1. Everyday Benefits of Understanding Variability Larry Weldon Statistics and Actuarial Science Simon Fraser University Canada

2. Missed Opportunity ? Formal Inference    H 0 p-value, … Informal Application Of Statistical Thinking

3. Stats Teachers And Consultants Students and Consultees General Public Formal Inference    H 0 p-value, …

4. Usefulness of Informal Stats Examples from … Sports Investment Peer Review Health Lotteries Need for Communication without Math Ordinary Language & Graphs

5. Sport – the quality illusion Role of Luck in Game Outcomes Teams closely matched Short-run results mislead Illusion that winning team is “better” Bigger payoff when underdog wins Bet the underdog!

6. Sport – when variability is the key Golf: Describing difficulty of holes Par is not a good measure of difficulty Variability of strokes is better Nicklaus Comment (Clarke(2007)) Role of Luck …

7. Investment – Back-the-winner fallacy Mutual Funds - a way of diversifying a small investment Which mutual fund? Look at past performance? Experience from symmetric random walk …

8. Trends that do not persist

9. Random Walk with Slight Trend - best ones obvious? Funds tend to mimic market indexes Use 5-year performance to select ‘best’ Check relative performance of ‘best’ compared to rest. Assume simulated quality of fund used for past 5 yrs is used for next 5 yrs.

10. START = 100

11. Mutual Fund Advice? Don’t expect past relative performance to be a good indicator of future relative performance.

12. Investment – variability vs risk Risk - probability of loss Versus Risk - variability of returns

13. Equities Win With Prob =.97 Bonds “risky”!

14. Investment Mix Advice? Depends on time horizon Not only tolerance for variability Long term - 100% equities Short term - mix equities & bonds

15. Research – the randomness of peer review - study via simulation Average referees accept 20% of average quality papers Referees vary in accepting 10%-50% of average papers Two referees accepting a paper -> publish. Two referees disagreeing -> third ref Two referees rejecting -> do not publish

16. Beta(2,2) Beta(3,12)

17. 6 13 6 Ultimately published: 6 +.20*13 (approx) =9 papers out of 100 16 others just as good!

18. Peer Review Flawed Does select good papers but Is unfair in this selection … Similar property of school admission systems, competition review boards, etc.

19. Health – mimicking the natural environment Variability - often called “error” Is it always bad? Quirky example - Brewster (2005) Random variability of oxygen supply on respirator more viable than constant supply. Variability is “natural”!

20. Lotteries – expectation and hope Cash flow –Ticket proceeds in (100%) –Prize money out (50%) –Good causes (35%) –Administration and Sales (15%) 50 % $1.00 ticket worth 50 cents, on average Typical lottery P(jackpot) =.0000007

21. How small is.0000007? Buy 100 tickets every week for 60 years Cost is $312,000. Chance of winning jackpot is = …. 2 percent!

22. Other Negatives Inflation decreases value of jackpot relative to ticket value Jackpot may need to be shared by others with same numbers on ticket Positives? Fun to hope and dream? Maybe other vehicles with better odds

23. Overview Some real-life processes better understood with statistical knowledge Little known effects can be made understandable to general public Professional statisticians should convey these effects to the public Perhaps statistics better appreciated Thank you for listening