1 Risk and Odds Stat 100A/Sanchez UCLA, Department of Statistics (Ross 8th edition, p 101 and Ross 9th ed p.68 talk about odds) Example 1 Smoking and Divorce Risk Data on smoking habits and divorce history for the 1669 respondents who had ever been married. Among smokers, 49% have been divorced, 51% have not. Among nonsmokers, 32% have been divorced, 68% have not. The difference between row percents indicates a relationship. Example 2 Tattoos and Ear Pierces Responses from n = 565 men to two questions: 1. Do you have a tattoo? 2. How many total ear pierces do you have? Among men with no ear pierces, 43/424 = 10% have a tattoo. Among men with one ear pierce, 16/70 = 23% have a tattoo. Among men with two or more ear pierces, 26/71 = 37% have a tattoo. % with a tattoo as number of ear pierces => relationship Could examine column percents (see graph above) or overall percents too. Example 3 Gender and Reasons for Taking Care of Your Body 1997 poll (random-digit dialing) of 1218 southern CA residents. Question: What is the most important reason why you try to take care of your body? Is it mostly to be attractive to others, mostly to keep healthy, or mostly to help your self-confidence, or what? Percent distribution of responses shown for men and women. Pattern of responses is very similar. Response does not seem to be related to gender. 2. Risk, Relative Risk, Odds Ratio, and Increased Risk Number in category Total number in group Risk = Example: Within a group of 200 individuals, asthma affects 24 people. In this group the risk of asthma is 24/200 = 0.12 or 12%. Risk is a conditional probability. Risk in category 1 Risk in category 2 Relative Risk = Example: For those who drive under the influence of alcohol, the relative risk of an accident is 15. => The risk of an accident for those who drive under the influence is 15 times the risk for those who don’t drive under the influence. • Relative risk = 1 => two risks are the same. • Risk in denominator often the baseline risk.2 Relative Risk of divorce = = 1.53 Example 1 Smoking and Divorce Risk (cont) In this example, the risk of divorce for smokers is 1.53 times the risk of divorce for nonsmokers. • For smokers: risk of divorce = 238/485 = 0.491 or 49.1%. • For nonsmokers: risk of divorce = 374/1184 = 0.316 or 31.6%. 49% 32% Difference in risks Baseline risk Percent increase in risk Note: When risk is smaller than baseline risk, relative risk < 1 and the percent “increase” will actually be negative, so we say percent decrease in risk. = x 100% = (relative risk – 1) x 100% Relative Risk of divorce for smokers = 1.53 Example 1 Smoking and Divorce Risk (cont) The risk of divorce is 53% higher for smokers than it is for nonsmokers. Percent increase in risk of divorce for smokers = (1.53 – 1) x 100% = 53% Difference in risks Baseline risk = x 100% = x 100% = 53% (49 – 32) 32 Odds = Number in category 1 to Number in category 2 = (Number in category 1/Number in category 2) to 1 Example: Odds of getting a divorce to not getting a divorce for smokers are 238 to 247 or 0.96 to 1. Odds of getting a divorce to not getting a divorce for nonsmokers are 374 to 810 or 0.46 to 1. Odds Ratio = 0.96 / 0.46 = 2.1 => the odds of divorce for smokers are about double the odds for nonsmokers. Odds Ratio = (Odds for group 1) / (Odds for group 2) Example 4 Disaster in the Skies? Look at risk of controller error per flight: In 1998: 5.5 errors per million flights In 1997: 4.8 errors per million flights “Errors by air traffic controllers climbed from 746 in fiscal 1997 to 878 in fiscal 1998, an 18% increase.” USA Today Risk of error increased but the actual risk is very
View Full Document
Unlocking...