If a test-statistics is expressed in z-values (instead of, for example, t-values), would it be appropriate to use those values for some further inferences? For example, to average a pair and another pair, to compare the difference between them and so on. As the values are standard normal this should be fine. However, are there some covert traps?
This would be a simple example - a logistic regression summary table:
GENDER HEIGHT CONDITION Estimate Std. Error z value female short A 2.1351 0.2517 8.481 female short B 1.3336 0.2336 5.710 female tall A 1.9229 0.2521 7.627 female tall B 1.4435 0.2364 6.105 male short A 0.6710 0.2142 3.132 male short B 0.8949 0.2184 4.098 male tall A 0.4108 0.2135 1.924 male tall B 1.2879 0.2206 5.839
So, if one would wish to compare short and tall females, or short females and males, would it work to take the average of z-values?