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.