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Most of the schools that I've looked at for PhD programs in Computer Science have between a 9-15% acceptance rate. I've noticed similar acceptance rates for other programs outside of computer science; yet almost everyone that I've ever spoken to has only applied to a handful of schools. This just doesn't make sense to me.

Let's just say that each school that I apply to has ~15% acceptance rate, then if I only apply to only 6 schools, I have roughly a 63% chance of getting accepted to at least one (1-probability of getting declined everywhere). That doesn't seem horrible, but if I know I want to do a PhD, I would like to have much higher odds, plus most of the programs are closer to a 10% admissions rate. I understand that applications are costly both monetarily and temporally speaking, but having a 37% chance of not getting into any programs is pretty bad. Whereas if I apply to 14 schools, I have about a 10% chance of not getting accepted anywhere. Can someone please explain the thought process behind this?

  • 37
    PhD students are not chosen randomly from those who apply! – boscovich Nov 11 '13 at 10:15
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    Your assumption that admission decision is independent is wrong. – John Hass Nov 11 '13 at 10:30
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    People only apply to a few select programs because they are looking to do a PhD on a topic that interests them. If you are happy to work on a huge number of topics, you may not be focused enough to start a PhD. – StrongBad Nov 11 '13 at 13:11
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    @daniel: Maybe this varies by field. In mathematics (in the US) I would say it's the minority of students who enter a PhD program knowing what they want to work on, or even in what area. Of those who do know, most change their mind. So at least in mathematics, not having a focused sense of what you want to work on is not necessarily a danger sign. – Nate Eldredge Nov 12 '13 at 5:51
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    Surprised that no one pointed out that it's not just, "I want to get a Ph.D". The PLACE where you get into matters, sometimes a lot, and often times more than the fact that you'll "get a Ph.D". – Irwin Nov 14 '13 at 17:40
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Although, I like your way of analytical thinking, some ouf your assumptions do not hold:

  1. Selection procedures of PhD programs are not random.
  2. The selection procedure of one PhD program is not independent from other programs, as it is likely based on similar characteristics and markers in your CVs. (Maybe, there is conditional independence given 3, but that is problematic because the value of 3 is relative to the local distribution of 4.)
  3. Your application profile does not change.
  4. You do not know who your competitors are which may also vary between programs (and time).

Therefore, I would assume that people use their applications as measures to test the unknown distribution of the accessibility of PhD programs. Unfortunately, this accessibility changes every term/year because of different populations of applicants. Furthermore, information about the specific demands and requirements of PhD programs is limited because it is time-consuming to look them up and sometimes they are simply hidden. That makes it reasonable to concentrate only on few programs and draw convenient samples. If applicants fail, it is easier to adapt, as your application costs were moderate, and to finally accept that there were better competitors and go on with life.

  • Oddly enough, I am quite familiar with the process, but I didn't know a better way to try to evaluate the probability of getting into an institution, given that I essentially have little to no data. In the least pretentious way possible, I am not worried about getting in, I just know quite a lot of people who only applied to a handful of top programs and was confused as to why they would do so. I guess what it comes down to me is that even if you are a ridiculously awesome candidate, if you only apply to a few schools, isn't there a non-negligible chance that you won't get in anywhere? – Steve P. Nov 11 '13 at 16:51
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    Of course, there is a real chance that you won't get in anywhere. But how can you figure out by yourself that this is due to your sample of programs and not your relative profile? It seems to me that the best strategy is to use some kind of a mixing approach applying at programs with both high/low reputation and high/low specialization. – non-numeric_argument Nov 11 '13 at 16:56
  • Fair enough. That's what I plan to do. – Steve P. Nov 11 '13 at 16:58
  • If I would have known that you ask the question for yourself, I would have answered somewhat less ironic. I hope that you do not feel offended! – non-numeric_argument Nov 12 '13 at 12:57
  • Not at all. It was clever and informative. – Steve P. Nov 12 '13 at 13:03
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There are so many factors you are ignoring in your analysis... No offense but I have to say that your understanding of recruitment is lacking a lot of depth. Recruitment strategies and practices vary quite a bit but below I tried to give some ideas to the shortcomings (IMHO) of your analysis.


TL;DR: Recruitment is a complex procedure that typically has many factors that are asymmetrically known to different parties. Writing applications, personal letters etc is almost an art in itself. Thus it's important to get a better understanding of the system before jumping into conclusions with misleading statistics.


Outcomes

You seem to take the outcome as a binary variable, while for a single application it might be a valid way to see it, for a single applicant it might be misleading. Based on the project at hand and the candidates in question, the fact that you didn't make it for that particular application isn't necessarily independent of any future incidents, or rather the other way around; your future applications will most likely not be independent of the previous one(s).

It's quite the contrary, actually. You might have significantly increased, or decreased, your chances for a future position with the same group, or at another group associated with the one you applied to. That's practically based on the competition (to which you are will be in the dark) for the project you applied to, and to the impression you have left on the admission committee or the individual PI/group leader. It's important to keep in mind that people talk. In other words, your reputation will most likely proceed you, whether that is positive or negative that's a different story.

Fairness

One might like to think otherwise, but life isn't always fair and recruitment is typically one of those scenarios. In most respectable universities, all open positions need to be publicly announced, which means that anyone in the world can practically apply to them. Furthermore, there are usually laws and regulations that are put in place to work against discrimination of any kind.

What might get forgotten, however, is that the projects aren't really randomly devised. It is not that uncommon for a position to be announced so specifically that it's essentially tailor-made for a candidate; practical examples of this case could be the continuation of a master thesis work, or any similar project work. Such a position could be de facto filled months in advance.

If you are applying to a position at a group with no prior knowledge of the place, you might actually be applying to a position that is already filled. However, many PIs use the public application procedure to "scout talent". In other words, you might not be an interesting target for the project/position you have applied to, but you might still be very interesting for an upcoming project (see previous section "Outcomes").

Spamming

If you are looking at numbers only, you might be mislead on accessing the real number of feasible candidates. I might be insensitive, or even offensive to a certain degree, but there are people who do not even read the job description and mass-apply (especially if it's free to apply). I work with bioinformatics, and among the other candidates there were some who apparently: "... always dreamed of the chance to be a radio engineer, and thus would gladly take the opportunity to ..." (I have not seen the application myself, as it'd be a conflict of interests. I heard about this much later at a pub gathering with my colleagues and boss)

You would be muddying the statistics if you count with people that would be sorted out almost immediately.

Hype

Word gets around, quickly... So more and more people want the same thing; "Did you hear {insert_famous_professor} group has announced a new position?!" While that is a normal human behavior, it also points out a fundamental defect in the way we reason; just because something is famous it's not necessarily better than something else that isn't as reknown. At this point it's also worth noting that a successful senior scientist isn't necessarily a good teacher of doing science. The distinction might not be very apparent prior to doing a PhD but a couple of years into academia, you start noticing the difference.

In other words, while most people swarm over a few number of positions, very few apply to many positions elsewhere. Ask any head-hunter (recruitment professionals) and they'll even give you statistics.

Suitability

Call me a snob if you will, but doing a PhD isn't a god-given right to all humans. It's a job, a career path and thus not suitable for everyone. Please note that I do not, in any way, mean that you are not suitable to do a PhD (it would not be my place to make a judgement, even if I knew you in person). I am merely stating that if a person is consistently getting a rejection, the chances are highly likely that the person is being unrealistic, or stronly under/over-valuing his/her skills. The negative effect of over-valuing is obvious, I suppose, but modesty or humility to the extreme could also impair one's chances of getting an acceptance.

Hope it helps!

  • Oddly enough, I am quite familiar with the process, but I didn't know a better way to try to evaluate the probability of getting into an institution, given that I essentially have little to no data. In the least pretentious way possible, I am not worried about getting in, I just know quite a lot of people who only applied to a handful of top programs and was confused as to why they would do so. I guess what it comes down to me is that even if you are a ridiculously awesome candidate, if you only apply to a few schools, isn't there a non-negligible chance that you won't get in anywhere? – Steve P. Nov 11 '13 at 16:50
  • Sure the risk always exists, but a good-enough (at least on paper) and driven candidate should not have a really hard time finding a position, given that it's a VERY narrow, specialised field. – posdef Nov 11 '13 at 17:01
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There are several levels on which one could answer your question:

  • One could say that people (even those applying for graduate school in quantitative fields) typically don't approach things logically. Someone will suggest a number of schools to them, and they will apply without doing such a probabilistic analysis.
  • The statistics you want to do such an analysis properly are just not accessible. I haven't been able to find any graduate programs in math (my subject) that publish admission stats. (EDIT: I was totally wrong about this. It seems that the secret is to look at central rather than department websites. For example, the stats for my department are here) You even if you wanted to carefully analyze things, the data isn't there. I think anecdotally, people have found that 6 or 7 schools with a good range of rankings is good enough. If people were doing this intelligently and still getting in nowhere, I think the CW would change.
  • I think the number of people who only apply to places where they have a 15% chance is small; smart students will apply to a couple of the best places (thus giving a few places very low acceptance rates) but also a range of places with lower ranking and easier admission. If you look at this thread, for example, you'll see very few people rejected from all the places they applied, even though you'll see many rejected from most of them. In general, grad schools outside the very top tier are pretty hungry for good students; admission to a top 5 program is of course very hard. Getting into a top 50 one might be easier than you think.
  • People who only apply to a couple of top places have revealed a preference: they are interested in getting a Ph.D., but only at a top place. This is a reasonable position; I'm not sure what objection you have with it. Just because you can get into some program doesn't make it a good idea.
  • This isn't precisely what Ben Crowell says below, but his comment and post reminded me: people tend to operate on short time horizons. The trouble and expense of more applications is very visible and concrete, and the trade-off of maybe going to a school which is worse on some dimension of prestige/fellowship/fit etc. is very indefinite and far off. Thus, people will tend to focus more on the former and somehow push off the latter to some corner of their mind.

    I've gotten the general sense that undergrads don't have a very visceral feel for how going to a higher vs. lower ranked graduate program affects their chances of success in academia. Of the faculty in my current department, almost all the PhDs from the US are accounted for by the Ivies, the University of California system, Chicago and MIT. At Oregon, where I was previously, I once calculated that half of the US PhDs in the department went to Harvard, MIT, Berkeley or Stanford. One can argue how much of that is selection bias, how much is getting a genuinely different education, and how much is just the power of the name, but I think they all play some part.

  • @BenCrowell I think you're reacting to something offhand which was not my main point (I think we may be interpreting "the best" a bit differently; I mean top 5, not top 20). To rephrase, I think most students very consciously try to include schools where they feel confident of getting in (or at least the schools amongst those which are acceptable which give them the best chance). People who apply to a few top places are telling you what's acceptable to them. – Ben Webster Nov 13 '13 at 5:23
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Others have pointed out that the probabilities are not all independent. Let's say that x is some objective measure of the quality of the program, and let x0 be the quality of a program for which you personally (not everyone in general) have a 50% probability of getting in. Then it may be reasonable to imagine that there is some function P, where P(x-x0) is your probability of getting into that school. P has a plateau at 1 on the left, another plateau at 0 on the right, and a fairly steep "knee" in the middle. If we don't know your x0, then the probabilities of admission are not all independent. But once we know your x0, it may not be unreasonable to assume that the probabilities P(x-x0) for all the different schools are independent. If the assumptions of this analysis are correct, then it explains why rational people would apply to a large number of schools. They're basically picking a whole bunch of schools for which they think P(x-x0) is small but non-negligible, i.e., programs that they judge themselves as just maybe having a chance of getting into. For example, I applied to 14 PhD programs in physics, almost all of them top-20 programs in the US. I also applied to a couple of backup schools that I was pretty sure I would get into. I ended up getting into the backup schools plus exactly one of the top-20 schools.

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