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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

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112

1960 1970 1980 1990 2000 2010

Time

Pre

sen

ted

Dat

a

Misleading Graphics

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106

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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?