Mull this one carefully. Say a mammogram is 90 percent accurate at spotting patients with breast cancer, and 93 percent accurate at spotting those without breast cancer. Breast cancer afflicts 0.8 percent of women tested. Your mammogram comes back positive. How likely is it that you have breast cancer?
Less than 10 percent, says “The Numbers Game” (Gotham), a chatty, brief, brightly informative and quite possibly essential book by a pair of blokish Brits (not statisticians or mathletes).
This number won’t be surprising to those who read that wonderful text Breaking the Law of Averages.
Read the whole book review here.
Pay especial attention to the examples at the end.
21%:An extra ounce of bacon a day increased the chance of colon cancer by this much in men, according to the American Institute of Cancer Research. While a huge percentage, it neglected to mention what that increase meant in raw numbers. Turns out, five men out of 100 get colorectal cancer in their lifetime. Bacon-eating increased it to six.