I stress again — it may well be that many or even all the FLDS parents are guilty of various crimes. But it's also important, in this case as well as in others, for the media to report statistical information in a useful way.

Take, for instance, this MSNBC headline, "Official: History of injuries to polygamist kids / At least 41 had broken bones; possible sex abuse of boys investigated." At least 41 kids have had broken bones — sounds like a serious problem.

But 41 out of how many? Paragraph seven reveals this: "More than 450 children are in state foster facilities from the raid."

What about the other information that would be necessary to make this data make sense? I refer, of course, to how many kids normally have broken bones without abuse. I don't know the percentage, but a quick Google search found [UPDATE: this replaces a much less reliable estimate I'd originally found] this study, which puts the risk of bone breakage at 1.3% per year per child (for 0-to-12-year-olds). Assuming this carries over to 0-to-18-year-olds (perhaps a mistaken assumption, especially since "The incidence increased linearly with age" up to age 12, but let's use it as a back-of-the-envelope estimate), this yields an estimate of about 20-25% of all minors having had a broken bone, which is to say that a minor of average age would have about a 10-12% chance of having had a broken bone. This can't automatically carry over to the FLDS kids, of course, for a variety of reasons; this is just one study that I quickly found; and some part of the broken bones reported in the study of may themselves have been caused by abuse. But still the "41" figure (which, recall, refers to children who "have had broken bones in the past") seems a lot less striking when one turns it into "under 10%" (41/450), and even less striking when one asks how this compares to the normal broken-bone rate among unabused children, which the study I found suggests is roughly 10% for the average child.

Now I stress again: Many of the FLDS kids might have been physically abused, even beyond the seeming early marriages of some of the girls and the alleged forced marriages of some of the girls and expulsion of some of the boys. The abuse rate might be higher than average. Of course the total broken bone rate may well be much higher than 10%, because not all the broken bones might have been identified. Sexual abuse at any rate, whether of teenage girls or young boys, is a serious crime that should be punished. And if there was indeed evidence of sexual abuse of young boys (with "young" meaning very young) then the removal of even small children might have been justified, contrary to my arguments below, which were based on press accounts that at the time had focused solely on the alleged sexual abuse of teenage girls.

But the particular news account here strikes me as a highly unhelpful, and potentially misleading, use of statistics, because it (1) includes the numerator in the headline, and leaves the denominator for paragraph seven, and (2) suggests that the number is significant evidence of abuse, without even trying to provide a comparison with the broken-bone rate among ordinary, nonabused children. The story does later quote the state agency as saying, "We do not have X-rays or complete medical information on many children so it is too early to draw any conclusions based on this information, but it is cause for concern and something we'll continue to examine," but that does little, I think, to undercut the attention that MSNBC focused on the 41 number in its headline.