statfan

The statistics department at UCLA is not as prestigious as Michigan's and Michigan is generally perceived to be a step above UCLA. That said, Michigan's program should set you up pretty well for academia given their historical strong academic placements. You will have enough time to figure out your research interests and you'll definitely find some professors' research interesting since both programs have many research areas.

UNC's program is inarguable better. They are not even close.

I think overall Toronto is a step above NCSU. As you can see from the faculty list of the statistics department at Toronto, most of them obtained their PhD from top schools in the world and consistently publish at top statistical journals. They even have 2 COPSS award winners. In particular, if you want to specialize in probability, Jeffery Rosenthal is a perfect choice. While NCSU has a good statistics department with a wide range of research areas, the department is generally perceived as more applied with close ties to industry. The academic placements at Toronto are better than those of NCSU.

Some schools do have an initial gpa cutoff and your gpa is around the borderline. If you can make that cutoff, I guess you will not be held back by your overall gpa too much. If you have strong letters and good grades in advanced proof-based courses, you may have a shot at some of the top 20 schools.

Your overall gpa is low but you did well in most math courses, and your ability to do math is what admissions committee mainly cares about. If your bombed electives courses that are not relevant, I don't think it's a big deal. If I were you, I would take more advanced proof-based courses such as grad level real analysis and possibly take the math subject GRE to strengthen my profile. If you do well in them, you should have a decent shot at schools between Penn State and Florida and I think it is not impossible to get into a couple of top 20 programs. However, competition is very stiff in recent years and you should add a few safeties outside of top 50.

You have more than sufficient math background to apply for statistics PhD. It's always good to know more math, and this will help for any quantitative disciplines. Much of the statistics theory is related to real analysis/measure theory, but this doesn't mean that algebra is not or will not be useful. Indeed, algebra is starting to gain its popularity in statistics and there is an emerging area called algebraic statistics. That being said, if you are interested in these courses and have the time, you can take both. However, these are not required for admission to statistics PhD.

There is no actual safe schools for statistics PhD admissions. It does not hurt to try a few reach schools but I would recommend you apply broadly since your math background is weaker than average applicants at those top schools you listed. I would apply to at least 3 schools in Penn State - Florida range.

I would mainly focus on larger programs such as Penn State, NC State, Iowa State etc. These are very solid programs and are easier to get into than their rankings would suggest. Since your math background is a bit thin, I would submit the math GRE score to schools that recommend it. Most test takers of the math GRE test are applying to math PhD. A 76th percentile, by definition, is not a low score, especially with your math background.

I found Daniel's response misleading. A 3.5 GPA from an Ivy is not stellar but good enough for master's admission. Master's programs usually have much higher admission rate than PhD programs and as long as you meet the minimum requirement you will be considered. Coming from an Ivy with decent a GPA helps a lot and I can see you get into top 10 master's programs for statistics.

You have excellent grades in your math and statistics courses. However, your list is very top heavy and your math background is a bit lacking for these top schools for statistics. I noticed that the real/complex analysis courses you took tend to be more computation-focused rather than proof-based. You would be better off if you took the advanced version of real/complex analysis etc. I think slightly lower grades (say 85-90) in more rigorous courses will look more impressive than near perfect grades in easier courses.

I did not get the interview and I am afraid that implies a rejection.

Has anyone heard back from Washington biostatistics?

A quick update: I got 760 on the Math subject GRE test, which is the 72th percentile. I don't know anything about abstract algebra, complex analysis and graph theory, so I consider it an ok but not great score. I already submitted to Stanford and UPenn, and I am wondering if I should submit it to schools that highly recommend the score like Chicago and Washington. When they assess my score, would they take what I have learnt into account?

You have a very good chance of getting into Waterloo. If you are a Canadian PR/citizen, you also have a good shot of getting into u of t. However, without real analysis, it would be difficult to crack top statistics phd programs. You can try to apply a few phd programs but I would mainly focus on masters programs in Canada, as most of them are research based. Assuming you get A's in real analysis and produce meaningful research during your masters, you will stand a chance at almost every top phd program.

The GRE Q is mainly high school level math and it acts as a filter. Almost everyone who applies to stat/biostat phd got a perfect or near perfect score on the GRE Q. That being said, if you score well, it won't help your application. However, a low score is a big red flag and will likely disqualify you immediately. I strongly recommend you to retake it if you have the time and money, and try to get your score over the 90th percentile (which I believe is 166).