Psychologists have colorful names for the illogical way that we treat percentages and ratios. Ellen Peters of Decision Research in Eugene, Oregon, calls it the "benign percentage," because inexplicably we don't find percentages as frightening as numbers. Cornell psychologists Valerie Reyna and Charles Brainerd use the anthropomorphic phrase "denominator neglect" to describe the jellybean phenomenon: Many of us illogically prefer 9/100 odd to 1/10 odds, meaning that we get overly focused on the top number, the numerator-which blinds us to the all important denominator. But we neglect it at our own peril.

The colorful jargon is appropriate, because get this: When asked about their feelings, those who chose the poorer odds were much less precise about what motivated their choice, suggesting that the emotional "hit" from the vision of nine winners was just too irresistible to pass up. They ignored the many white jellybeans in the large bowl, because they lacked emotional power; they focused instead on the nine brightly colored jelly beans. It simply felt "right" to reach into the bowl with more colored beans.

The message of my chapter on the "Arithmetic Heuristic" is that numbers are emotional quantities-not just abstract symbols on a piece of paper. But before you dismiss this as a laboratory novelty, consider the recent study that Peters did in rural Ghana. She wanted to explore the link between formal education and health-specifically the idea that education leads to better (less heuristic) thinking, which translates into healthier choices down the line. To do so, she tested the villagers' critical thinking skills, including a form of innumeracy much like that seen in the jelly bean study.

The so-called Stickman task presents two hypothetical villages as circles, each populated with stick figures: Red stick figures are HIV-infected, and black stick figures are not. The idea is to judge the risk associated with a randomly selected villager, based on the population of stick figures. One village might have four red figures out of eight, for instance, and another three red figures out of four. Those with poor numeracy skills will look at the absolute number of infected villagers (four is greater than three) rather than the percentage-the real indicator of risk.

This is the same mistake many of us make with the jelly bean test, but in rural Ghana it can be a deadly miscalculation. Peters combined this numeracy score with other cognitive test scores for each volunteer, and then she measured their actual knowledge of AIDS and HIV prevention: Do condoms protect against the disease? Is it okay to wash and reuse a condom? Can AIDS be transmitted by a blood transfusion? By witchcraft? And so forth.

Finally, she interviewed each volunteer about his or her actual protective behaviors, including: going to AIDS classes; talking with one's sexual partner about HIV and AIDS; getting tested, or urging a partner to get tested; and condom use. Then she crunched all the data together, and the results were unambiguous. As reported is the journal Psychological Science, more years of schooling led to sharper skills like numeracy, and these enhanced intellectual abilities in turn led to more protective health behavior. Importantly, mere knowledge of HIV and AIDS facts did not in itself predict healthy living. It appears that cognitive abilities like numeracy better equip people to use their basic knowledge, to extrapolate to new situations and reason statistically in everyday life.

These findings have implications, especially for sub-Saharan African nations. Over the past decade, an estimated $8.9 billion has been spent in the region to disseminate basic knowledge about AIDS, in an effort to stem the ravages of the disease. These findings suggest that these efforts may not be enough-that they must also include interventions to help at-risk adults reason with the facts they have. Put another way, in may not be a coincidence that this part of Africa is home to both the largest unschooled population in the world and the largest AIDS-infected population.