How to Lie with Statistics (and Probability)

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# How to Lie with Statistics (and Probability) - PowerPoint PPT Presentation

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)

Bruce Schmeiser

Purdue University

IE230

April 29, 2011

Acknowledgments

Introduction

The Sample with the Built-in Bias

The Well-Chosen Average

The Little Figures That Are Not There

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

Biased Sampling

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

• Mean versus median versus mode
• Average Microsoft employee income

• Mean versus median versus mode
• Average Microsoft employee income
• Ill-defined experiment
• Average family income
• Average interstate speed

200 #

100 #

0 #

Men

Women

Changing Definitions

• High blood pressure
• Poverty level

Assume Equally Likely

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

Correlation Does Not Imply Causality

• South Seas Islands: Christianity and STDs

Correlation Does Not Imply Causality

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

Correlation Does Not Imply Causality

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

Implicit Assumptions

I pay you \$2X , where

X = “number of coin flips until head”

Then X = 1, 2, 3,… .

Implicit Assumptions

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

= ∞

Implicit Assumptions

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?