The construction of data to reflect the research objective, and how randomisation tests make such data usable

Abstract

When comparing the central values of two independent groups, should a t-test be performed, or should the observations be transformed into their ranks and a Wilcoxon-Mann-Whitney test performed? This paper argues that neither should automatically be chosen. Instead, provided that software for conducting randomisation tests is available, the chief concern should be with obtaining data values that are a good reflection of scientific reality and appropriate to the objective of the research; if necessary, the data values should be transformed so that this is so. The subsequent use of a randomisation (permutation) test will mean that failure of the transformed data values to satisfy assumptions such as normality and equality of variances will not be of concern.