## Numeracy, frequency, and Bayesian reasoning

Keith points me to this article by Gretchen Chapman and Jingjing Liu:

Previous research has demonstrated that Bayesian reasoning performance is improved if uncertainty information is presented as natural frequencies rather than single-event probabilities. A questionnaire study of 342 college students replicated this effect but also found that the performance-boosting benefits of the natural frequency presentation occurred primarily for participants who scored high in numeracy. This finding suggests that even comprehension and manipulation of natural frequencies requires a certain threshold of numeracy abilities, and that the beneficial effects of natural frequency presentation may not be as general as previously believed.

Sounds interesting. Unfortunately the article has no killer graph to make the point. In psychology, the killer graph often takes the form of a plot with two lines that cross, thus demonstrating the interaction of interaction of interest. Maybe Chapman and Liu could do this for their next article.

P.S. I gotta say, it would be pretty cool to be named “Jingjing.” Sort of a Boutros Boutros or Mike Michaelson thing going on here.

1. Will says:

Australia once had a Governor General named Isaac Isaacs (http://en.wikipedia.org/wiki/Sir_Isaac_Isaacs). His name was so cool that he was given a knighthood!

2. freddy says:

…looks like the Bayesian statistics entry is not the only thing that could be improved on Wikipedia

3. Andy Fugard says:

Knew about the advantages of frequencies, didn't know this paper; thanks for the pointer. Interesting working through this with a 2×2 contingency table:

1. Roughly 1% of babies have Down’s
syndrome [P(D) = .01]. If the baby has Down's syndrome, there is a 90% chance that the result will be positive [infer joint for positive test and Down's from P(pos|D)*P(D) = .9 * .01 = .009].

2. Roughly 100 [marginal] babies out of 10,000 [total] have Down’s syndrome. Of these 100 babies with Down’s syndrome, 90 [directly write in the joint] will have a positive test
result.

In 2, you get a lot for free. In 1, you have the added complication of interpretating the natural language "if" (philosophers are continuing to argue about this) and you have to compute P(B|A)P(A) to get the joint frequency.

A more direct mapping from the frequencies to the percentages might be sonething like: "Roughly 1% of the total number of babies sampled have Down’s syndrome. Of these 1%, 90% will have a positive test result."

4. Weiwei Cheng says:

My name is Weiwei :D

5. noahpoah says:

Here's the killer graph (enlarge as necessary): X