EXAMPLE 4.15 False Positives in Job Drug Testing

Job applicants in both the public and the private sector are often finding that preemployment drug testing is a requirement. The Society for Human Resource Management found that 71% of larger organizations require drug testing of new job applicants and that 44% of these organizations randomly test hired employees.⁶ From an applicant's or employee's perspective, one primary concern with drug testing is a “false-positive” result, that is, an indication of drug use when the individual has indeed not used drugs. If a job applicant tests positive, some companies allow the applicant to pay for a retest. For existing employees, a positive result is sometimes followed up with a more sophisticated and expensive test. Beyond cost considerations, there are issues of defamation, wrongful discharge, and emotional distress.

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The enzyme multiplied immunoassay technique, or EMIT, applied to urine samples is one of the most common tests for illegal drugs because it is fast and inexpensive. Applied to people who are free of illegal drugs, EMIT has been reported to have false-positive rates ranging from 0.2% to 2.5%. If 150 employees are tested and all 150 are free of illegal drugs, what is the probability that at least one false positive will occur, assuming a 0.2% false positive rate?

It is reasonable to assume as part of the probability model that the test results for different individuals are independent. The probability that the test is positive for a single person is 0.2%, or 0.002, so the probability of a negative result is by the complement rule. The probability of at least one false-positive among the 150 people tested is, therefore,

The probability is greater than 1/4 that at least one of the 150 people will test positive for illegal drugs even though no one has taken such drugs.