@juillet The mathematician part of me would like to clarify some statements. Of course, a 15% acceptance rate can be interpreted as a probability, and we can certainly treat it like one. However, it is a prior probability, because it doesn’t include any information about the applicants. If we did have further information about the applicant, then theoretically we could have computed a posterior probability (or ideally a posterior probability distribution), which combines the prior probability and the conditional probabilities of acceptance, given that information.
What I believe you are saying is that
The applicant has such information, so she does not have the rely upon just the prior. I agree with that. However, since we as commentators don't have detailed information about the applicant or her field of study, all we can really use is a prior probability.
The conditional probabilities of acceptance, given applicant information, are not easy to obtain, which accounts for your statement that the probabilities are "unknown". In other words, you are saying that the confidence interval for any probability estimate might be large. I agree with that too.
What I disagree with is any assertion that probabilistic reasoning is irrelevant either in this situation, or in most situations in life.
I mean it is possible to treat it like an uninformative probability, but that would be an ecological fallacy. Saying that 15% of the people who apply will get accepted is not the same thing as saying that individual students have a 15% chance of getting accepted.
One example is that a student - because of the fit of their research or some other reason - may actually have a higher chance of admission at a school with a lower admission rate. Imagine a program with a 10% admission rate, but where the students’ interests are a good fit for 4 professors, vs. a program with a 20% admission rate but where the student doesn’t neatly fit with any of the PIs there. All other things equal, the student is probably a better fit for the technically more selective program, and may have a better chance of admission there. Some schools also may have higher admission rates for superficial factors, like location. Even though the outward admission rate is, let’s say, 7%, the admission rate of actual qualified applicants (and not people who don’t understand the basic premise of graduate study) may be higher.
That’s what I mean when I say that the probability is unknown - not simply that we as commentators don’t have detailed information, but that the applicant themselves will never really have access to all the information necessary to calculate a hardcore numerical probability of acceptance. They can make a decent qualitative guess based on their application factors, but there are other internal things (who’s going on sabbatical, who missed out on that big grant - or just got one, who internally announced a retirement, who anticipates taking on the president’s daughter as a grad student next year, etc.) they won’t know that also affect who a department takes for students. Often students get denied not because they aren’t excellent students, but because of some internal departmental reason.
As someone with quite a bit of training in quantitative psychology and statistics, I would never contend that
I don’t think it’s helpful for students to ruminate over percentages of admission though; I think thinking about general likelihoods in a qualitative sense is more useful by seeing how the student’s portfolio compares with people who have been admitted in the past. That’s probabilistic reasoning too, just without putting fine numbers on it - thinking about it in broader terms.
I just don’t want students worrying or counting themselves out because they see a number like 5% (aka Stanford’s economics PhD program), especially because they can’t know all the factors that contribute to that 5% or even how many of those 700 applicants are even qualified, competitive applicants.
One other practical matter is whether your student can live on the stipend. Lower ranked programs often have stipends that really aren’t going to cover basic living expenses. Also whether the program offers health insurance if your kid needs it (mine did). A less popular location can be a place where stipend $s go farther, so that can be a bit of a silver lining.
My daughter started her PhD program less than a month ago. One suggestion is to attend at least one summer university program during undergrad. My daughter applied to several, and the one that she attended between junior and senior year is where she ended up for graduate school. She had enjoyed her summer there, and she felt like she knew what she was getting into when she committed her next 5+ years to living and working at the school.
@mommyrocks, try not to worry too much. Your daughter has a great resume and she will have some excellent options.
