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I am an undergraduate mathematics student who is looking to apply to a Statistics PhD program. I asked a few professors how much letter of recommendation help a student get in to a PhD program and I was told the following.

Not much. Often professors don't want to insult a student, so they write good letters. Lots of people get good letter, yours won't make a difference.

and

Letters of recommendation are everything. They practically are your application.

and

They help some, but it depends on who it is from. If it is from a stat professor that is good. A math professor is OK too, but stat would be preferred. If they are not stat or math, they won't care at all.

As you can imagine, I am now even less clear of how much a good letter helps.

Is it true letters of practically make or break your application? Or are they simply a formality?

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    You should say which country you are talking about. The perception of LoRs is highly country-specific. The first statement sounds pretty european (maybe asian), the second and the third sound more US-centric. – xLeitix Sep 21 '14 at 20:47
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    @Enthusastic the 'statistics' tag isn't supposed to be about statistics as a field of study; it's about the use of statistics in academia/statistics about academia. (We don't really have discipline-specific tags for subdisciplines.) When it is used about statistics as a discipline, it's an incorrect usage. (Actually, the tag as currently defined is ambiguous and needs some cleanup) – ff524 Sep 21 '14 at 22:22
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I have no direct experience with statistics programs, but I know of no reason to think they differ from math programs in this respect. Assuming that's the case, letters of recommendation are absolutely critical, at least in U.S. universities. I agree with the person who told you they practically are your application, and I'm mystified by how someone could tell you they make no difference. (I wonder whether it's someone who has never served on an admissions committee or was educated in a very different system.)

It's true that just about everyone gets what might appear to be good letters. The issue isn't whether they say bad things about you, but rather how strong they are and how compelling a case they make. I've certainly seen many cases of letters written by the same person that differ enormously in their effect, even though they are all nominally positive.

The third piece of advice you received in no way contradicts the second. It's not enough for a letter just to include flattering comments about you. It needs to make a compelling case for why you will be successful in statistics, written by someone who knows exactly what it takes to succeed in this field, has seen other strong students to whom you can be compared, and has a reputation to protect that will keep them from exaggerating or trying to manipulate the admissions committee. A senior statistician is the best case, but a junior statistician or a mathematician may also be able to do a fine job. A letter from a chemist will not be helpful, and a letter from a professor of literature, no matter how enthusiastic it is, will hurt your case (by demonstrating that you have no idea how the application process works or that you couldn't find anyone more relevant who thinks highly of you).

Exactly what is required depends on where you are applying. At the top departments, you need letters that make a very strong case indeed. Even outstanding students will be rejected, and you need letters that set you apart from the others. At much lower ranked departments, it might be possible to make a favorable impression based largely on grades and test scores, but even then you'll still need good enough letters. (The bar will just be lower.)

  • I would disagree that a letter from someone outside math or stats would make a difference. A letter from someone with whom you worked on a research project would be valuable in commenting on general research skills, habits, and temperament. These shouldn't change when one changes topics. – aeismail Oct 9 '14 at 16:50
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    @aeismail: My impression is that they could change a lot. Having done wonderful research in history or experimental biology would carry little weight in math admissions (the skill set, temperament, etc. sound really different - perhaps I'm wrong about that, but I'd bet it would be a commonly held belief among mathematicians). It could help establish that you are smart and hard working, but the application isn't likely to go well if there isn't already plenty of other evidence for that, and a letter from another field seems much less likely to be the deciding factor in favor of a candidate. – Anonymous Mathematician Oct 9 '14 at 17:25
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This is a piece of my personal experience: when I was admitted to a top 15-ish department of statistics in the U.S., I was told (a bit later, when I came and chatted with the graduate studies director) that a valuable weight in support of my application came from (1) a professor in Econ department who was not related to stat department but who knew (2) the author of the reference letter, another econometrician from Europe, (3) whose book I was then translating into Russian (so I kept bugging person 2 with typo clarifications, suggested examples, etc.). Person (1) was a better statistician than many, with several cool computational methods under his belt, a couple of very rigorous books, and known for teaching measure-theory-based probability to his econ students (if my memory serves me right, undergraduate students).

So I would say that Opinion 3 is probably misplaced. A quantitative biologist may be able to say more about you as a statistician (i.e., a person who has to combine data, a bit of substantive expertise, computing, and statistical methods) than your abstract algebra teacher.

Generally, as others suggested, this depends on the culture of a particular institution. Some do look at the letters, some don't. Since you don't know which side a particular school falls into, treat them as if they are your application.

  • How letters are viewed definitely depends upon the country, but within the US does it depend "on the culture of a particular institution"? In particular (unless I misunderstood?) you seem to suggest that there are some US statistics departments who don't look at recommendation letters. Really?? – Pete L. Clark Oct 9 '14 at 15:57
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Others may have different views but for me, if you are about to admit someone you know nothing about for a long term commitment, you can only rely on some objective and subjective sources:

  • Academic record.

  • Recommendation letters.

  • Interview.

All are important. Letters tend to be standard in the sense that everyone writes about how good the candidate is (even some supervisors make the future candidate write their own letters and then they will just sign it!). However, letters give you the opportunity to directly contact the person recommending the candidate, and ask them about specific aspects you may be worried about. For example any character flaws that can be hidden in the interview and do not show in the academic record (and most likely where not included in the recommendation letter). Or some remarkable skill that was not highlighted enough in the recommendation letter but you consider very important. In summary, it is important to have the opinion of a third person that knows the candidate. Recommendation letters may be an important source of information when accepting a Ph.D. candidate in particular and when hiring someone in general.

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