Everyday Benefits of Understanding Variability

Larry Weldon

Statistics and Actuarial Science

Simon Fraser University

Canada

Missed Opportunity ?

Formal Inference H0

p-value, …

Informal Application Of Statistical Thinking

Stats TeachersAnd Consultants

Students and Consultees

General Public

Formal Inference H0

p-value, …

Usefulness of Informal StatsExamples from …

• Sports• Investment• Peer Review• Health• Lotteries

Need for Communication without Math

Ordinary Language & Graphs

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!

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 …

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 …

Trends that do not persist

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.

START = 100

Mutual Fund Advice?

Don’t expect past relative performance to be a good indicator of future relative performance.

Investment – variability vs risk

• Risk - probability of loss

Versus

• Risk - variability of returns

Equities WinWith Prob = .97Bonds “risky”!

Investment Mix Advice?

• Depends on time horizon

• Not only tolerance for variability

• Long term - 100% equities

• Short term - mix equities & bonds

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 do not publish

Beta(2,2)

Beta(3,12)

6

13

6

Ultimately published:

6 + .20*13 (approx)

=9 papers out of 100

16 others just as good!

Peer Review Flawed

• Does select good papers but

• Is unfair in this selection …

• Similar property of school admission systems, competition review boards, etc.

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”!

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

How small is .0000007?

• Buy 100 tickets every week for 60 years

• Cost is $312,000.

• Chance of winning jackpot is = ….

2 percent!

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

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