Output for each unique set of values of the group-by variables (GBVs) is a p- value which when compared to the user’s choice of alpha, the probability threshold, determines whether the null hypothesis (p=p*, p≤p*, or p>p*) should be rejected for the GBV set. Though both binomial and Ztest results are provided for all N, for the approximate value obtained from the Z-test (nP) is appropriate when N is large. For values of N over 100, only the Z-test is performed. Otherwise, the value bP returned is the p_value of the one-tailed or two-tailed test, depending on the user’s choice.