Compliance ChecksThe Probable Implications of Probability

William DeJong, PhD

Boston University School of Public Health

Youth Alcohol Prevention Center

Responsible Retailing ForumResponsible Retailing Research

April 19, 2006

Key Points

! Frequent non-compliance is a fact of life, even for retailers with relatively high rates of clerk compliance with the law!

? Given that, what is a reasonable standard of performance to which retailers can be held?

Probability for Event Sequences

• The probability that a sequence of events will occur is equal to the product of their individual probabilities

• Example: What is the probability of tossing a coin and getting “tails” twice?– 0.50 x 0.50 = 0.25 OR 1/2 x 1/2 = 1/4

• Example: What is the probability of tossing a coin and getting “tails” and then tossing a die and getting “6”?– 0.50 x 0.167 = 0.083 OR 1/2 x 1/6 = 1/12

Mystery Shops

Set p = probability that a clerk will check ID for an individual mystery shop

1- p = probability that a clerk will NOT check ID for an individual mystery shop

Sequence of Mystery Shops

Probability that a clerk will check ID for all of the mystery shops: 2 visits: p x p 3 visits: p x p x p 4 visits: 1- (p4) . . . and so on

Probability that a clerk will NOT check ID for at least one mystery shop: 2 visits: 1- (p x p) 3 visits: 1- (p x p x p) 4 visits: 1- (p4) . . . and so on

Probability: Clerk Will Check ID for All Mystery Shop Inspections

Number of MS

1 (p) 2 (p2) 3 (p3) 4 (p4) 5 (p5)

p = .60 .60 .36 .22 .13 .08

p = .80 .80 .64 .51 .41 .33

p = .90 .90 .81 .73 .66 .59

p = .95 .95 .90 .86 .81 .77

Probability: Clerk Will NOT Check ID forat Least One Mystery Shop Inspection

Number of MS

1 (1-p) 2 (1-p2) 3 (1-p3) 4 (1-p4) 5 (1-p5)

p = .60 .40 .64 .78 .87 .92

p = .80 .20 .36 .49 .59 .67

p = .90 .10 .19 .27 .34 .41

p = .95 .05 .10 .14 .19 .23

Reality Check

• With clerk compliance at 90%, then the probability of at least 1 out of 5 MS inspections showing non-compliance is .41.

• Imagine a community (Utopia) where every

alcohol retailer could bring the staff up to 90% compliance.

With 5 MS inspections each, 41% of the retailers would be found in violation of the law at least once.

Do the Math

Let’s do 10 mystery shop inspections:

• Retailer’s compliance rate = 90%– Probability of at least one MS inspection

showing non-compliance = 65%!

• Retailer’s compliance rate = 95%– Probability of at least one MS inspection

showing non-compliance = 40%!

Conclusion

Frequent non-compliance is a fact of life, even for retailers with high rates

of clerk compliance with the law

The Difficulty of Detecting Relatively Low Compliance Rates

• Compliance rate = 70%– Probability of detection

• 1 visit = 30%

• 2 visits = 51%

• Compliance rate = 80%– Probability of detection

• 1 visit = 20%

• 2 visits = 36%

Policy Implications• Fact: Even with near universal compliance,

there is a substantial probability of non-compliance over multiple inspections.

– What constitutes a “reasonable” response to a first offense?

Policy Implications

• Fact: The greater the number of MS inspections, the greater the probability of non-universal compliance.

– What is a reasonable number of MS inspections to conduct within a given time frame?

– What is a reasonable number of non-compliance findings before harsher sanctions (license suspension or revocation) are applied?