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I have made good experience with using the modified Z-score for outlier detection in approximately normally distributed data, which was also discussed e.g. here and here.

However, if applying many tests I suppose that FDR correction becomes necessary. My plan is to utilize the p values for that purpose, i.e., by applying Bonferroni or BH correction. Now my question is, if the modified Z score can be applied for the calculation of p values just as for the standard Z scores, i.e., by utilizing the cumulative standard normal distribution function.

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  • $\begingroup$ The answer is Yes, though I have forgotten the details which were implemented in a program written by Iglewicz for the stats package RS-1. RS-1 was a Bolt Beranek and Newman program that was eventually retired. In my opinion, it was a very good test for researchers. $\endgroup$ – David Raunig Jul 6 '20 at 19:35
  • $\begingroup$ It might help to post the definition of the modified $Z$ score. $\endgroup$ – Dedekind Cuts Jul 6 '20 at 22:48

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