Does a positive mammogram mean a woman has breast cancer? Does a positive HIV test mean someone is infected with the virus? As ordinary people confront the laws of probability, the odds of misinterpretation and false alarms rise. Two German psychologists have found a better way to teach basic statistical concepts, based on the way people naturally weigh the odds. This approach can help patients, and the doctors who advise them, more accurately assess the meaning of test results.

Peter Sedlmeier, Ph.D., of the Chemnitz University of Technology and Gerd Gigerenzer, Ph.D., of the Max Planck Institute for Human Development in Berlin, tested their approach using computer-based tutorials that cover basic binary statistical literacy (the outcome is either this or that), that took students up to two hours to complete. The psychologists' findings appear in the September issue of the Journal of Experimental Psychology: General, published by the American Psychological Association (APA).

In their article, Sedlmeier and Gigerenzer contrast two approaches to statistical training. Percentage-based rules would state, for example (using hypothetical numbers), "If a woman undergoing mammography has breast cancer, the probability that she will test positive is 80%." Natural-frequency rules would state, using the same example, "Eight of every 10 women with breast cancer who undergo mammography will test positive." Whereas percentages view probabilities in light of a fixed number, 100, natural frequencies don't share a common norm. Still, the authors predicted that the latter approach would be easier for people to learn because it taps a natural ability to count the observable, without having to use symbolic abstraction. Previous research has shown that people calculate the odds of any given event more easily and accurately using natural frequencies, which the authors say represents information in a way that is attuned to our "cognitive algorithms" for reasoning with certain kinds of data.

This may be one reason why typical percentage-based statistical training has been ineffective, say the authors, causing problems when health-care providers counsel patients -- often inconsistently and/or inaccurately -- about the chances of disease associated with (for example) positive HIV blood tests and positive mammograms. In these cases, doctors and patients have to layer new information, such as an individual's positive mammogram, onto more general information, such as how many people in a given group have breast cancer and how many of those with positive mammograms have breast cancer, to arrive at the odds that the individual in question may actually have the disease.

Sedlmeier and Gigerenzer conducted a series of studies with students at the University of Chicago, the Free University of Berlin and the University of Munich; there was almost no difference in the groups' results. Up to four dozen students took part in each study. The authors created several different computer-based tutorials that used percentage-based rules or natural-frequency rules, and predicted that the latter would work better. The results were consistent: Students who took the percentage-based rule tutorial showed a substantial short-term increase in performance with excellent transfer, but it decayed over several weeks. People who took the natural-frequency tutorial had a noticeably higher training effect (i.e. they got more cases "right"), equally good transfer to other problems, and, most significantly, no loss of performance after 15 weeks.

Sedlmeier summarizes the results: "Both groups learned, but the natural-frequency group learned better and it lasted longer, with no decay." In their article, the authors propose further research into multi-variable (not just binary) statistical training, training for "shortcuts" in making probability estimates, and the uses of such brief tutorial programs for mathematical and statistical literacy. For example, they speculate about convenient, cost-effective computer-based tutorials that could teach high-school students how best to evaluate the results of pregnancy, HIV or drug tests. "The teaching of statistical literacy," the authors conclude, "can take advantage of human psychology."

Peter Sedlmeier can be reached by email at peter.sedlmeier@phil.tu-chemnitz.

The full text of the article is available at theAmerican Psychological Association website.