. Author manuscript; available in PMC: 2016 Jun 24.

Published in final edited form as: Stat Biopharm Res. 2015 Jun 24;7(2):126–147. doi: 10.1080/19466315.2015.1004270

Table 1.

Summary of the combination tests and their associated critical values. Pure AC methods reject for values larger than the critical value. Pure MINP methods and the TPM reject for values smaller than the critical value.

Test	Statistic	Critical Value	Type
Fisher	$- 2 \sum_{i} \ln (p_{i})$	$Ψ_{2 m}^{- 1} (1 - α)$	AC
Chi-Squared	$\sum_{i} Ψ_{1}^{- 1} (1 - α)$	$Ψ_{m}^{- 1} (1 - α)$	AC
Liptak	$\sum_{i} Φ^{- 1} (1 - P_{i})$	$\sqrt{m} Φ (1 - α)$	AC
Bonferroni	mp ₍₁₎	α	MINP
Simes	min_i mp_(i)/i	α	MINP
Tippett	1 – (1 – p₍₁₎)^m	α	MINP