Hand Computation of Bonferroni Critical Values

Abstract

Use of the Bonferroni t-test procedure often requires computation of “odd” critical values of Student's t. The formula given by Perlmutter and Myers (1973) for computing such critical values provides very inaccurate estimates for low degrees of freedom and/or for the small values of at which often arise in applications of the Bonferroni t. Zelen and Severo (1964) compiled several formulae which can be adapted to hand computation of the required critical values but provided no information on their accuracy. Computation of true values of at for each formula for degrees of freedom between 1 and 1000 and nominal ats between .05 and 10−6 permits the user of the Bonferroni t test to choose the simplest formula which provides adequate accuracy.