Compliance Checks The Probable Implications of Probability William DeJong, PhD Boston University School of Public Health Youth Alcohol Prevention Center Responsible Retailing Forum Responsible 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 = 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- (p 4 ) ... 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- (p 4 ) ... and so on

Probability: Clerk Will Check ID for All Mystery Shop Inspections Number of MS 1 (p)2 (p 2 )3 (p 3 )4 (p 4 )5 (p 5 ) p = p = p = p =

Probability: Clerk Will NOT Check ID for at Least One Mystery Shop Inspection Number of MS 1 (1-p)2 (1-p 2 )3 (1-p 3 )4 (1-p 4 )5 (1-p 5 ) p = p = p = p =

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?