Journalistic innumeracy

 Newspapers, of course, thrive on sensationalism, which in turn relies on scare statistics.  A certain form of innumeracy relies very heavily on a false use of the concept of percentages.  An example comes from an article in last Tuesday's Washington Post by columnist Karen Attiah, who attended a gun show in North Texas and wrote a column about women, guns, and pregnancy. It includes the following two sentences about death rates for pregnant women:

"The study, conducted by Tulane University researchers, revealed that the “pregnancy-associated homicide” rate in 2018 and 2019 was 3.62 per 100,000 women — 16 percent higher than homicides of women who are not pregnant or haven’t recently given birth. Homicide beat hemorrhage and pregnancy-related hypertension as the top single cause of death."

Now the killing of a pregnant woman is horrifying, just as any homicide is horrifying, but I want to go a little further into these numbers.  Let's start by figuring out a raw number, based on a single year, 2019.  There were 3,745,540 live births in the US in that year. 3 in 100 of those births were parts of multiple births--that means about 112,000 live births, and thus, about 3,634,000 women had their pregnancies go to full term.  Dividing that number by 100,000 yields a 36.3.  3.62 times 36.3 equals 132.  That is apparently a close approximation of the total number of murdered women who were either pregnant or had just given birth during 2019.  The total number of woman murdered in the US during 2019, according to the FBI, was 2991.  That means that 4 percent of the women murdered in the United States in 1991 were pregnant or had just given birth.  96 percent of them were not.

Ms. Attiah's article, however, claims that a pregnant woman runs a greater statistical risk of homicide than one who is not pregnant--that the risk is "16 per cent" higher.  What that means to her, I think, is that while about 132  pregnant women (or women who had just given birth)  were murdered during 2019, a comparable sample of non-pregnant women--that is, about 3,634,000--would have included 114 homicide victims.  (132 is 16 percent higher than 114).  But the first question that she and her editors should have tried to answer was, is a difference between 114 and 132 out of a sample of  more than 3.6 million statistically significant?  I strongly suspect that it is not, and that it is just as likely to be random.

More important, however, is the misuse here of the concept of percentage.  Percent means "per hundred," and it is computed by dividing a subgroup of a sample by the total size of the sample.  These statistics, however, aren't based on "per hundred," but on dividing per hundred thousand, that is, a thousand times as much.  The percentage, literally, of pregnant women murdered in 2019 was about  .00036 percent.  The percentage of non-pregnant women murdered was about .000031 percent.  That isn't 16 percent higher--it is in fact .00005 percent higher.  16 percent higher, however, seems like a significant difference, while .00005 percent higher obviously is not.  

But that is not all.  The statement that 132 is 16 percent higher than 112 takes 112--the number of women murdered in the non-pregnant sample--as the total sample itself.  That's a basic statistical error, in my opinion, but I see it all the time, particularly in politically sensitive statistics.  

 Two years ago, a New York Times story on school suspensions of black girls noted, "In Iowa, Black girls were nine times more likely to be arrested at school than white girls, according to a state-by-state analysis conducted by the American Civil Liberties Union."  If one clicked the link to the study, one found that Iowa (which has a very small black population) was just one of three states to show a figure that high--states like Virginia and Florid showed only two or three times as many.  Totally absent from the story, however, were any figures on how likely it was, really, for a black or white student to be suspended.  I did some checking and found that about 2 percent of female white students and 10 percent of  female black students were suspended, on average.  The author of that article would have called that "five times as many" black students--but a more accurate way to put it would be that black girls are about 8 percent more likely to be suspended than white ones--and 90 percent of black girls never get suspended.  That, however, does not sound like a national crisis.  The Times and other major newspapers need editors that will ask these questions.

The Karen Attiah column raises another question as well.  It's about the murders of a relatively small group of women--132 our of a total of 2991 murdered women in the US in 2019.  It does not mention that 10,908 men were murdered in 2019--that is, four times as many.  Similarly, the Times ran a story about an "epidemic of femicide" in Central America not long ago, without ever mentioning that the murder of men remains far, far more common.   The reason, once again, that no editor asked Attiah about that is that our major newspapers, like our major universities, now divide the world into the virtuous oppressed on the one hand--women, minorities, and LGBTQ--and privileged oppressors on the other.  Within that narrative, those 10,908 men are unworthy of mention.  Female and minority op-ed columnists now boldly proclaim that their job is to focus on their own demographic.  This is bad journalism and bad citizenship, and we are paying a big price for it..