PSLS.PPT.Ch22

# PSLS.PPT.Ch22 - Chisquaretestfor twowaytables PSLS chapter...

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Chi square test for  two-way tables PSLS chapter 22 © 2009 W.H. Freeman and Company

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Objectives (PSLS chapter 22) The chi-square test for two-way tables Two-way tables Conditions for the chi square test Hypotheses Expected counts for two-way tables Chi-square test for two-way tables of fit Simpson’s paradox
400 1380 416 1823 188 1168 An experiment has a two-way, or block, design if two categorical factors are studied with several levels of each factor. Two-way tables organize data about two categorical variables with any number of levels/treatments obtained from a two-way, or block, design. ( There are now two ways to group the data. ) Two-way tables    First factor: Parent smoking status Second factor: Student smoking status High school students were asked whether they smoke, and whether their parents smoke:

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Does parental smoking influence the smoking habits of their high school children? Conditional distribution for student smoking for different parental smoking status: P(student smokes | both parent) = 400/1780 = 22.5% P(student smokes | one parent) = 18.6% P(student smokes | neither parent) = 13.9% 400 1380 416 1823 188 1168 Marginal distribution for parental smoking: P(both parent) = 1780/5375 = 33.1% P(one parent) = 41.7% P(neither parent) = 25.2%
The marginal distributions summarize each categorical variable independently. But the 2-way table actually describes the relationship between both categorical variables. The cells of a 2-way table represent the intersection of a given level of one categorical factor with a given level of the other categorical factor ( conditional probabilities ). The chi-square test can also test the

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## PSLS.PPT.Ch22 - Chisquaretestfor twowaytables PSLS chapter...

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