Noise in PhD Admissions

[TroyBarnes]

I'm a long time lurker on the forums. I often see advice, which is to find which departments that have students who have similar profiles as myself. While that advice makes sense to me, it does seem like there is a high level of variability. I've seen someone with a 3.1 GPA and no research experience, make it into several top stats departments, and they stated that their rec letters made their application. I've also seen straight A students with glowing letters, strong math prep, and very optimistic opinions on gradcafe, get rejected from top programs. Additionally, I've seen applicants get rejected by schools in the 50-20 range, but accepted to schools in the 20-10 range. 

Maybe its just my recall bias from scrolling through these forums too much. Maybe its because visitors to this forum are obsessed with going to grad school - no ridicule intended, I am the same. 

But how large is the variability in PhD admissions? How does variability change as a function of US News rankings? What are some reasons the admissions committee would favor the underdog, with a low GPA and less math prep - is it the research fit, given the pinned post on this forum? Also since most of us here have had statistical/math training to some degree, has anyone tried to model this, with maybe something like a logistic regression? P(acceptance) = f(department name, gpa, gre, us news rank, gradcafe sentiment, ... )

 

PS: I am very anxious as I am in the process of applying, forgive me if my questions are too brash.  

[Nothalfgood]

Where are the functional data analysts when you need them?!

My guess is that most variance is explained by recommendation letters. Other criteria like GPA, GRE scores, and statements of purpose seem to typically be used as binary predictors, i.e. some weight is given to an application if the general GRE Q score is above 165, but if it's lower, then there's a weight penalty. Maybe the form of our relationship is something like 

P(acceptance) = 0.01*1_{{GRE Q >= 165}} + 0.01*1_{{GPA >= 3.3}} + 0.01*1_{{SoP not terrible}} + 0.1*(Rec Letters) + c

where the function 1A is the indicator function over the set A, (Rec Letters) is some enthusiasm score for the letters on a scale of 1-10, and c is a bias term.

My takeaway from conversations that I've had with my recommenders lead me to believe that my admission results are mostly out of my hands now. I've already gotten all the grades I'll have before they see my transcript. I've already done whatever research I could finish before they see my CV. They're also more interested in whether my professors think I'm grad school ready than if I am. So now I'm just filling out the paperwork and hoping for the best! It doesn't alleviate all the anxiety for me, but at least I can rest assured that all of the difficult parts of applying are either behind or beyond me now.

[TroyBarnes]

Thanks for the reply. I was thinking the equation would look something like that. After all, if you max out your scores and GPA, you still would not achieve P(accept) = 1. The only way to achieve P=1 is if rec letters >= 0.97 by your model. I've also been told that 0.33 is the highest any applicant can expect for grad admissions; a stat professor and I were basically evaluating the chance I get into at least 1 program. And I suppose the bias term(s) would pool in things like international/domestic applicant, URM/non URM, prestige of previous institutions etc. 

Anyway, thanks for your perspective. Application cycles have always made me nervous since high school days. 

Edited November 18, 2020 by TroyBarnes