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h8 - Odds Ratios and Related Ideas

# h8 - Odds Ratios and Related Ideas - STAT 201 Handout 8...

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STAT 201 — Handout 8 Odds Ratios and Related Ideas Class Example We had a (fictitious) data set that summarized into the following contingency table : gender midterm performance good bad F 44 40 84 M 46 34 80 90 74 n = 164 Our goal was to see if gender ( explanatory or blocking variable) influences midterm performance ( response variable). We plotted a “bivariate” bar chart for the 4 bivariate categories of (F,G), (F,B), (M,G), and (M,B): Male Female Count good bad Q: Does the question show any relationship between the variables? We can study the preliminary statistics for this data set: 1. Within the Female block : % good = 44/84 = 52.4% % bad = 40/84 = 47.6% good-bad ratio = 52.4/47.6 (= 44/40) = 1.10 Thus, among females the “goods” are 1.10 times more prevalent than the “bads.” 2. Within the Male block : % good = 46/80 = 57.5% % bad = 34/80 = 42.5% good-bad ratio = 57.5/42.5 (= 46/34) = 1.35 Thus, among males, the “goods” are 1.35 times more prevalent than the “bads.”

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3. compare the good-bad ratios between blocks via odds ratio : odds ratio = female good-bad ratio male good-bad ratio = 1 . 10 1 . 35 = 0 . 81 Thus, the good-bad contrast among females is only 81% of that among males (i.e. the
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h8 - Odds Ratios and Related Ideas - STAT 201 Handout 8...

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