Essay Review: Abusing Probabilities, and Other Pseudo-Skeptics' Misdeeds. Reality Check: How Science Deniers Threaten Our Future by Donald R. Prothero

Abstract

A common ploy by pseudo-skeptics [1] is to make a correct statement warning against a general sort of error, followed by committing that error in some minimal sort of disguise. For instance, warn against taking correlations as reflecting causation but do that very thing concerning, say, carbon dioxide and global temperature; or about cancer and smoking: "the link between cancer and smoking is about 99%" (p. 32).

No source is given for this claim, reprehensible in a book that professes to be evidence-based. But what does this even mean? Is a link a cause, as the context implies but as the book explicitly warns against presuming?

Does it mean that 99 out of 100 smokers will get cancer? Or that 99 out of 100 researchers say so? Or that only 1 study out of 100 did not support the connection? Or that there is a 1% probability that smoking does not cause cancer?

Whatever the meaning, "Based on statistical analysis, we can show that if something has a 99% likelihood of occurring, or being true, then this level of confidence is so overwhelming that it would be foolish to ignore it" (p. 32).

This is nonsense. There is no statistical analysis that determines whether or not something is foolish. Foolishness is a human characteristic diagnosed subjectively and statistical analysis has nothing to say about it.

The asserted foolishness is then "illustrated" by the high likelihood of injury or death if one jumps off a building, an entirely inappropriate, unwarranted analogy. The evidence about the consequences of  jumping off buildings is quite directly observable, no inferences needed; by contrast, the link between cancer and smoking is based on inferences from data that are probabilistic: analyzing records from people who have smoked varying amounts for varying lengths of time and applying statistical tests of significance.

The most subtly misleading or deceitful aspect of that "99%" assertion is the implication that smokers will inevitably get lung cancer, and this illustrates a highly important point about probabilities and their (mis)interpretation, a point that crops up in a number of quite different matters.

If a smoker dies of lung cancer, there is a high likelihood that smoking was a causative factor; but that is not at all the same as saying that smoking is highly likely to cause death by lung cancer. In actual fact: "Smoking accounts for 30 percent of all cancer deaths and 87 percent of lung cancer deaths" but "fewer than 10 percent of lifelong smokers will get lung cancer" (Wanjek 2008).