Learning Strategies

A wire-service article appeared yesterday on the Boston Globe’s website, boston.com, but now the article has mysteriously disappeared. Fortunately most of it is still available elsewhere, so we can examine its questionable use of statistics. It begins by reporting some vaguely alarming statistics:

A state Department of Public Health study finds that certain types of cancer are far above the state average in some western Massachusetts communities.

But don’t get too alarmed:

Nine other western Massachusetts towns had cancer rates below state average.

Gee, what a surprise! Some towns had cancer rates above average, and others had cancer rates below average. No numbers, of course, except for an unclear observation that “pancreatic cancer among men in Easthampton is 128 percent above the average.” Given the general level of reporting in this article, we don’t even know whether they really mean 128% above the mean (or is it median?); very possibly they mean 128% of the mean (or median). In any case, we know nothing about the actual incidence of pancreatic cancer or the population of Easthampton. Perhaps the state mean would have predicted 1.3 cases and there were really 3, which is hardly likely to be statistically significant.

I know, numbers don’t sell. But they are essential if we’re to understand the point behind this article. Of course some towns are above average and others are below, but what does that prove?

Interestingly, the sentences omitted from this version include the observations that town A is above average in pancreatic cancer, B in breast cancer, C in stomach cancer, and so forth. No one town is above average in more than one type. This leads us to be even more suspicious about the statistical significance here.

Labels: math, teaching and learning