is not linear but I'd like to know the precise meaning of these results.
Thank you in advance for any help on this.

I think one thing people are missing is that variance adds in quadrature.  Without more information, it is impossible to say what the source of the problem is.  But it could be possible that the variance of Z is just sufficiently high to fail to reject the null.
