The Independence Problem
The data in this chapter consist of a random sample from a bivariate population. Our basic interest here is in the statistical relationship between the two variables involved in the bivariate structure. In particular, we will discuss procedures for deciding whether or not these two variables are independent and, if not independent, for assessing both the type and degree of dependency that exists between them.
In Section 8.1, we present a distribution-free test for independence that is based on signs of appropriate products of differences. Section 8.2 presents an estimator of the measure of association defined by (8.2). Section 8.3 contains an asymptotically distribution-free confidence interval for . Section 8.4 uses Efron's bootstrap method to obtain a different asymptotically distribution-free confidence interval for . Section 8.5 presents a distribution-free test for independence based on ranks. Section 8.6 contains a distribution-free test of independence, which is consistent against a broader class of alternatives than those classes of alternatives that can be detected by the tests of Sections 8.1 and 8.5. Section 8.7 considers the ...