# part16 - Public Health 6450 Fall 2011 Lynn Eberly and Andy...

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Unformatted text preview: Public Health 6450 Fall 2011 Lynn Eberly and Andy Mugglin Division of Biostatistics School of Public Health University of Minnesota [email protected] Part 16 Review Chi-square tests for H : independence Chi-square tests for H : homogeneity of proportions Extending the Chi-Square Test to Larger Tables A warning about contingency tables Where are we going? Previously: I Two-by-two tables and study designs for comparing Binomial proportions (not in M&M) I Relative risks and odds ratios for comparing Binomial proportions (not in M&M) Current topics: I Chi-square test for H : independence in two-by-two tables (Ch. 9.1-9.2) I Chi-square test for H : p 1 = p 2 in two-by-two tables (Ch. 9.2) I Chi-square test for larger tables (Ch. 9.1-9.2) Next topic: I Chi-square test for paired sample two-by-two tables (not in M,M&C) Eberly and Mugglin PubH 6450 Fall 2011 Part 16 2 / 49 Review Chi-square tests for H : independence Chi-square tests for H : homogeneity of proportions Extending the Chi-Square Test to Larger Tables A warning about contingency tables Probabilities from a sample estimate the population probabilities Chi-square Test of Independence Detailed Example Cross-sectional two-by-two tables As we’ve seen, the data from a cross-sectional sample that is categorized by two binary variables can be summarized in a table: Variable 2 Variable 1 Yes No Total Yes a b a + b No c d c + d Total a + c b + d n Variable 1 might be ‘exposure’ and Variable 2 might be ‘disease’ but they don’t have to be. We will continue to work with tables like this, and with the probabilities that can be computed from tables like this. Eberly and Mugglin PubH 6450 Fall 2011 Part 16 3 / 49 Review Chi-square tests for H : independence Chi-square tests for H : homogeneity of proportions Extending the Chi-Square Test to Larger Tables A warning about contingency tables Probabilities from a sample estimate the population probabilities Chi-square Test of Independence Detailed Example Probabilities in a sample Consider this exposure by disease example, obtained from a cross-sectional survey done in 1979 of veterans who entered military service between 1965 and 1975. Sleep Problems Yes No Total Service in Yes 173 599 772 Vietnam No 160 851 1011 Total 333 1450 1783 Eberly and Mugglin PubH 6450 Fall 2011 Part 16 4 / 49 Review Chi-square tests for H : independence Chi-square tests for H : homogeneity of proportions Extending the Chi-Square Test to Larger Tables A warning about contingency tables Probabilities from a sample estimate the population probabilities Chi-square Test of Independence Detailed Example Probabilities in a sample: Joint We can convert those counts to the joint probabilities in the sample by dividing each cell by the total sample size: Sleep Problems Yes No Total Service in Yes 173 1783 = 0 . 097 599 1783 = 0 . 336 Vietnam No 160 1783 = 0 . 090 851 1783 = 0 . 477 Total 1783 1783 = 1 and we can see that the joint probabilities add up to 1. These joint probabilities are...
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part16 - Public Health 6450 Fall 2011 Lynn Eberly and Andy...

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