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HYPOTHESIS TESTING BETWEEN TWO OR MORE CATEGORICAL VARIABLES The Chi-Square Distribution and Test for Independence
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Agenda Wrapping up the t-test program example Chi-Square and Chi-Square test of independence 2
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Chi-Square Distribution 3 The chi-square distribution results when independent variables with standard normal distributions are squared and summed.
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Chi-square Degrees of freedom 4 df = (r-1) (c-1) Where r = # of rows, c = # of columns Thus, in any 2x2 contingency table, the degrees of freedom = 1. As the degrees of freedom increase, the distribution shifts to the right and the critical values of chi- square become larger.
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Chi-Square Test of Independence 5
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Using the Chi-Square Test 6 Often used with contingency tables (i.e., crosstabulations) E.g., gender x student The chi-square test of independence tests whether the columns are contingent on the rows in the table. In this case, the null hypothesis is that there is no relationship between row and column frequencies. H 0 : The 2 variables are independent.
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Requirements for Chi-Square test 7 Must be a random sample from population Data must be in raw frequencies Variables must be independent Categories for each I.V. must be mutually exclusive and exhaustive
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Example Crosstab: Gender x Student 8 StudentNot StudentTotal Males 46 (40.97) 71 (76.02) 117 Females 37 (42.03) 83 (77.97) 120 Total83154237 Observed Expected
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Special Cases Fisher’s Exact Test When you have a 2 x 2 table with expected frequencies less than 5. Strength of Association Some use Cramer’s V (for any two nominal variables) or Phi (for 2 x 2 tables) to give a value of association between the variables. 9
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Practical Examples: 10 chi2dist.do chisquare.do Auto.dta
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