Applying Probability and Decision Errors to Health – from G. Gigerenzer et al (2007), PSPI,8:2, 53-96.
Basic Numeracy Assessment Scale
1. A person taking Drug A has a 1% chance of having an allergic reaction. If 1,000 people take Drug A,
how many would you expect to have an allergic reaction? ___ person(s) out of 1,000
2. A person taking Drug B has a 1 in 1,000 chance of an allergic reaction. What percent of people
taking Drug B will have an allergic reaction?
____%
3. Imagine that I flip a coin 1,000 times. What is your best guess about how many times the coin would
come up heads in 1,000 flips?
____ times out of 1,000
____________________________________________________________________________________
Health Example 1: Assume you conduct breast cancer screening using mammography in a certain
region. You know the following information about the women in this region:

The probability that a woman has breast cancer is 1% (prevalence)

If a woman has breast cancer, the probability that she tests positive is 90% (sensitivity)

If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9%
(false-positive rate)
A woman tests positive. She wants to know from you whether that means that she has breast cancer for
sure, or what the chances are. What is the best answer?
1. The probability that she has breast cancer is about 81%.
2. Out of 10 women with a positive mammogram, about 9 have breast cancer.
3. Out of 10 women with a positive mammogram, about 1 has breast cancer.
4. The probability that she has breast cancer is about 1%.
Example 2 Risk Reduction: Mammography screening reduces mortality from breast cancer by about 25%. Assume
that 1,000 women age 40 and over participate in mammography screening. How many fewer women are likely to die
of breast cancer?
a. 1 [66%]
b. 25 [16%]
c. 100 [3%]
d. 250 [15%]
___________________________________________________________________________________
Applying Probability and Decision Errors to Health – from G. Gigerenzer et al (2007), PSPI,8:2, 53-96.
Percentage of Physicians Answering Basic Numeracy Questions Correctly (From Schwartz & Woloshin, 2000)
Question Physicians at Grand Rounds n= 585
Convert 1% to 10 in 1,000
Convert 1 in 1,000 to 0.1%
How many heads in 1,000 coin flips?
91%
75%
100%
Volume 8—
Fig. 7. What does a 25% relative risk reduction mean? A representative sample of 1,000 German
citizens was asked: “Early detection with mammography reduces the risk of dying from breast
cancer by 25%.
Gigerenzer G et al. Psychological Science in the Public
Interest 2007;8:53-96
Copyright © by Association for Psychological Science