I wonder if it is valid to perform a statistical test on t-values or z-scores. For instance, if one gets two groups of t-values, every t-value is generated from an individual t-test and the value itself is used to represent "effect size or standardized effect", then one wants to know whether the effect size in groupA is significantly larger than groupB, so Mann-Whitney test on these two groups of t-values is conducted. Or in another case, one just wants to test if the mean of all t-values in groupA is significantly larger than 0, so a t-test is conducted on these t-values. Are these processes valid? It sounds weird for me to do tests on test statistics, but I don't have a theoretical backup. It seems t-value is used as the standardized effect for each individual in each group because there are multiple measurements for each individual. Then t-value is a better choice than mean for the second step test between groups, because it also considers variance. However, if the question is about whether the effect is different between two groups, the input should still be the values of the variable of interest, then a mixed-effect or hierarchical model is more appropriate than a two-step test. Am I right? Thanks a lot.
I am Not Sure whether this answers the question, but rather than looking at the t or z values you can look at the standardized effect size d (Cohens d). Effect sizes can be meta-analyzed and within meta analysis there is an approach called meta-regression that allows you to examine whether study variables predict differences between effect size (such as a dummy variable coding group 1 or 2).