Inconsistencies with Nonparametric Procedures and Statistics: Combinatoric and Asymptotic Results

10/07/2008 - 12:15pm
10/07/2008 - 1:10pm
Anna E. Bargagliotti (University of Memphis)

Nonparametric statistical tests can be used to differentiate among alternatives. Each test is uniquely identified with a procedure that analyzes ranked data. Procedure results are then incorporated into a test statistic. Inconsistencies among tests occur at both the procedure level and the statistic level. In this talk, I will characterize symmetry structures of data that explain why different procedures can output different rankings when analyzing the same data. In addition, I will quantify the number of ways that two ranked data sets can be aggregated and define a strict condition data must satisfy in order to ensure consistent procedure results. Finally, I will discuss how procedure inconsistencies affect the test statistics. Using the Kruskal-Wallis test as an example, I will outline how to asymptotically find the probability with which the null is rejected.

ML 211