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

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

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

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 do not publish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
Ultimately published:
*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) =

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. Maybe other vehicles with better odds
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