6
$\begingroup$

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?

$\endgroup$
1
  • $\begingroup$ modified the wikipedia page aligned with answers below. $\endgroup$
    – tim
    Sep 14 '15 at 19:09
10
$\begingroup$

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 $Z_i$.

$\endgroup$
4
  • 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.