Inferring and Explaining

108 simply no causal relationship between the two the women in the same age range sufered from occurrences.Tis all suggests four possible causal the disease. Tis tells us something potentially relationships between any two events, A and B . very important about gender and heart disease. InferrIng and exPlaInIng 1. A caused B . 2. B caused A . 3. Some third “common cause,” C , indepen- dently caused both A and B . 4. There is no causal relationship between A and B . We shall see, directly, that there is a ffh pos- sible causal relationship between A and B , but I’m saving that as a surprise. Just what we have so far, though, allows us to explain the correla- tion between ice cream sales and forest fres. Nate Silver says “there is no causation,” but this is a little careless. He’s right, of course, that A is not the cause of B nor B the cause of A . But there is a causal relationship that best explains the correlation. C (the summer heat) is the common cause of the increased ice cream sales and greater number of forest fres. Explaining the Numbers Much of statistical reasoning in the social and natural sciences can easily be reconstructed as a related pair of inferences to the best explanation. In the frst inference, the explanatory question focuses on a quantitative relationship. We typi- cally have some study or sample that is asserted to tell us something about a larger group or popu- lation. Consider the extensive medical data that was uncoveredover several decades in the famous Framingham study. Medical researchers were surprised todiscover that 29percent of themen in the forty- to forty-nine-year range sufered from coronary heart disease, while only 14 percent of e 1 . Of the 771 men in the forty- to forty-nine- year age group, 29 percent showed some signs of coronary heart disease. e 2 . Of the 954 women in the forty- to forty-nine-year age group, only 14 percent showed signs of coronary heart disease. t 0 . Coronary heart disease appears much more often in men than in women. One rival explanation that I believe current medical advances force us to take seriously is that coronary heart disease is much more prevalent in woman than was recognized by medical experts at the time of the Framingham study—then current diagnostic indicators failed to correctly identify all the signs of coronary heart disease in women. So the following may better explain some of the gender disparity: t 1 . All the clinical indicators of coronary heart disease in women were not recognized at the time of the study. But let’s grant that the Framingham data truly indicated some real gender disparity and that the samples do suggest that coronary heart dis- ease was more prevalent in men. Explaining the Correlations Noticing this striking correlation between gen- der and heart disease is only the frst step in fg- uring out what is going on here. We might think that there’s something deeply biological going on.