Gigerenzer says that we must teach risk literacy in medical school and statistical literacy to all in primary school. He and his colleagues go into considerable detail to say how this should be done. Teaching statistics early is not sufficient. It is also essential to represent probabilistic information in forms that the human mind can grasp. To this end, visual and hands-on material can enable a playful development of statistical thinking. For instance, tinker-cubes are lego-like units that first graders can use to represent simple events, to combine to represent joint events, and to count to determine conditional frequencies.

Gigerenzer suggests that people love baseball statistics, are interested in graphs about stock indices, have heard of probabilities of rain, worry about the chance of a major earthquake, and are concerned about cholesterol and blood pressure. How safe is the contraceptive pill? What is the error margin for polls and surveys? Is there a probability that extraterrestrial life exists? Personal relevance is what makes statistics so interesting. To build up motivation, curricula should start with relevant everyday problems and teach statistics as a problem-solving method.

Of course, first the teachers will need to be taught.

Finally, the numbers in risk communications need to be presented in a transparent manner. Gigerenzer’s suggestions are:

**Use frequency statements, not single-event probabilities**. One nontransparent representation is a single-event probability statement. It is defined as a statement in which a probability refers to a singular person or event rather than to a class. A good illustration is weather prediction: ‘‘There is a 30% probability of rain tomorrow’’ is a single-event probability. By definition, no reference class is mentioned, but since people tend to think in terms of classes, misunderstanding is inevitable. Some citizens believe the statement to mean that it will rain tomorrow 30% of the time, others that it will rain in 30% of the area, or that it will rain on 30% of the days for which the announcement was made The ambiguity of the reference class—time, area, or days—can be avoided by making a frequency statement, such as ‘‘it will rain in 30% of the days.’’

Similarly, when in clinical practice a physician tells a patient: ‘‘If you take Prozac, you have a 30 to 50% chance of developing a sexual problem, such as impotence or loss of interest,’’ this single-event statement invites misunderstanding. As in the case of probabilities of rain, confusion will mostly go unnoticed. After learning of this problem, one psychiatrist changed the way he communicated the risk to his patients from single-event statements to frequency statements: ‘‘Out of every 10 patients who take Prozac, 3 to 5 experience a sexual problem.’’ Psychologically that made a difference: Patients who were informed in terms of frequencies were less anxious about taking Prozac. When the psychiatrist asked his patients how they had understood the single-event statement, it turned out that many had thought that something would go awry in 30 to 50 percent of their sexual encounters. The psychiatrist had been thinking of all his patients who take Prozac, whereas his patients

thought of themselves alone.

**Use absolute risks, not relative risks**. A common finding is that relative risk reductions lead people to systematically overestimate treatment effects. Why are relative risks confusing for many people? As mentioned before, this statistic is mute about the baseline risks and the absolute effect size. Frankly, relative risk is practically designed to overestimate. Researchers, doctors, drug companies, all want there to be demand for their services and puffing up the risk so it is more noticeable is one way to do it.

**Use mortality rates, not survival rates**. According to Gigerenzer, survival rates confuse physicians and make them draw unwarranted conclusions, while mortality rates are clearly understood. Of Gigerenzer’s suggestions, this seems to be the weakest. Both rates can confuse, although survival rates are easier to manipulate. Again context is an issue. It seems to me that a hospital could compare the survival rates of its stage 3 breast cancer patients over time and that would be meaningful.

**Use natural frequencies, not conditional probabilities**. Estimating the probability of disease given a positive test (or any other posterior probability) is much easier with natural frequencies than with conditional probabilities (sensitivities and specificities). Note that this distinction refers to situations where two variables are considered: Natural frequencies are joint frequencies. Our brains cannot easily handle conditional probabilities.