Lecture 18_chi-square

Lecture 18_chi-square - 11/29/2010 2 (Chi-Square) Test of...

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11/29/2010 1 χ 2 (Chi-Square) Test of Independence 1 2 χ 2 Test 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 means χ 2 Test Overview • The χ 2 is 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 categories 3
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11/29/2010 2 χ 2 Test 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) 4 χ 2 Test 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 5 χ 2 Test Overview • You examine observed frequencies in the data to see how many individuals fall in each category • The magnitude of the χ 2 test 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
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11/29/2010 3 Example χ 2 Research Questions • Are patterns of political affiliation the same across different geographical regions? • Is the percentage of heart attacks the same for those who take aspirin and those who do not? • Are rates of smoking cessation the same for people who use the patch vs. those who quit cold turkey? 7
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This note was uploaded on 02/17/2011 for the course PYSC 227 taught by Professor Fairchild during the Spring '10 term at South Carolina.

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Lecture 18_chi-square - 11/29/2010 2 (Chi-Square) Test of...

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