Copyright © 2011 Pearson Education, Inc. Numbers in the Real World

Discussion then Paragraph of thoughts Web Consumer Price Index, find latest news release PPI Read recent overview and news releases CCI Find recent news, what does it measure Human Development Index, find most recent copy of this report Find arguments on both sides of question, whether the CPI overstates inflation. World CPI – find a recent news report that includes a reference Index numbers – find a recent news report that includes and index number other than CPI Accurate CPI – find a news story that talks about some long-term economic change that is tied to inflation. Copyright © 2011 Pearson Education, Inc.

Slide 3-4 Unit 3E : How numbers can be deceiving How Numbers Deceive: Polygraphs, Mammograms, and More

Treatment for Acne CN (1) Notice the new treatment had a higher cure rate both for patients with mild acne and for patients with severe acne. 1. Is it fair for the company to claim that its new treatment is better than the old treatment? Copyright © 2011 Pearson Education, Inc. Slide 3-5

Overall the old treatment had the higher cure rate, despite the fact that the new treatment had a higher rate for both mild and severe acne cases. This example illustrates that it is possible for a set of data to give different results in each of several groups than it does when the groups are taken together. Copyright © 2011 Pearson Education, Inc. Slide 3-6

3-E Copyright © 2011 Pearson Education, Inc. Slide 3-7 It is possible for a set of data to give different results in each of several groups than it does when the groups are taken together. If you look carefully, you’ll see that it occurs because of the way in which the overall results were divided into unequally sized groups. Simpson’s Paradox

3-E Copyright © 2011 Pearson Education, Inc. Slide 3-8 Since Shaq has the better shooting percentages in both the first half and second half of the game, can he claim that he has the better game compared to Vince? No. Vince’s overall shooting percentage is 8/14 = 57.1%, while Shaq’s is 7/14 = 50%. Shaq, Vince, and Simpson’s Paradox

3-E Is it Discrimination? CN (2) One famous case involved an investigation of possible gender discrimination in graduate programs at the University of California, Berkley. Examining graduate admissions for 1973, university officials found that male applicants were being admitted at a significantly higher rate than female applicants. Look closely at the data in Table 3.7 on p Would it be reasonable to conclude Dept. A discriminates against men? Why or Why not? Slide 3-9

3-E Does Smoking Make you Live Longer? CN (3) Early 1970’s medical study in England Among smoking adults 24% died in 20 years Among non smoking adults 31 died in 20 years 3. Do these results suggest that smoking can make you live longer? Copyright © 2011 Pearson Education, Inc. Slide 3-10

3-E Copyright © 2011 Pearson Education, Inc. Slide 3-11 Test Results true positive false positive true negative false negative A test correctly reports a positive result A test incorrectly reports a positive result A test correctly reports a negative result A test incorrectly reports a negative result

3-E Does a Positive Mammogram Mean Cancer? CN (4) 4. Does tumors found in a mammogram mean the patient has cancer? Tumors – any kind of abnormal swelling or tissue growth Malignant tumors – cancerous tumors Benign tumors – non cancerous tumors Mammograms – not perfect Positive result does not necessarily mean breast cancer. Careful analysis shows that a patients chance is still only about 5%. Copyright © 2011 Pearson Education, Inc. Slide 3-12

3-E Copyright © 2011 Pearson Education, Inc. Slide 3-13 Mammograms Suppose that 10,000 women with breast tumors are given mammograms, 1% of whom have malignant tumors. The other 99% have benign tumors. If the mammogram is 85% accurate, how many of the women whose results show a malignant tumor actually have a benign tumor? The test results indicated that 1570 women have malignant tumors, but 1485 of these women actually have benign tumors.

3-E False Negatives CN (5) Suppose you are a doctor seeing a patient with a breast tumor. Her mammogram comes back negative. 5. Based on the numbers in the previous table, what is the chance that she has cancer? Copyright © 2011 Pearson Education, Inc. Slide 3-14

3-E Copyright © 2011 Pearson Education, Inc. Slide 3-15 Polygraphs Suppose that 1000 people take the polygraph test, 10 of whom lie, and the polygraph is 90% accurate. How many of those applicants who were accused of lying were actually telling the truth?

3-E Polygraphs and Drug Tests CN (6) 90% accurate polygraph test can lead to a surprising number of false accusations. Polygraph, often called a “lie detector,” measures a variety of bodily functions including heart rate, skin temperature, and blood pressure. Polygraph operators look for subtle changes in these functions that typically occur when people lie. Polygraph tests have never been allowed as evidence in criminal proceedings. 6. Why do you think they are not allowed? Slide 3-16

3-E Polygraphs 90% accuracy far to low for justice The percentage of people who are falsely accused in any real situation depends on both accuracy of the test and the proportion of people who are lying. Studies show that polygraphs are easily fooled by people who train to beat them. Copyright © 2011 Pearson Education, Inc. Slide 3-17

3-E Slide 3-18 Political Mathematics CN (7) Republicans: Tax cut would benefit all families and the middle class would receive slightly greater benefits. Democrats: Tax cut would send disproportionate benefits to the rich. 7. Which side is more fair?

3-E A Cut or an Increase CN (8) Government spending for a populare 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. Lobbyists immediately go into action. Those who support complain about tax cuts. Those who oppose complain it is being increased when it should be cut. 8. Is one side lying? Assume the CPI rises by 3%. Explain Copyright © 2011 Pearson Education, Inc. Slide 3-19

3-E Study for Chapter 3 3A: Absolute and relative change. Absolute and relative difference. 3B: Scientific notation, order of magnitude 3C: Significant digits, random/systematic error, absolute/relative error, accuracy/precision 3D: Index number, reference value, CPI, inflation 3E: Simpsons paradox/test results - F+, T+, F-, T- Chapter 3 Test Next Time Copyright © 2011 Pearson Education, Inc. Slide 3-20