An Improved t Table for Simultaneous Control on g Contrasts

Abstract

Assuming a constant α, tables of t were developed using the Šidák multiplicative inequality: when doing g different contrasts the familywise rate of Type 1 errors, fwi ≤ 1 − (1 − α) ^g . Values of t are given that yield fwi = .01, .05, .10, or .20 for number of contrasts, g = 2(1)10, 15(5)50 and degrees of freedom, v = 2(1)30, 40, 60, 120, ∞. These t values are smaller than those in the previous Dunn (1961) tables, thus yielding slightly improved power.

Key Words:

• Bonferroni additive inequality
• Familywise Type I error rate
• Multiple comparisons
• Šidák multiplicative inequality
• Simultaneous inference
• Student's t.