Excellent feedback from readers on my speculations about the sex disparity
among victims of the Las Vegas shooter: 36 women, 22 men.
Several readers observed that the disparity is not statistically remarkable on reasonable assumptions about the composition of the concert audience.
Here are the arguments.
- Assume that precisely half the concert attendees as a whole are each sex: 50 percent male, 50 percent female. The issue then maps into a simple coin-tossing problem.
If I toss a fair coin 58 times, what’s the probability I’ll get a 36-22 or worse (i.e. further from the 50-50 average) split in either direction, H-T or T-H?Answer
: 8.7 percent.
That’s worth an eyebrow-squinch, but it’s not really eyebrow-raising
The customary (although perforce arbitrary) standard for raising a statistician’s eyebrows is five
percent. That would correspond to a 37-21 split or worse. We’re near the edge there, but not over it.
- You can work the numbers the other way, too.
We don’t actually know the proportion of females among the concert attendees overall. Maybe it wasn’t precisely half. OK, let’s call it p
Now ask the question: Given that a random selection of 58 from that population had 22 males and 36 females, what can we deduce about likely values for p
: On that customary standard, p
is probably (i.e. at the 95 percent level of probability) between 48 percent and 74 percent.
Note that includes the possibility of an even split, or even of a slight male majority, 51 or 52 percent.
Bottom line here: Neither of those answers raises the statistician’s eyebrows. Neither is remarkably improbable.
So we are likely just seeing random statistical fluctuation here.
Many thanks to all who emailed in.