I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in 100. And your client has a “dirty” (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given— say 99 in 100—are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false. T D = event that the test result is dirty T C = event that the test result is clean D = event that the person tested is actually dirty C = event that the person tested is actually clean P(T D|D) = 0.99 P(C) = 0.99 P(T D|C) = 0.01 P(D) = 0.01 What is the probability of a random test resulting in dirty? What is the probability of person being clean given that their test re- sult is dirty? Is this consistent with the quote given?
In an article that appears on the website of the American Statistical Asso-
ciation (www.amstat.org/meetings/jsm/2000 /usei/gunn.pdf, retrieved April 25, 2017),
Carlton Gunn, a public defender in Seattle, Washington, wrote about how he uses statis-
tics in his work as an attorney. He states:
I personally have used statistics in trying to challenge the reliability of drug
testing results. Suppose the chance of a mistake in the taking and processing
of a urine sample for a drug test is just 1 in 100. And your client has a “dirty”
(i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not
necessarily. If the vast majority of all tests given— say 99 in 100—are truly
clean, then you get one false dirty and one true dirty in every 100 tests, so
that half of the dirty tests are false.
T D =
T C = event that the test result is clean
D = event that the person tested is actually dirty
C = event that the person tested is actually clean
P(T D|D) = 0.99 P(C) = 0.99
P(T D|C) = 0.01 P(D) = 0.01
What is the
What is the probability of person being clean given that their test re-
sult is dirty? Is this consistent with the quote given?
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