I describe the use of the Bonferroni and Holm formulas as approximations for Šidák and Holland–Copenhaver formulas when issues of precision are encountered, especially with q-values corresponding to very small p-values.
HollandB. S., and CopenhaverM. D.1987. An improved sequentially rejective Bonferroni test procedure. Biometrics43: 417–423.
2.
HolmS.1979. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics6: 65–70.
3.
NewsonR.2003. Confidence intervals and p-values for delivery to the end user. Stata Journal3: 245–269.
4.
NewsonR., and the ALSPAC Study Team. 2003. Multiple-test procedures and smile plots. Stata Journal3: 109–132.
5.
NewsonR. B.2010. Frequentist q-values for multiple-test procedures. Stata Journal10: 568–584.
6.
ŠidákZ.1967. Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association62: 626–633.
