Drastic drop in program's acceptance rate in one year

[noumenope]

So this is what UCSD's polisci doctoral program lists as their recent admission ratios. I'm wondering, does anyone know what's going on behind the scenes in a case like this? UCSD has always been extremely highly-regarded so it's not just a recognition thing. Lack of funding? It's not a low-quality applicants issue because the avg GRE scores they post are very high for polisci. Basically I'm trying to figure out if there's any reason to believe that acceptance rate might go up to its 5-year average again this year.

 

Admission Ratios

Year	Admitted/Applications	Number of New Students
2008	25%	18
2009	24%	17
2010	20%	15
2011	17%	12
2012	18%	19
2013	21%	21
2014	12%	7
2015	12%	12

[gughok]

Important fact about the graduate admissions process: committees hedge the number of acceptances they send out against the proportion of matriculation they expect.

So suppose a university wants fifteen graduate students for the next year - but usually only half of admitted students matriculate. Then they might accept around thirty applicants with the gamble that half will turn down the offer. What if, one year, around twenty students matriculate? "No problem", they say, "it's only one year". The next year, however, another twenty matriculate. Now the program is in a position where they have ten more students in a five year period than they had planned. This is bad.

For their next few years, then, they will likely send out fewer acceptances, probably still with the expectation that only half will matriculate, but now forced into the position of aiming to have fewer matriculations, too.

Of course, this is just one possible explanation - but looking at the numbers, they fit the theory: there are consistently between 12-18 new students every year, around the 15 mark. Then, two years in a row, we see a huge excess of 19 and then 21. The 7 students the next year might reflect the department's effort to rein things in.

Again, this isn't necessarily what happened - but it happens a lot.

[TakeruK]

The numbers by themselves just show that 2014 and 2015 are marginally different from the six years before that. The six year average over 2008-2013 is 17 students per year, so if you assume it is a Poisson process (not exactly perfect but a good approximation), then there is a 2-in-3 chance that any given year would be different by 4 students in either direction and 1-in-20 chance that it would be different by 8 students. 2014 could be the 1-in-20, and 2015 is definitely within the 2-in-3 chance. 

So, by itself, I don't think the numbers yet indicate a significant trend. 

However, this trend along with some other correlation might indicate something. For example, you should consider the number of faculty members at the school. If some faculty left or retired in 2013 or so, then it would make sense that the number of students accepted is declining.

Or, if a large number of faculty members took sabbatical in 2014, then they might not have taken new students and that year might be abnormal.

Or, if a large number of students expected to graduate in 2013 delayed their graduation, then 2014 might have a smaller class so that there is enough funding to go around. 

Or, as has happened at my school, we had one year that was smaller than the others and the reason was partly due to a decrease in NASA funding that particular year (the one with the government shutdown) and also a dip in applicant quality. Top programs, like the one you are providing numbers for, might choose to just admit fewer students if there aren't enough that are at the calibre of the former students (i.e. saving that funding for next year). They are not going to accept students that are simply "good enough".

So, I think unless you find other correlations to go with the numbers, I would not think the drop is drastic nor significant.

Finally, you'll notice that I chose to look at the absolute number of students rather than the percentage drop. I think absolute numbers are more meaningful because all of the factors that constrain admission deal with absolute numbers (e..g "How many students can we fund?") and not "Let's accept the top X%". You'll notice that it seems like the number of applications has gone up! In 2008, 72 people applied; but in 2015, 100 people did (although 2014 is a weird year in this regard too, only 58 people applied).

Instead, I would just look at this table and say, on average, this school admits 16 students per year.

[noumenope]

For their next few years, then, they will likely send out fewer acceptances, probably still with the expectation that only half will matriculate, but now forced into the position of aiming to have fewer matriculations, too.

Of course, this is just one possible explanation - but looking at the numbers, they fit the theory: there are consistently between 12-18 new students every year, around the 15 mark. Then, two years in a row, we see a huge excess of 19 and then 21. The 7 students the next year might reflect the department's effort to rein things in.

This totally makes sense. I guess there's no real way to know if (assuming your assumptions are correct) 2 years of low acceptances make up for it enough that they feel they can accept and matriculate more students this year.

Finally, you'll notice that I chose to look at the absolute number of students rather than the percentage drop. I think absolute numbers are more meaningful because all of the factors that constrain admission deal with absolute numbers (e..g "How many students can we fund?") and not "Let's accept the top X%". You'll notice that it seems like the number of applications has gone up! In 2008, 72 people applied; but in 2015, 100 people did (although 2014 is a weird year in this regard too, only 58 people applied).

Instead, I would just look at this table and say, on average, this school admits 16 students per year.

Great idea to use Poisson to analyze the distribution. But I think your calculation of how many people applied each year is off. Usually the number of new students (in this field's programs) is equal to about 40-50% of the number of students they accepted for admission. But proportionately speaking, all of what you said applies and makes sense.

[TakeruK]

But I think your calculation of how many people applied each year is off. Usually the number of new students (in this field's programs) is equal to about 40-50% of the number of students they accepted for admission. But proportionately speaking, all of what you said applies and makes sense.

You're right! I misinterpreted "admitted/applications" as in the number of people that were admitted (i.e. matriculated) into the program, but I see now that it is the percentage of people that got an offer  Oops!