The Skeptics' Guide to the Universe: How to Know What's Really Real in a World Increasingly Full of Fake

by Steven Novella

Here is the question: What is the predictive value of a positive mammogram in a forty-year-old woman, or what are the odds that she actually has breast cancer because her mammogram was positive? With a 90 percent specificity you might be tempted to say 90 percent, but that would be wrong. The real answer is 7.5 percent. This is because 99 out of 100 forty-year-old women do not have breast cancer, so with a 10 percent false-positive rate there will be about 10 women out of 100 who test positive but don’t have breast cancer. Only about 0.8 of the 1 in 100 women who have breast cancer will test positive. So, out of 100 women, 9.9 will test positive but be negative, and 0.8 will test positive and be positive. So if you are a forty-year-old woman and test positive, chances are much greater it’s a false positive (0.8 true positive / 10.7 total positive x 100 = 7.5%).