Day 82 of 150 Logic Difficulty 5/10

Natural frequencies make Bayesian reasoning click

Quick answer

Natural frequencies make Bayesian reasoning click. Today's question (Bayesian reasoning with natural frequencies) asks about a finding from Gigerenzer, G., & Hoffrage, U. in 1995. The correct option is Natural frequencies (e.g., '8 out of 10 sick patients test positive; 95 out of 990 healthy ones also test positive') — full explanation, primary source, and glossary cross-links below.

Today's question

Gigerenzer and Hoffrage (1995) showed that doctors and laypeople made far better Bayesian inferences when test-result information was presented as:

  1. A Conditional probabilities (e.g., 'sensitivity is 80%, false-positive rate 10%')
  2. B Natural frequencies (e.g., '8 out of 10 sick patients test positive; 95 out of 990 healthy ones also test positive')
  3. C Odds ratios
  4. D Pure verbal descriptions, with no numbers
Reveal the answer and explanation

Correct: B — Natural frequencies (e.g., '8 out of 10 sick patients test positive; 95 out of 990 healthy ones also test positive')

Gigerenzer and Hoffrage (1995) showed that the notorious difficulty of Bayesian inference problems (e.g., 'given a positive mammogram, what is the probability of breast cancer?') largely vanishes when probabilities are reformatted as natural frequencies — counts of cases out of a reference population. With the same numerical content, accuracy on classic medical and legal Bayesian problems jumped from roughly 16% to 46% in their experiments. They argued evolution adapted human reasoning to count-like ecological data; modern probability formats translate poorly. The result has reshaped medical statistics teaching and risk communication.

About the source

Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102(4), 684–704.

Every Cognition Bible question cites a primary source — a paper, book chapter, or monograph that exists, that we can point to on Google Scholar, and whose finding the question accurately summarizes. No fabricated authority strings, no name-drops without paper-level grounding.

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