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How to Lie with Statistics(and Probability)
Bruce SchmeiserPurdue University
IE230April 29, 2011
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Fifty-Year-Old Reference
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“This book is sort of a primerin ways to use statistics to deceive.”
AcknowledgmentsIntroduction
The Sample with the Built-in BiasThe Well-Chosen AverageThe Little Figures That Are Not ThereMuch Ado about Practically NothingThe Gee-Whiz GraphThe One-Dimensional PictureThe Semi-attached FigurePost Hoc Rides AgainHow to StatisticulateHow to Talk Back to a Statistic
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Biased Sampling
•1948 Presidential election•4 out of 5 dentists recommend Crest•Letters of recommendation•Purdue course evaluations
www.ratemyprofessors.com
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Confusion about Averages
•Mean versus median versus mode•Average Microsoft employee income•Average HBS graduating income
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Confusion about Averages
•Mean versus median versus mode•Average Microsoft employee income•Average HBS graduating income
•Ill-defined experiment•Average family income•Average interstate speed•Inspection paradox
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106
107
108
109
110
111
112
1960 1970 1980 1990 2000 2010
Time
Pre
sen
ted
Dat
a
Misleading Graphics
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106
107
108
109
110
111
112
1960 1970 1980 1990 2000 2010
Time
Pre
sen
ted
Dat
a
Misleading Graphics
0
20
40
60
80
100
120
1960 1970 1980 1990 2000 2010
Time
Pre
sen
ted
Dat
a
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Misleading Figures
0 #
100 #
200 #
Men Women
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Changing Definitions
•High blood pressure•Poverty level
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Assume Equally Likely
•Monte Hall•Lottery design•Slot machines•Dice: P(D1 + D2 = 3) = P(D1 + D2 = 7)
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Correlation Does Not Imply Causality
•South Seas Islands: Christianity and STDs
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Correlation Does Not Imply Causality
•South Seas Islands: Christianity and STDs•Good attitude and long life
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Correlation Does Not Imply Causality
•South Seas Islands: Christianity and STDs•Good attitude and long life •Hours of sleep and weight
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Implicit Assumptions
St. Petersburg ParadoxI pay you $2X , where
X = “number of coin flips until head”Then X = 1, 2, 3,… .
∞
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Implicit Assumptions
St. Petersburg ParadoxI pay you $2X , where
X = “number of coin flips until head”Then X = 1, 2, 3,… .Result:
E( $2X ) = Σ∞
x=1 2x P( X = x )
= Σ∞
x=1 2x ( ½ ) x
= Σ∞
x=1 1
= ∞
∞
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Implicit Assumptions
St. Petersburg ParadoxI pay you $2X , where
X = “number of coin flips until head”Then X = 1, 2, 3,… .Result:
E( $2X ) = Σ∞
x=1 2x P( X = x )
= Σ∞
x=1 2x ( ½ ) x
= Σ∞
x=1 1
= ∞
∞
Why won’t you pay
$10?