Lecture 7Odds, Odds Ratios and

Risk

STAT 3120Statistical 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.