Lecture 7 Odds, Odds Ratios and Risk STAT 3120 Statistical Methods I.

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Lecture 7 Odds, Odds Ratios and Risk STAT 3120 Statistical Methods I

STAT3120 – ODDS A few notes about odds… From the previous example, if we define “promotion” as “success” and “no promotion” as failure, then we can state the odds of success as: Probability of Success/Probability of Failure The overall probability of success was 25% and the overall probability of failure was 75%. So, the odds of success are.25/.75 or.33…the odds of failure are.75/.25 or 3.0

STAT3120 – ODDS Odds of.33 would indicate that success is 3 times less likely than failure…similarly, odds of 3.0 would indicate that failure is 3 times more likely than is success. The odds of promotion for women is.1250/.8750 =.1429…and the odds of non-promotion for women is 7.0…indicating that non-promotion for women is 7 times more likely. The odds of promotion for men is.333/.666 =.5 and the odds of non-promotion for men is 2.0…indicating that non- promotion for men is 2 times more likely.

STAT3120 – ODDS Odds Ratios are a measurement of association for 2x2 contingency tables that equals the odds in row 1 divided by the odds in row 2… So the odds ratio for promotion for men and women is.333/.1250 or 2.66 – meaning that the odds of men being promoted is about 2.66 times the odds of women being promoted.

STAT3120 – ODDS Another example… A 2003 National household study on drug abuse indicated that for Americans aged 26-34, 51% has used marijuana at least once in their lifetime and 18% had used cocaine at least once. Find the odds of having used marijuana. Find the odds of having used cocaine. Find the odds ratio comparing marijuana usage to cocaine usage.