Kaiser’s beef

The Numbersense guy writes in:

Have you seen this?

It has one of your pet peeves… let’s draw some data-driven line in the categorical variable and show significance.

To make it worse, he adds a final paragraph saying essentially this is just a silly exercise that I hastily put together and don’t take it seriously!

Kaiser was pointing me to a news article by economist Justin Wolfers, entitled “Fewer Women Run Big Companies Than Men Named John.”

Here’s what I wrote back to Kaiser:

I took a look and it doesn’t seem so bad. Basically the sex difference is so huge that it can be dramatized in this clever way. So I’m not quite sure what you dislike about it.

Kaiser explained:

Here’s my beef with it…

Just to make up some numbers. Let’s say there are 500 male CEOs and 25 female CEOs so the aggregate index is 20.

Instead of reporting that number, they reduce the count of male CEOs while keeping the females fixed. So let’s say 200 of those male CEOs are named Richard, William, John, and whatever the 4th name is. So they now report an index of 200/25 = 8.

Problem 1 is that this only “works” if they cherry pick the top male names, probably the 4 most common names from the period where most CEOs are born. As he admitted at the end, this index is not robust as names change in popularity over time. Kind of like that economist who said that anyone whose surname begins with A-N has a better chance of winning the Nobel Prize (or some such thing).

Problem 2: we may need an experiment to discover which of the following two statements are more effective/persuasive:

a) there are 20 male CEOs for every female CEO in America
b) there are 8 male CEOs named Richard, Wiliam, John and David for every female CEO in America

For me, I think b) is more complex to understand and in fact the magnitude of the issue has been artificially reduced by restricting to 4 names!

How about that?

I replied that I agree that the picking-names approach destroys much of the quantitative comparisons. Still, I think the point here is that the differences are so huge that this doesn’t matter. It’s a dramatic comparison. The relevant point, perhaps, is that these ratios shouldn’t be used as any sort of “index” for comparisons between scenarios. If Wolfers just wants to present the story as a way of dramatizing the underrepresentation of women, that works. But it would not be correct to use this to compare representation of women in different fields or in different eras.

I wonder if the problem is that econ has these gimmicky measures, for example the cost-of-living index constructed using the price of the Big Mac, etc. I don’t know why, but these sorts of gimmicks seem to have some sort of appeal.

15 Comments

1. Radford Neal says:

The difference between this and the Big Mac index is that most people have little idea what fraction of men are named John. So this “dramatization” dramatically reduces people’s ability to actually grasp what the situation is. In contrast, although the Big Mac index has the problem that it’s not as robust as the real comsumer price index, it doesn’t distort or obscure the magnitude of price changes. Plus, the lack of robustness of looking at men named John is probably much greater than the lack of robustness of looking at Big Macs.

2. Rahul says:

Why is the big mac index gimmickey? For one it cannot be gamed much.

Unlike a basket of commodities.

3. Dave Giles says:

For the record: “The Economist” magazine introduced “The Big Mac Index” as a fun way of measuring Purchasing Power Parity, not Cost of Living.

4. Phil says:

This reminds me of a story from Tony Randall’s excellent memoir, “Which Reminds Me…” The story features Danny Simon, brother of famous comedy playwright Neil Simon. Danny, too, was a comedy writer — Wikipedia says he wrote for “Your Show of Shows, The Colgate Comedy Hour, The Phil Silvers Show, Make Room for Daddy, My Three Sons, The Carol Burnett Show, Kraft Music Hall, Diff’rent Strokes, and The Facts of Life.” According to Randall, Danny and some other comedy writers were arguing about how a sketch should go, and Danny said “We should do it my way, because I’m the funniest writer in Hollywood.” One of the other writers replied “Danny, you’re not even the funniest writer in your family.”

• Phil says:

By the way, I think the “…men named John” comparison is a great attention-getter. Discussion of the actual numbers can come next.

I saw an article a few years ago about people who do ultra-deep diving. (I’m not talking about free diving, I’m talking about diving with gear, rebreathers, etc., to, um, unfathomable depths.) As a way of emphasizing how few people have ever been that deep in a dive suit, the article said “More people have walked on the moon.” Such an arresting thought. Of course it conveys less information than simply giving the number, but this is a much better way of making the point.

• StefanP says:

Yes, in Sweden a similar approach got headlines in the press some time ago, just switch “John” with “Anders”. Attention-grabber yes, but that is what it is all about nowadyas?

Anyway, seven of the moon-walkers are alive out of the original dozen. I did not know that.

• James Annan says:

I think that’s a poor example. Pretty much by definition, any near-record performance will have been achieved by a very few people. More people have landed on the moon than run sub-9.8 for 100m, but so what? More people have landed on the moon than have lived in my house, but that doesn’t really add much o my achievement in buying it! I thought the original “men named John” thing was a dramatic way of making a point, even if not very quantitative.

5. Anonymous says:

What proportion of garbage collectors are female?

• Rahul says:

I’d guess, lesser fraction than are CEOs. Relevance?

• Anonymous says:

Relevance of CEO stat?

The issue is whether fractions are evidence of discrimination or simply of self selection.

• Rahul says:

Could be self selection in some cases & discrimination in others?

Have you had women complain about discrimination at garbage collection hiring interviews?

• Anonymous says:

It may just be coincidence that discrimination is alleged in the juiciest postings.

This is not to deny the reality of gender discrimination.

Just making the point that simplistic comparisons don’t pass the laugh test.

6. Kaiser says:

Wow, the delay on the blog is getting longer. This exchange took place so long ago I had to re-read the article. I discussed this article with my students, after which I have a Bayesian objection to this Index (regardless of the base). A good number of students look at a statement such as “there are 8 CEOS named Richard, William, John and David for every female CEO” and intuitively believe that the chance of becoming CEO is 8 times higher for men named Richard, William, John or David relative to a woman. Oops.