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Feb. 13

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

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Feb. 13

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

  2. 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

  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

  4. 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

  5. Total of programs A and B • Men: (400+50) / (650+350) = 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?

  6. 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

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

  8. Approximate Results by Gender

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

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

  11. 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.

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

  13. Expected Counts

  14. Expected Counts

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

  16. 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”

  17. In our example - • 13.2 is larger than 3.84 • CONCLUDE= there is a statistically significant relationship • So, we believe there is a relationship in the larger population

  18. 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

  19. 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

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