Here is one easy way to improve everyday Bayesian reasoning: use natural frequencies instead of probabilities. Consider two ways of communicating a situation:
Probability format
1% of women have breast cancer
If a woman has breast cancer, there’s an 70% chance the mammogram is positive
If a woman does not have breast cancer, there’s a 10% chance the mammogram is positive.
Natural frequency format
Out of 1,000 women, 10 have breast cancer
Of those 10 who have cancer, 7 test positive
Of the 990 without cancer, 99 test positive
For each of the two formats above, ask this question to a group of people: “A woman tests positive. What is the probability she has cancer?”. Which do you think gives better results?
References
Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: frequency formats. Psychological review, 102(4), 684.
Hoffrage, U., Lindsey, S., Hertwig, R., & Gigerenzer, G. (2000). Communicating statistical information. Science, 290(5500), 2261-2262.
Hoffrage, U., Gigerenzer, G., Krauss, S., & Martignon, L. (2002). Representation facilitates reasoning: What natural frequencies are and what they are not. Cognition, 84(3), 343-352.
Here is one easy way to improve everyday Bayesian reasoning: use natural frequencies instead of probabilities. Consider two ways of communicating a situation:
Probability format
1% of women have breast cancer
If a woman has breast cancer, there’s an 70% chance the mammogram is positive
If a woman does not have breast cancer, there’s a 10% chance the mammogram is positive.
Natural frequency format
Out of 1,000 women, 10 have breast cancer
Of those 10 who have cancer, 7 test positive
Of the 990 without cancer, 99 test positive
For each of the two formats above, ask this question to a group of people: “A woman tests positive. What is the probability she has cancer?”. Which do you think gives better results?
References
Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: frequency formats. Psychological review, 102(4), 684.
Hoffrage, U., Lindsey, S., Hertwig, R., & Gigerenzer, G. (2000). Communicating statistical information. Science, 290(5500), 2261-2262.
Hoffrage, U., Gigerenzer, G., Krauss, S., & Martignon, L. (2002). Representation facilitates reasoning: What natural frequencies are and what they are not. Cognition, 84(3), 343-352.