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Numbers in the Real World
Copyright © 2011 Pearson Education, Inc.
Discussion then Paragraph of thoughts
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Web
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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
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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.
Unit 3E : How numbers can be deceiving
How Numbers Deceive:
Polygraphs,
Mammograms, and
More
Copyright © 2011 Pearson Education, Inc.
Slide 3-4
Treatment for Acne
CN (1)
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Notice the new treatment had a higher cure rate
both for patients with mild acne and for patients
with severe acne.
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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
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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.
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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
Simpson’s Paradox
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.
Copyright © 2011 Pearson Education, Inc.
Slide 3-7
3-E
Shaq, Vince, and Simpson’s Paradox
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%.
Copyright © 2011 Pearson Education, Inc.
Slide 3-8
3-E
Is it Discrimination?
CN (2)
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One famous case involved an investigation of
possible gender discrimination in graduate
programs at the University of California, Berkley.
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Examining graduate admissions for 1973, university
officials found that male applicants were being admitted
at a significantly higher rate than female applicants.
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Look closely at the data in Table 3.7 on p.185
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2. Would it be reasonable to conclude Dept. A
discriminates against men? Why or Why not?
Slide 3-9
Does Smoking Make you Live Longer?
CN (3)
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3-E
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
Test Results
true positive
A test correctly reports a
positive result
false positive
A test incorrectly reports a
positive result
true negative
A test correctly reports a
negative result
false negative
A test incorrectly reports a
negative result
Copyright © 2011 Pearson Education, Inc.
Slide 3-11
3-E
Does a Positive Mammogram Mean Cancer?
CN (4)
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4. Does tumors found in a mammogram mean the
patient has cancer?
Tumors – any kind of abnormal swelling or tissue
growth
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Malignant tumors – cancerous tumors
Benign tumors – non cancerous tumors
Mammograms – not perfect
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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
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.
Copyright © 2011 Pearson Education, Inc.
Slide 3-13
False Negatives
CN (5)
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3-E
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
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?
Copyright © 2011 Pearson Education, Inc.
Slide 3-15
3-E
Polygraphs and Drug Tests
CN (6)
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90% accurate polygraph test can lead to a
surprising number of false accusations.
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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
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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.
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Studies show that polygraphs are easily fooled by
people who train to beat them.
Copyright © 2011 Pearson Education, Inc.
Slide 3-17
3-E
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?
Slide 3-18
3-E
A Cut or an Increase
CN (8)
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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.
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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
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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-
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Chapter 3 Test Next Time
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Copyright © 2011 Pearson Education, Inc.
Slide 3-20