Compliance Checks The Probable Implications of Probability

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Compliance ChecksThe 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

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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?

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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

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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

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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

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Probability Clerk Will Check ID for All Mystery
Shop Inspections
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Probability Clerk Will NOT Check ID forat Least
One Mystery Shop Inspection
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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.

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Do the Math

• Lets do 10 mystery shop inspections
• Retailers compliance rate 90
• Probability of at least one MS inspection showing
  non-compliance 65!
• Retailers compliance rate 95
• Probability of at least one MS inspection showing
  non-compliance 40!

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Conclusion

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

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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

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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?

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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?