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Everyday Benefits of Understanding Variability

Everyday Benefits of Understanding Variability. Larry Weldon Statistics and Actuarial Science Simon Fraser University Canada. Missed Opportunity ?. Informal Application Of Statistical Thinking. Formal Inference   H 0 p-value, …. Stats Teachers And Consultants. Formal

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Everyday Benefits of Understanding Variability

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

  2. Missed Opportunity ? Informal Application Of Statistical Thinking • Formal • Inference •   H0 p-value, …

  3. Stats Teachers And Consultants • Formal • Inference •   H0 p-value, … Students and Consultees General Public

  4. Usefulness of Informal StatsExamples 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

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