Power Curves and SAS Code to Aid in Selecting and Calculating Non-Parametric ANCOVA Procedures

• Activity Number: 321
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 12:00 PM to 1:50 PM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Robert Shull*+ and Paul Nakonezny
• Affiliation(s): Geisinger Health System and University of North Texas

Abstract

Empirically derived power curves and SAS routines are presented for non-parametric alternatives to the parametric ANCOVA F test. Alternative procedures are by (1) Quade (1967); (2) McSweeney-Porter (1971); (3) Burnett-Barr (1977); (4) Rogosa (1980); (5) Conover-Iman (1982); (6) Hettmansperger (1984); and (7) Puri-Sen-Harwell-Serlin (1985). Computer code for each technique is written in SAS version 8.1. A simulation, with 10,000 replications, determined null rejection rates for equal group sizes of 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 75, 90, 100. This study used a one-way fixed effects design, with three groups, one dependent variable, and one covariate (r =.3). Random normal (mean=0, std=1) sampling was created with the SAS RANNOR function. Location shifts were 1, 2, or 3 sigma units. Two general conditions were used: (a) violation of between-group homoscedasticity and (b) no violation of assumptions. Empirical Type I error rates were within Cochran's limits. The (2), (4), (5) and (7) techniques compared favorably in power to the parametric test. The (1) and (6) techniques' power was significantly lower for cell sizes less than 50. The (3) technique cannot be recommended