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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?

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  • $\begingroup$ I don't understand, but I want to say no. $\endgroup$ – user2974951 Jul 11 '19 at 12:52
  • $\begingroup$ Imagine that you get a list of z-values and p-values from some logistic regression. Those z-values are standardized. So, it should be possible to, for example, average them, calculate the difference etc. That is my question: would that be kosher? $\endgroup$ – striatum Jul 11 '19 at 17:16
  • $\begingroup$ Why would you do that? What would you gain from that? $\endgroup$ – user2974951 Jul 12 '19 at 5:39
  • $\begingroup$ To be perfectly honest, I am asking this on the principle grounds, not because there is some particular problem I need to take care of. I do find this very interesting. And I can easily see how this can turn into a concrete example/case: for example, I can imagine two (or more) experimentally manipulated factors, some of which would/could have more than two levels; possibility to combine z-values from the analysis could be valuable, where one could join (average) levels of, say, native languages or nationalities and compare/contrast them etc. Does this make sense? $\endgroup$ – striatum Jul 12 '19 at 8:16
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    $\begingroup$ Is Stouffer's method relevant here? If not I rather agree with @user2974951. $\endgroup$ – mdewey Jul 12 '19 at 13:19
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Thanks to mdeway and patience of user2974951 I believe that Stouffer's method is indeed relevant here. A detailed discussion can be found on CrossValidated here.

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