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When several variates are measured on the individuals of a single sample, it is often of interest to test whether or not two population correlation coefficients are equal. For example, in the behavioral sciences, it is often desirable to know whether two mental tests have equal test-retest reliability. In the present paper, eight asymptotically robust tests are proposed and are studied along with two parametric tests recommended by previous studies. Monte Carlo simulation is used to compare the small sample performance of these ten tests under the null hypothesis Ho: ρ12= ρ34where ρabis the population product moment correlation coefficient between variables Xaand Xb. Seven distributions are considered; a normal distribution, two mixed normal distributions, and four other nonnormal distributions.

Asymptotic tests are suggested for testing the equality of two multiple correlation coefficients calculated from a single sample from a multivariate normal distribution. An F test is possible only when the two dependent variables coincide and one set of independent variables is a subset of the second set. Tests are compared by simulation for situations in which the F test is inapplicable. Special attention is paid to cases in which asymptotic normality of the test statistics does not hold.

Class specific stratified posterior probability estimators of misclassification probabilities in discriminant analysis simulations are introduced. These estimators afford a significant variance reduction over the usual count estimators. Sufficient conditions for a variance reduction are given. The stratified posterior probability estimator is generalized to other class specific expectations.

This paper discusses multiple t tests and confidence intervals based on a Bonferroni Inequality and a slight improvement which can be made in some cases.It is rather well known but bears repeating, that when m tests are made, each with significance level αi, the overall significance of the m tests is less than or equal to [image omitted] . Similarly m confidence intervals, each with confidence level 1-αi, have an overall confidence level greater than or equal to [image omitted] . Such tests and confidence intervals, based on the simplest Bonferroni inequality [2], can be used for any sets or parameters and for any underlying distribution. They are thus general and convenient (provided tables are available) and often surprisingly good [1]. Usually the αi are taken to be equal to α/m, where α is the desired significance level (or 1-α is the desired confidence level).