About combining multiple test statistics, Wikipedia says

This Z-score (for the overall meta-analysis) is appropriate for one-sided right-tailed p-values; minor modifications can be made if two-sided or left-tailed p-values are being analyzed.

What are those minor modifications?

  • $\begingroup$ modified the wikipedia page aligned with answers below. $\endgroup$
    – tim
    Sep 14 '15 at 19:09

1) If two-sided p-values are being analyzed, you use the two-sided p-value in the calculation of the $Z_i$. The two-sided p-value is $\tilde{p}_i = p_i/2$.

2) If left-tailed p-values are used, you use $1-p_i$ instead of $p_i$ in the calculation of the $Z_i$.

  • 1
    $\begingroup$ I don’t get the rationale of your definition of $\widetilde p_i$. I would have put $Z_i = \Phi^{-1}(1-p_i/2)$, and use as a score $\sum Z_i^2$ which follows a χ²(k) distribution. $\endgroup$
    – Elvis
    Dec 21 '11 at 19:35
  • $\begingroup$ @ElvisJaggerAbdul-Jabbar: You are correct, I was suffering a momentary fit of stupidity. I've edited the answer appropriately. $\endgroup$
    – jbowman
    Dec 21 '11 at 19:59
  • $\begingroup$ I was apparently suffering the same kind of syndrome, as I now don’t understand why I wanted to take the same of squared $Z_i$. I think your answer is now perfect (+1). $\endgroup$
    – Elvis
    Dec 21 '11 at 20:58
  • $\begingroup$ If the test is two-sided, then low p-value can correspond as well to Z=10 as to Z=-10. Why are always keeping the sign positive? $\endgroup$
    – quant_dev
    Jan 6 '19 at 22:00

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