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Lecture 10

ADM2304 Lecture 10: 10

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Tony Quon

BadDebt > Could be displayed as a twoway table: YesNo Row Total Marital Statuse102 20262128 Unmarried 31 11072 Col. T133 30673200 e.g, Marginal Percentages: Row Percentages: Of married couples, what had bad debts? = (1022128)100 = 4.79 Of unmarried couples, what had bad debts? = (311072)100 = 2.89 Column Percentages: Of bad debts, what were from married couples? = (102133)100 = 76.7 Of good debts, what were from married couples? = (20263067)100 = 66.1 Contingency Table (or Twoway Table, Cross tabulation, Crosstab): SES (SocioEconomic Status) Oij High Middle Low Current 51 22 43 116 Smoking Former 92 21 28 141 Status Never 68 9 22 99 211 52 93 356 How do we determine whether this table gives reason to believe that there is a relationship between the row variable and the column variable? Method: > Assume that there is no relationship between row and column and compare the observed frequencies with what one would expect IF the two variables were independent > H0: Row and column variables are independent Key idea: IF you have independence between the row and column variables then: > Pr(in ith row and jth column) = Pr(in ith row)Pr(in jth col) > Pr(SES = Low SS = Current) = Pr(SES = Low)Pr(SS = Current) Expected Counts R C j Pr(ith row)Pr( jthcol) = i n n
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