11/29/20101χ2(Chi-Square) Test of Independence12χ2Test Overview•Up to this point, we have focused on statistical tests that examined mean differences among two or more groups on the value of an outcome variable•We used scores in the sample data to make the inferences about population means•Obviously, not all research questions involve continuous outcome measures and/or sample meansχ2Test Overview•The χ2is used to examine relationships between two categorical variables when the outcome variable is nominal•Recall that nominal variables only allow for qualitative classification--- i.e., they are measured in terms of whether the subjects belong to distinctively different categories3
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11/29/20102χ2Test Overview•More on nominal variables: –You do not quantify or rank order the categories of a nominal variable--- no one category is better/worse or higher/lower–You cannot say that a given individual has more or less of the quality represented by the variable–All you can say is that individuals are different in terms of the variable (e.g., two individuals are of different race or gender)4χ2Test Overview•With nominal (i.e., categorical) outcome variables, you test a null hypothesis that the frequency, or percentage, of people in each category is the same for two or more different groups•This is conceptually the same as an independent t-test or an ANOVA, except the dependent variable is nominal--- and thus evaluated in terms of frequencies 5χ2Test Overview•You examine observed frequencies in the data to see how many individuals fall in each category•The magnitude of the χ2test statistic reflects the amount of discrepancy between the observed frequencies you see and the frequencies that you would expect to see if the null hypothesis were true ( i.e. if the variables are not related to one another).6