Analysis - Research / Commentary

What do medical test really tell us?

Statistics in Medicine - Last Update: Aug 20, 2022

Do doctors understand test results? What do medical test really tell us? Not much if you don't understand statistics and specifically Bayes Theorem. The following scenario was presented to hundreds of medical professionals in a series of statistical workshops.

1. Ten out of every 1,000 women have breast cancer ("1% Prior or Prevalence").

2. If a woman has breast cancer, the probability that she tests positive is 90% ("Sensitivity").

3. If a woman does not have breast cancer, the probability that she test negative is 91% ("Specificity")

"A 50-year-old woman, no symptoms, participates in routine mammography screening. She tests positive, is alarmed, and wants to know from you whether she has breast cancer for certain or what the chances are. Apart from the screening results, you know nothing else about this woman. How many women who test positive actually have breast cancer?"

The probability that the woman has cancer is 1/11 or approximately a 9% chance.


In a population of 1000 the Sensitivity rate of 90% translates to a "True Positive" of 9. A Specificity rate of 91% with this Sensitivity rate yields a "False Positive" of 89. Applying Bayes Theorem:


If you guessed 9/10 or 90% don't feel bad. In many of the seminars so did most of the doctors!

Adopted from: BBC World Service, "Do doctors understand test results?"

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