A Nonparametric Fitted Test for the Behrens-Fisher Problem

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Paul Lupinacci*+ and Terry Hyslop
• Affiliation(s): Villanova University and Thomas Jefferson University
• Keywords: nonparametric ; Behrens-Fisher ;

Abstract

The comparison of the means of two independent populations has been traditionally approached with Students' t-test. When the usual homogeneity of variances assumption is not reasonable, the problem has been called the Behrens-Fisher problem. Our work extends the nonparametric work of Fligner and Policello. They proposed a test based on placements--i.e., the number of observations in the second sample that are smaller than the ith observation in the first sample. Their nonparametric approach gives rise to a large table of critical values based on the number of observations in each sample and the level of significance. We expand on their approach by proposing a fitted test that eliminates the need for these tables. We fit a function to the critical values in their table so that the critical values can be estimated. Simulation studies are used to compare our fitted test to the Fligner and Policello test and to other parametric and nonparametric tests that have been proposed for the Behrens-Fisher problem. These simulation studies compare the various tests on the basis of power and Type I error rate under varying sample sizes, variances, and population distributions.