This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 462
Type: Topic Contributed
Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #306569
Title: Exact Distribution-Free Tests for Ordinal Data: Stochastic Inequalities and Kendall's Tau
Author(s): Karl H. Schlag*+
Companies: Universitat Pompeu Fabra
Address: Ramon Trias Fargas 25-27, Barcelona, 08005, Spain
Keywords: exact ; distribution-free ; nonparametric ; ordinal ; hypothesis testing
Abstract:

We show how to test a stochastic inequality based on two independent samples of ordinal data. The concern is whether outcomes generated by one r.v. tend to be larger than that of another. Given a sample of matched pairs of ordinal data, we show how to test whether two r.v.s are positively associated (as measured by Kendall's tau). The tests we derive are the first for these settings that are both exact and distribution-free. "Exact" means that the level of the test is formally proven for the given finite sample sizes without relying on asymptotic theory. The proof relies on constructing a more conservative but randomized test and then eliminating randomness by using a cutoff, formally applying the Markov inequality to bound type I and type II errors. Examples include comparing blood loss of two surgical methods and testing Engel's law.


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