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The Chi-Squared Test

The Chi-Squared Test. The Chi-Squared test is a general/broad test that is often used to test whether or not two variables are dependent on each other. One of the the two variables is a row in a table the other variable is a column in a table. The entire table is called a contingency table.

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The Chi-Squared Test

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  1. The Chi-Squared Test The Chi-Squared test is a general/broad test that is often used to test whether or not two variables are dependent on each other. One of the the two variables is a row in a table the other variable is a column in a table. The entire table is called a contingency table. Chi-Squared tests take the general form below: • Chi-Squared tests can be used to address the following questions: • Do observed frequencies differ from expectations? • Are proportions in groups significantly different from each other? • Are categories independent of one another or is there a relationship/dependence? Example: A 5 row contingency table, df=(r-1) OPMA 3306 has been a required course at UTA for over 20 years, historical distribution of grades for this class has been; 5% A’s, 25% B’s, 40% C’s, 25% D’s, and 5% F’s. Weltman’s most recent OPMA 3306 class results from 150 students were 11 A’s, 32 B’s, 62 C’s, 29 D’s, and 16 F’s. Are Weltman’s class grades significantly different from the overall OPMA sections? Interpret results of Weltman’s last OPMA class with respect to the overall OPMA sections. 14.07 = chi-sq*, Reject H0. with at least 95% confidence, Weltman’s recent grade distributions are different from prior historical OPMA distribution of grades. Additionally, in Weltman’s recent section, more students had F’s than in prior OPMA classes overall. 9.488 = CV

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  3. Example: A (2 X 3) contingency table, df=(r-1)(c-1) Is there a relationship/dependence between income group and political candidate support? Source gallup.com poll publlished 6/4/2012

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