What are natural frequencies?

A 2011 Cochrane Review concluded that health professionals and consumers “understood natural frequencies better than probabilities.”1 A 2011 Annals of Internal Medicine article reported the opposite, that “natural frequencies are not the best format for communicating the absolute benefits and harms of treatment”2 How should physicians deal with these contradictory messages?

As is often the case, the contradiction lies in the definitions, not in the data. Ulrich Hoffrage and I introduced the term “natural frequencies” in the late 1990s and conducted the first studies showing that they foster understanding of the positive predictive value among lay people, doctors, and medical students.3 4 5 6 What is a natural frequency? It is a joint frequency of two events, such as the number of patients with disease and who have a positive test result, and is an alternative to presenting the same information in conditional probabilities, such as sensitivities and specificities. Conditional probabilities tend to cloud the minds of many people, including health professionals, as the following problem illustrates (for convenience, probabilities are expressed in percentages).

Assume you use mammography in a certain region …