Exact permutation inference for two sample repeated measures data

Abstract

Experiments in which very few units are measured many times sometimes present particular difficulties. Interest often centers on simple location shifts between two treatment groups, but appropriate modeling of the error distribution can be challenging. For example, normality may be difficult to verify, or a single transformation stabilizing variance or improving normality for all units and all measurements may not exist. We propose an analysis of two sample repeated measures data based on the permutation distribution of units. This provides a distribution free alternative to standard analyses. The analysis includes testing, estimation and confidence intervals. By assuming a certain structure in the location shift model, the dimension of the problem is reduced by analyzing linear combinations of the marginal statistics. Recently proposed algorithms for computation of two sample permutation distributions, require only a few seconds for experiments having as many as 100 units and any number of repeated measures. The test has high asymptotic efficiency and good power with respect to tests based on the normal distribution. Since the computational burden is minimal, approximation of the permutation distribution is unnecessary.

Keywords:

• Distribution free methods
• Longitudinal data
• Multivariate linear rank statistics
• Split plot design