A Test of Independence in Two-Way Contingency Tables Based on Maximal Correlation
Maximal correlation has several desirable properties as a measure of dependence, including the fact that it vanishes if and only if the variables are independent. Except for a few special cases, it is hard to evaluate maximal correlation explicitly. In this dissertation, we focus on two-dimensional contingency tables and discuss a procedure for estimating maximal correlation, which we use for constructing a test of independence. For large samples, we present the asymptotic null distribution of the test statistic. For small samples or tables with sparseness, we use exact inferential methods, where we employ maximal correlation as the ordering criterion. We compare the maximal correlation test with other tests of independence by Monte Carlo simulations. When the underlying continuous variables are dependent but uncorrelated, we point out some cases for which the new test is more powerful.
School:Bowling Green State University
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:testing independence maximal correlation contingency tables
Date of Publication:01/01/2007