Tuesday, December 10, 2002

Department of self-parody: This New York Times article says

Women Who Lead Colleges See Slower Growth in Ranks

"[T]he number of women tapped to become college presidents has leveled
off in recent years, after increasing steeply from the mid-1980's through the late 1990's,
according to a survey of more than 2,500 two- and four-year institutions.

"The survey, by the American Council on Education, found that from
1986 to 2001, the percentage of college presidents who were women
jumped to 21.1, from 9.5 percent. From 1998 to 2001, the increase
was only 1.8 percentage points.

"Similar shifts in hiring occurred among minorities, whose ranks among
college presidents increased to 12.8 percent in 2001 from 8.1 percent
in 1986. Since 1998, however, the share of minorities running institutions
of higher education rose by just 1.5 percentage points. If historically black
and Latino institutions are not counted, only one in 10 colleges or universities
is run by a minority."

Women first: From 1986 to 2001, there was an average increase of .733 percentage points per year in women's share of college and university presidencies. From 1998 until 2001, that racing growth screeched to a halt... of merely .6 percentage points per year.
To put the ACE's and the NYT's point more effectively, don't compare 1986-2001 with 1998-2001; compare instead 1986-1998 with 1998-2001. Then we get (21.5-9.5-1.8)/12, or an average increase of .85 percentage points per year over those twelve years, compared with the same average increase of .6 points per year over the final three years. A decline? Sure. A "levelling off after increasing steeply?" Seems like a heck of a stretch to me. (For a graphic representation, click here.)

It's worse for the story's treatment of minorities: An increase of .267 percentage points per year 1986-1998; an increase of .5 percentage points per year 1998-2001. In other words, the pace of minority hiring for presidencies has picked up over the last three years-- by nearly as much as the pace has decreased for women; not at all a "similar shift" to the purported levelling off among women presidents. And the analysis in the rest of the article, concerning the alleged increased conservatism among boards of trustees, proceeds as if for women and minorities alike there has been a dramatic slowdown (or even an outright reversal) in the assumption of college presidencies.

(Note: it has occured to me as a possibility that the numbers reported for 2001 were supposed to be attributed to 1998. That would have made for a genuine levelling off in both cases. But I can't find any sign in the ACE press release that there has been such a mistake.)

To reiterate: The levelling off in the hiring of women is tiny, and the pace of minority hiring has increased not decreased (though by a similarly tiny margin). If not for the fact that this appears to be an ACE problem rather than an NYT problem in the first instance, this article would perfectly fulfill the old "World Ends: Women, Minorities Hardest Hit" joke about the Times. On the other hand, the fact that the NYT ran this article at all (as opposed to articles based on the thousands of other press releases it receives each day), and that no one stopped to check the arithmetic, might qualify the piece as a fulfillment of the joke after all.

UPDATE: Readers Paul Cashman and Bob Perera object that I should have used compound growth rates. Mr. Cashman writes:

Typically when we deal in growth rates or percentages, the key figure is CAGR -- compound annual growth rate, or the constant percentage by which some amount grows over a period of time. For example, when the statement is made that the stock market has returned an average of 8% since 1929, or inflation averaged 3.2% between 1980-2000, it's the CAGR that's being referred to. When businesspeople do return on investment analysis, they're looking for the constant rate of growth of some investment over a period. Mathematically, we have:

ending_amount = starting_amount * (1 + CAGR) ** years

which becomes:

CAGR = ((ending_amount/starting_amount) ** (1/years)) -1

Applying this analysis to the Times story, we see:

CAGR for women presidents, 1986-1998 is 6.1%
CAGR for women presidents, 1998-2001 is 3.0%
CAGR for minority presidents, 1986 -1998 is 2.8%
CAGR for minority presidents, 1998-2001 is 4.2%

So the growth in women presidents in the recent period is half of what is was in the earlier period, while in the recent period minorities are being hired as college presidents at a rate 50% higher than they were in the earlier period.

Here's part of what I wrote back:

I'll note your dissent online; but I had considered the issue you raise before
writing my post. (I carefully wrote in terms of percentage point increases,
not percentage increases, for just that reason.)

What the cases you refer to have in common with each other, and not with this
case, is compounding. That is, next year I'll earn interest on the interest I
earned this year. Next year inflation will increase even this year's inflated
prices. I just can't see the relevance of compounding to the case at hand.

To put it a different way: The NYT made it sound like the first derivative of
women-presidents-over-time had dramatically fallen. It hasn't. You correctly
argue that the second derivative has fallen dramatically. But I can't make out
the substantive interest of that fact. The number of women presidents, their
share of the total, has continued to rise at a nearly-steady rate. The
of increase in the number of women presidents has slowed, as you say. But,
well, so what?

The way Mr. Perera puts it:
Dr. Levy's conclusions still more or less hold but using linear (as he does)
instead of compound growth puts most of the percentage gains into early years,
which could be valid (I have no data) but is probably wrong.

It seems to me that compounding can't be relevant in the same way when the underlying variable is has an upper boundary-- which both number of presidencies and share of presidencies do. In a variable with that characteristic, the compounded growth rate must eventually fall over time. And in this particular variable it seems perfectly plausible and uninteresting to me that the year-on-year percentage gains weremuch higher in earlier years (Mr. Perera's point). Wouldn't they have to be? When initial values are tiny, but increases can only happen in whole numbers (i.e. from 1 woman president we can't go to 1.05 but must go to 2), then the percentage gains early on are huge. But if we keep hiring one net new woman president per year, then the number of women presidents and women's share of presidencies both rise steadily over time (hiring doesn't "level off") even though the compound annual growth rate falls dramatically (from 100% in the first year to 50% in the second year to 33% in the third year...)

But I might be wrong about this. If I am, then the substantive interpretation changes as follows: there still hasn't been a "similar shift" in the hiring of minority presidents; indeed, the dissimilarity becomes even more dramatic. A shift from a CAGR of 6.1% to 3% in the hiring of women presidents still seems to me pretty different from the image created by "leveled off" vs. "increasing steeply" (for a graphic representation using those figures click here) but it's admittedly closer to that than is .85 percentage points per year vs. .6 percentage points per year. If CAGR is the correct measurement then I have some egg on my face; but the NYT's substantive interpretation still looks like nonsense. With a CAGR of 3%, it's not the case that Boards of Trustees are increasingly conservative (even assuming an equation between "conservative" and "not hiring women presidents during times of uncertainty.") It's just the case that the rate at which they are becoming less conservative has slowed.

One more point: if I was wrong in my initial post, the blame lies on me; please don't harass Andrew Sullivan for linking to my post...

No comments: