Using SAS® to Perform Robust I-Sample Analysis of Means Type Randomization Tests for Variances

A SAS macro for performing Analysis of Means (ANOM) type randomization tests for testing the equality of I variances is presented. Randomization techniques for testing statistical hypotheses can be used when parametric tests are inappropriate. Suppose that I independent samples have been collected. Randomization tests are based on shuffles or rearrangements of the (combined) sample. Putting each of the I samples “in a bowl” forms the combined sample. Drawing samples “from the bowl” forms a shuffle. Shuffles can be made with replacement (bootstrap shuffling) or without replacement (permutation shuffling). The tests that are presented offer two advantages. They are robust to non-normality and they allow the user to graphically present the results via a decision chart similar to a Shewhart control chart. The decision chart facilitates easy assessment of both statistical and practical significance. Selected results from a Monte Carlo study used to identify robust randomization tests that exhibit excellent power when compared to other robust tests will be presented. INTRODUCTION Often it is useful to test whether each of I populations have the same variance. This homogeneity of variance (HOV) hypothesis may be written 2 2 1 0 : I H σ σ = = (1) where 2 i σ is the variance of the th i population. The alternative hypothesis is : A H not 0 H . This paper is concerned with is the case where 2 > I ; that is, where three or more populations are being compared. The focus will be on one-way balanced designs, but the discussions extend to unbalanced and more complex designs.