Feb. 13 Chapter 12, Try 1-9 Read Ch. 15 for next Monday No meeting Friday

Quiz from end of last time 40 of 100 men have high blood pressure 50 of 200 women have high blood pressure For men, risk of high b.p. = 40/100 =.40 Relative risk for men compared to women =.40 / (50/200) =.40 /.25 = 1.6 For women odds of high b.p. = 50 to 150, which could be reduced to 1 to 3

Simpson’s Paradox Nature of relationship is different for whole group than it is for each subgroup CAUSE – Confounding effect of a third variable

Graduate Admissions Example In graduate academic program A: –400 of 650 men applicants admitted (61.5%) –50 of 75 women applicants admitted (66.7%) In graduate academic program B: –50 of 350 men applicants admitted (14.3%) –125 of 425 women applicants admitted (29.4%) Women had higher acceptance rate in both programs

Total of programs A and B Men: (400+50) / ( ) = 450/1000 = 45% admitted Women: (50+125) / (75+425) = 175/500 = 35% admitted Overall, acceptance rate is higher for men even though women had higher acceptance in each program. What’s going on?

Confounding Program B is harder to get into Most women apply to program B Program A is easier to get into Most men apply to program A

Stat 200 survey question Have you ever driven under the influence of alcohol or drugs?

Approximate Results by Gender

A Research Question Is there a “statistically significant” relationship? Does the relationship observed in the sample also hold in the population?

Chi-Square Procedure A Chi-square test is used to analyze statistical significance.

The idea of Chi-Square Chi-square measures the difference between the observed counts and “expected counts” Expected counts = the counts that would occur if there were no relationship.

Properties of Expected Counts Same row and column totals as observed counts Row percentages are the same in each row.

Expected Counts

Chi-square Statistic Sum of (obs.-exp) 2 /exp where sum is over all cells. For our example, Chi-square=13.2

Chi-Square and Statistical Significance Guideline: A chi-square value is statistically significant if it is over 3.84 Why? – Values over 3.84 will occur less than 5% of the time “just by luck”

In our example is larger than 3.84 CONCLUDE= there is a statistically significant relationship So, we believe there is a relationship in the larger population

Example In Stat 200, students classified by handedness and gender. 56 of 545 (10.3%) of females are left- handed 43 of 355 (12.1%) of males left-handed. Not significant, Chi-square=0.741 So, apparently no relationship between handedness and gender

Example In Stat 200, students classified by whether they smoke cigarettes and whether they’ve smoked marijuana in last 6 months. 217 of 735 (29.5%) of non-smokers of cigs have smoked marijuana 109 of 160 cig smokers (68%) have smoked marijuana. Significant, Chi-square=84.5 ; So, there is a relationship between cig and marijuana smoking