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How to Lie with Statistics (and Probability). Bruce Schmeiser Purdue University. IE230 April 29, 2011. Fifty-Year-Old Reference. “This book is sort of a primer in ways to use statistics to deceive.”. Acknowledgments Introduction The Sample with the Built-in Bias The Well-Chosen Average

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How to Lie with Statistics (and Probability)


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how to lie with statistics and probability

How to Lie with Statistics(and Probability)

Bruce Schmeiser

Purdue University

IE230

April 29, 2011

this book is sort of a primer in ways to use statistics to deceive
“This book is sort of a primerin ways to use statistics to deceive.”

Acknowledgments

Introduction

The Sample with the Built-in Bias

The Well-Chosen Average

The Little Figures That Are Not There

Much Ado about Practically Nothing

The Gee-Whiz Graph

The One-Dimensional Picture

The Semi-attached Figure

Post Hoc Rides Again

How to Statisticulate

How to Talk Back to a Statistic

slide4

Biased Sampling

  • 1948 Presidential election
  • 4 out of 5 dentists recommend Crest
  • Letters of recommendation
  • Purdue course evaluations
    • www.ratemyprofessors.com
slide5

Confusion about Averages

  • Mean versus median versus mode
    • Average Microsoft employee income
    • Average HBS graduating income
slide6

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
slide9

Misleading Figures

200 #

100 #

0 #

Men

Women

slide10

Changing Definitions

  • High blood pressure
  • Poverty level
slide11

Assume Equally Likely

  • Monte Hall
  • Lottery design
  • Slot machines
  • Dice: P(D1 + D2 = 3)= P(D1 + D2 = 7)
slide12

Correlation Does Not Imply Causality

  • South Seas Islands: Christianity and STDs
slide13

Correlation Does Not Imply Causality

  • South Seas Islands: Christianity and STDs
  • Good attitude and long life
slide14

Correlation Does Not Imply Causality

  • South Seas Islands: Christianity and STDs
  • Good attitude and long life
  • Hours of sleep and weight
slide15

Implicit Assumptions

St. Petersburg Paradox

I pay you $2X , where

X = “number of coin flips until head”

Then X = 1, 2, 3,… .

slide16

Implicit Assumptions

St. Petersburg Paradox

I pay you $2X , where

X = “number of coin flips until head”

Then X = 1, 2, 3,… .

Result:

E( $2X ) = Σ∞x=1 2xP( X = x )

= Σ∞x=1 2x( ½ ) x

= Σ∞x=1 1

= ∞

slide17

Implicit Assumptions

St. Petersburg Paradox

I pay you $2X , where

X = “number of coin flips until head”

Then X = 1, 2, 3,… .

Result:

E( $2X ) = Σ∞x=1 2xP( X = x )

= Σ∞x=1 2x( ½ ) x

= Σ∞x=1 1

= ∞

Why won’t you pay $10?