Women who participate in breast cancer screening from 50 to 69 live on average 12 more days. This is the best case scenario. Gerd has more such compelling numbers in his book, Calculated Risks. Gerd shares such numbers to launch a front on assault on the misunderstanding of risk. His key point is:

“Overcoming innumeracy is like completing a three-step program to statistical literacy. The first step is to **defeat the illusion of certainty**. The second step is to **learn about the actual risks of relevant events**and actions. The third step is to **communicate the risks in an understandable way and to draw inferences without falling prey to clouded thinking**.”

Gerd’s key contributions are on the third point. Gerd identifies three problems with risk communication:

- using relative risk than Numbers Needed to Treat (NNT) or absolute risk,
- Using single-event probabilities, and
- Using conditional probabilities than ‘natural frequencies.’

Gerd doesn’t explain what he means by natural frequencies in the book but some of his other work does. Here’s a clarifying example that illustrates how the same information can be given in two different ways, the second of which is in the form of natural frequencies:

“The probability that a woman of age 40 has breast cancer is about 1 percent. If she has breast cancer, the probability that she tests positive on a screening mammogram is 90 percent. If she does not have breast cancer, the probability that she nevertheless tests positive is 9 percent. What are the chances that a woman who tests positive actually has breast cancer?”

vs.

“Think of 100 women. One has breast cancer, and she will probably test positive. Of the 99 who do not have breast cancer, 9 will also test positive. Thus, a total of 10 women will test positive. How many of those who test positive actually have breast cancer?”

For those in a hurry, here are my notes on the book.

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