How to Lie with Statistics (and Probability)

1. How to Lie with Statistics(and Probability) Bruce Schmeiser Purdue University IE230 April 29, 2011

2. Fifty-Year-Old Reference

3. “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

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

5. Confusion about Averages • Mean versus median versus mode • Average Microsoft employee income • Average HBS graduating income

6. 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

7. Misleading Graphics

8. Misleading Graphics

9. Misleading Figures 200 # 100 # 0 # Men Women

10. Changing Definitions • High blood pressure • Poverty level

11. Assume Equally Likely • Monte Hall • Lottery design • Slot machines • Dice: P(D1 + D2 = 3)= P(D1 + D2 = 7)

12. Correlation Does Not Imply Causality • South Seas Islands: Christianity and STDs

13. Correlation Does Not Imply Causality • South Seas Islands: Christianity and STDs • Good attitude and long life

14. Correlation Does Not Imply Causality • South Seas Islands: Christianity and STDs • Good attitude and long life • Hours of sleep and weight

15. Implicit Assumptions St. Petersburg Paradox I pay you $2X , where X = “number of coin flips until head” Then X = 1, 2, 3,… . ∞

16. 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 = ∞ ∞

17. 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?