# Teaching how to construct natural frequency trees out of probability information

### What is the boost?

Knowing how to construct natural frequency trees out of probability information helps people successfully make Bayesian inferences (e.g., to understand what a positive test result really means).

The boost above involves four steps:

**Read the problem description represented in probabilities**.**Draw a natural frequency tree**. The root node (at the top) represents the total number of cases and is then broken down into four subclasses.**Fill in the numbers**. For convenience, set the root node to 100 patients. Insert the base-rate frequency in the “sepsis” node by calculating 10% of 100 patients (= 10). Fill in the “no sepsis” node by subtracting the patients with sepsis from the total number of patients (100 - 10 = 90). Divide the 10 patients in the sepsis node into 8 showing the symptoms (80%) and 2 not showing the symptoms (the remaining 20%). Divide the 90 patients in the “no sepsis” node into 9 showing the symptoms (90%) and 81 not showing the symptoms (the remaining 10%).**Calculate the posterior probability.**With all numbers filled in, the probability of sepsis given the presence of symptoms can be easily calculated: $8/(8 + 9) = .47$ or 47%.

### Which challenges does the boost tackle?

Risks that are communicated using opaque statistical representations based on conditional probabilities can be difficult to grasp (see the natural frequencies section).

### Which competences does the boost foster?

The ability to translate probability information into a natural frequency tree, then to apply Bayes’s rule to calculate a posterior probability.

### What is the evidence behind it?

Sedlmeier and Gigerenzer (2001) offered training in natural frequency trees. They compared it with training in conditional probability trees and rule-based training in Bayes’s rule. Although the immediate effect was strong for all training programs, only the training in natural frequency trees showed no decay over time: The immediate training effect of a median of 93% Bayesian solutions, compared to a median of 14% at baseline, remained stable over a period of 15 weeks.

### Key reference

Sedlmeier, P., & Gigerenzer, G. (2001). Teaching Bayesian reasoning in less than two hours. *Journal of Experimental Psychology: General, 130*(3), 380–400. https://doi.org/10.1037/0096-3445.130.3.380