With a 99 per cent accuracy, it seems reasonable to think only one per cent of employees will be wrongly accused of doing drugs. Not so, because of a little thing called the base rate: If 10 per cent of workers are actually on drugs (the base rate), a test 99 per cent accurate will falsely accuse people eight per cent of the time, not one per cent. That means almost one out of every 10 people testing positive will be innocent.
How does that work? Here’s the math. Assume we test 1,000 people. Of these, 100 are intoxicated (10 per cent base rate) and our test will identify 99 of them. Nine hundred are not intoxicated but the one per cent error rate in the test means nine of them will be falsely identified as intoxicated. So in all, 108 people will test positive for drugs, of which nine (or 8.3 per cent) are innocent.
It takes a minute to grasp the math but it is worth the effort. Then, as the article continues, imagine what happens when the tests aren't 99% accurate, but more like 38-68% and then add in gaming of the tests (psst... can I borrow some urine?). Suddenly the potential impact false positives takes on more urgency and the concerns of labour groups is more understandable. Not only do these tests not reduce the incidence of workplace injury, but they raise a significant spectre of false accusations. Makes you wonder what is behind this whole endeavour.
For those keen to learn more, an interesting (albeit older) article on this topic is "Predictive probabilities in employee drug testing".
-- Bob Barnetson