This morning I heard this piece (linked below) on NPR.  The thrust was that Marine units with women in them performed worse in combat simulations than did those with men only.  There could be many explanations of this.  I want to flag one that was not raised in the NPR piece.  http://www.npr.org/sections/thetwo-way/2015/09/10/439190586/marine-corps-study-finds-all-male-combat-units-faster-than-mixed-units

My understanding from this article is that some of the performance differences were likely due to muscle mass.  How much weight can people carry around for how long?  Probably those with more muscle mass can carry more weight.  I am no expert on the following, but my best read is that men tend to have more muscle mass.  I would not be surprised if the men, on average, could carry more.  But…someone women doubtless could carry more than some men. I’ll elaborate below.

I could not find the distributions of muscle mass for men and women, but I did find one for height, and I can use this to illustrate the point.  Here’s the link:

https://sugarandslugs.files.wordpress.com/2011/02/heights1.png?w=480&h=292

Men tend to be taller than women.  If we draw a particular cutoff for inclusion in our group (say “the Marines!”) (say, 169 cm in the graph), the height of men above the cutoff will be greater than the height of the women above the cutoff.  All have to be above 169 cm, but the average man taller than 169 will still be taller than the average woman above 169 cm.  So…if they are doing a height-related task men will do better than women, even though the same cutoff is being used to let someone in.

Is this the same thing with the Marine Corps?  If so, a uniform standard for muscle mass (or how much weight one can carry, for that matter) will leave a group included in the Marines in which women tend to underperform relative to men who have surpassed that uniform standard.

But…and this is key…by including women you can raise the standard and do better overall.  Some women will carry more than some men and those men can be displaced from the group leaving you better off overall.

Look back at the height chart. If I need a particular number of people and I want the tallest, I can reach the requisite number of tall people at a higher cutoff if I include women than if I do not.  Thus inclusion of women leaves us with two things (a) a group that overall performs better on height-related tasks (which is what should matter!); and (b) a group in which women underperform relative to men on height-related tasks.

If the analogy holds, the Marines should not worry a whit if the groups with women underperform relative to groups with men.  That’s not the relevant question.  What they should worry about is whether they can be more exclusive (that is, set a higher standard for inclusion in combat service) by including women, and thus as a whole perform better.

Obviously this is a more complicated situation than I described.  But I was stunned when I listened that no one discussed this as an issue.  These are not stupid people. But I wonder if they have spent any serious amount of time thinking about stats.

If you want to think clearly, please, please, please spend a good chunk of time learning, at a deep level, about basic statistics.