Nonparametric Multiple Comparisons in Repeated Measures Designs for Data with Ties

Abstract

We consider some multiple comparison problems in repeated measures designs for data with ties, particularly ordinal data; the methods are also applicable to continuous data, with or without ties. A unified asymptotic theory of rank tests of Brunner, Puri and Sen (1995) and Akritas and Brunner (1997) is utilized to derive large sample multiple comparison procedures (MCP's). First, we consider a single treatment and address the problem of comparing its time effects with respect to the baseline. Multiple sign tests and rank tests (and the corresponding simultaneous confidence intervals) are derived for this problem. Next, we consider two treatments and address the problem of testing for treatment × time interactions by comparing their time effects with respect to the baseline. Simulation studies are conducted to study the type I familywise error rates and powers of competing procedures under different distributional models. The data from a psychiatric study are analyzed using the above MCP's to answer the clinicians' questions.