Monday, March 10, 2008

Don't Blame this on Math

In yesterday's New York Times, we are told "Math Suggests College Frenzy Will Soon Ease." Actually, I don't get the math in a couple of places. Let's start here:

Projections show that by next year or the year after, the annual number of high school graduates in the United States will peak at about 2.9 million after a 15-year climb. The number is then expected to decline until about 2015. Most universities expect this to translate into fewer applications and less selectivity, with most students probably finding it easier to get into college.
The article cites projections from the Western Interstate Commission for Higher Education. How can there only be 2.9 million high school graduates per year?

We know from the American Community Survey that in 2006, there were 17.5 million students enrolled in high school and that enrollment rates for those under age 17 are 95% or higher. We also know that only 7% of teens 16-19 are classified as high school dropouts. So we are looking at a graduation number that's in the neighborhood of 17.5*(1/4)*(0.93) = 4.1 million.

So I don't trust the WICHE projections, but it is worth considering the simple population movements. Here is a graph of the number of 18-year olds by year, based on Census projections:

So there is a dip coming up in the population of 18-year olds that will turn back the clock by about 10 years.

Is that a lot or a little? As one example, for the Class of 2010 at Dartmouth, there were 13,938 applicants, of whom 2,186 or 15.7% were admitted. If this were the peak, and we applied the changes in the projections (a drop to 90.7% of the peak), that would boost the admit rate to 15.7/0.907 = 16.9% before it began to fall again. I don't think we'll notice any easing in the frenzy here in Hanover.


ErikR said...

Depending on the assumptions made, you can get a number almost that small. I don't know what assumptions are realistic...but I just wanted to look at the math.

If we assume all dropouts occur between the junior and senior years, the 3 underclasses are each 4.68M and the senior class is 3.46M. Now, if the high-school population drops by 10% overall, we have 3.1M graduates. Not too far from the 2.9M number.

ErikR said...

Here are some assumptions that give 2.9M graduates:

1) 8% of the high-school age poplulation are high-school dropouts

2) The high-school age population is 19M ( = 17.5 / 92% )

3) One quarter of the high school age population entered as freshman each of the last 4 years.

This gives a graduation rate of 3.23M per year (= 19M/4 - 19M * 8% ).

If we assume a 10% drop in the total high school population in the future, then the graduation rate becomes 2.9M per year (90% of 3.23M)

ErikR said...

Heh, sorry about filling up your comment section!

The assumptions I was making result in a "lumpy" graduation rate. 1 year low, 3 years high. It doesn't really make sense to assume that all the drop-outs occur one year, and then none for 3 years.

So I guess I agree with you that the numbers they report don't make much sense.

Tom said...

The article misses the key element entirely. It's not the number of kids (which, after all, is much smaller than 30 years ago in the baby boom) but the ease of applying. The fact is that every possible kid puts in an application to the top schools through the common application. This is good for the schools, in that they see all possible applicants. It's also confusing for consumers, who see miniscule acceptance rates, because at least half of the applicants are patently unqualified to attend the top institutions, but it's worth the $75 for a chance at a lottery ticket to fame and fortune.

We could reduce the "frenzy" by simply limiting the common app to 6 schools. (Average for this year's senior class at my daughter's high school: 12. High: 23) But the colleges have no incentive to do this (why not take the free $75 bucks when it takes 5 minutes to reject half the applicants?) and money seems to be no object to the parents of the kids applying to every school under the sun...

Patrick R. Sullivan said...

But Jay Greene finds the graduation rate to be only 70% or so, by comparing the number of 8th graders enrolled in public schools four years earlier to the number of high school diplomas issued.

Anonymous said...

Admit rate is closely tied to matriculation rate. If nearly 100% of accepted students matriculate (the Harvard model) you are in good shape in keeping that admit percentage low. If matriculation rate goes down, admit rate must increase.

So, if Dartmouth wants to keep their nice admit number they shouldn't focus so much on raw numbers of high school grads, but look at what it takes to roll accepted students to matriculated students.

Colleges who win at this game in the next several years, in my opinion, will be those that eliminated or reduced loans in the financial aid packaging, and generally are offering better assistance to the group formerly known as the middle and upper middle classes.

We are going through the college app process right now with our second child, who used the common app to apply to many good schools. The right one will be the one that accepts and offers an excellent aid package (preferably without loan burden).