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Section 3E How Numbers Deceive: Polygraphs, Mammograms and More

Section 3E How Numbers Deceive: Polygraphs, Mammograms and More. Pages 199-212. 3-E. Ex1/200- Who Played Better?. Shaq has higher shooting percentages than Vince in both the first half and second half of the game. So, Shaq had the “better” game.

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Section 3E How Numbers Deceive: Polygraphs, Mammograms and More

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  1. Section 3EHow Numbers Deceive: Polygraphs, Mammograms and More Pages 199-212

  2. 3-E Ex1/200- Who Played Better? Shaq has higher shooting percentages than Vince in both the first half and second half of the game. So, Shaq had the “better” game. BUT, Vince has a higher shooting percentage than Shaq for the entire game. So, Vince had the “better” game. Shaq: 7/14 = .5 = 50% Vince: 8/14 = .57 = 57%

  3. 3-E Simpson’s Paradox Simpson’s Paradox(pg 200) occurs when something appears better in each of two or more comparison groups, but is actually worse overall. It occurs because the numbers/counts in each comparison group are so unequal. Abuse of Percentages: Don’t average percentages!

  4. 3-E Simpson’s Paradox Pg201 University of California – BerkeleyGraduate Admissions, 1973Gender Discrimination?? Women were being discriminated against!

  5. 3-E The admission rates for women are actually higher than those for men in all but Departments C and E, and the rates were quite close in those departments. Women were admitted at a significantly lower rate overall BUT no individual department was guilty of this practice. WOW!

  6. 3-E About Mammograms (pg202) About 1 in 100 (1%) breast tumors turn out to be malignant. Mammograms are 85% accurate • identify 85% of malignant tumors as malignant. • misidentify 15% of malignant tumors as benign. False Negative • identify 85% of benign tumors as benign. • misidentify 15% of benign tumors as malignant. False Positive negative mammogram means no cancer – benign. positive mammogram means cancer – malignant.

  7. 3-E pg 202- When a doctor tells a woman that her mammogram is positive, what should he also tell her about her chances that she actually has cancer? Build a summary chart (based on percent of) for 10000 mammograms of women with breast tumors.

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  10. 3-E Use the summary chart to answer the question.

  11. 3-E pg 202- When a doctor tells a woman that her mammogram is positive, what should he also tell her about her chances that she actually has cancer? Of those women with positive mammograms, only 85 out of 1570 or 85/1570 = .054 = 5.4% actually have cancer.

  12. 3-E Ex3/203- When a doctor tells a woman that her mammogram is negative, what should he also tell her about her chances that she actually has cancer? Of those women with negative mammograms, 15 out of 8430 or 15 / 8430 = =.0018 = .18% actually have cancer(about 2 women in 1000.)

  13. 3-E About Polygraphs (pp 203-4) • Suppose 1% of job applicants lie. • Suppose a polygraph is 90% accurate • correctly identifies 90% of liars as liars- misidentifies 10% of liars as truth tellers • correctly identifies 90% of truth tellers as truth • tellers. • misidentifies 10% of truth tellers as liars. • positive polygraph means lying detected. • negative polygraph means no lying detected.

  14. 3-E (pp 203-4) Suppose 1000 applicants take the polygraph test. How many of those applicants who were accused of lying (and rejected for the job) actually told the truth? Build a summary chart (based on percent of) for 1000 applicants.

  15. 3-E Of those applicants that failed the polygraph, 99 out of 108 or 99/108 = .917 = 91.7% were actually telling the truth. [Of those applicants that passed the polygraph, 1 out of 892 or 1/892 = .0011 = .11% were actually lying.]

  16. 3-E Tree Diagram for Polygraphs So 99/108 = 91.7% of those who are accused of lying are not actually lying.

  17. 3-E About Drug Tests (ex4/204) • Suppose 4% of athletes take banned drugs. • Suppose a drug test is 95% accurate • correctly identifies 95% of drug uses as drug users.- misidentifies 5% of drug users as clean. • correctly identifies 95% of clean athletes as clean. • misidentifies 5% of clean athletes as drug users. • positive drug test means drugs detected. • negative drug test means no drugs detected.

  18. 3-E ex4/200 Suppose 1000 athletes at a regional high school track meet submit urine samples. What percentage of the athletes who fail the test are falsely suspended from the team? Build a summary chart (based on percent of) for 1000 athletes.

  19. 3-E Of those athletes that failed the drug test, 48 out of 86 or 48/86 = .56 = 56% were actually clean and falsely suspended. [Of those athletes that passed the drug test, 2 out of 914 or 2/914 = .0021 = .21% were drug users.]

  20. 3-E (ex5/206) A Cut or an Increase? Government spending for a popular education program was $100 million last year. When Congress prepares its budget for next year, spending for the program is slated to rise to $102 million. The Consumer Price Index is expected to rise by 3% over the next year. Is spending on this program being increased or cut? Absolute change: $102 million - $100 million = $2 million This is an increase in spending. Relative change: $2 million / $100 million = 2% This is a decrease in spending relative to the inflation rate (3%).

  21. 3-E Homework Pages 207-212 # 22, 25,27, 28, 30, 31

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