Transcript Compliance Checks The Probable Implications of Probability

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 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 for
at Least One Mystery Shop Inspection
2 (1-p2) 3 (1-p3) 4 (1-p4) 5 (1-p5)
Number
of MS
1 (1-p)
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 noncompliance 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 noncompliance findings before harsher
sanctions (license suspension or
revocation) are applied?