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Contents11 Association Between Introduction .. Measure of Association .. Chapter Summary .. Chi square Based Measures .. Phi .. Contingency coefficient .. Cramer s V .. Summary of Chi square Based Measures .. Reduction in Error Measures .. 786766 Chapter 11 Association IntroductionIn previous chapters, much of the discussion concerned a single variable,describing a distribution, calculating summary statistics, obtaining intervalestimates for parameters and testing hypotheses concerning these parame-ters. Statistics that describe or make inferences about a single distributionare referred to asunivariate statistics. While univariate statistics formthe basis for many other types of statistics, none of the issues concerningrelationships among variables can be answered by examining only a singlevariable. In order to examine relationships among variables, it is neces-sary to move to at least the level ofbivariate statistics, examining twovariables. Frequently the researcher wishes to move beyond this tomul-tivariate statistics, where the relationships among several variables aresimultaneously classification tables, used to determine independence and depen-dence for events and for variables, are one type of bivariate statistics.

Table 11.1 gives the chi square test for independence for the weak rela-tionship between sex and opinion, originally given in Table 6.9. The flrst entry in each cell of the table is the count, or observed number of cases. The number in brackets in each cell of the table is the expected number of

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