Applying for PhD/Masters in Statistics

[prospectivestudent89]

Hello,

I graduated from the University of Connecticut in May of 2011. I received my BA in Economics with Honors and only a 3.64 GPA (I was unfocused until Senior year and had bad years Freshman/Junior years, family illnesses did affect me I think). I am currently pursuing my MS in Mathematics at Fairfield University. I hope to have over a 3.9 GPA by graduation next spring. I took the GRE last summer with little preparation and earned a 790Q/450V/4.0AWA. I bought a book on vocabulary and am hoping to get my verbal score up. I also want a perfect score on the quant. I will be retaking the general GRE in either the summer or fall. I was hoping to apply to PhD/Masters programs for the Fall of 2013. I would be willing to get a masters before a PhD if it was from a top tier school like Harvard, Stanford, Berkeley, etc. However, what would be my chances of getting into a top tier school even for the masters program? Do I have to take and ace the Math GRE? Do I have no shot?

Thank you

[Matt W]

What are your math courses, textbooks used and grades?

[prospectivestudent89]

Freshman:

B+ In Calc 1, Calculus Early Transcendentals (Stewart)

B in Calc 2, Calculus Early Transcendentals (Stewart)

Senior:

A in Cal 3, Calculus Early Transcendentals (Stewart)

A in Applied Linear Algebra, Linear Algebra and it's Applications (Lay)- There weren't actually many applications.

UCONN Continuing Studies (Summer after graduation):

A in Probability, Elementary Probability for Applications (Durrett)- It's calculus based.

A- in Elementary Differential Equations (ODE), Differential Equations (Blanchard)

Fairfield (Likely grades)

A in Applied Math II (PDE), An Introduction to Partial Differential Equations with Matlab (Coleman)

A- in Complex Analysis, Complex Variables and Applications (Brown&Churchill)

As you can probably tell I had much better focus Senior year. I never should have gotten Bs in Calc 1&2.

Edited April 26, 2012 by prospectivestudent89

[lonelymonk]

One need not have a cent score in sub GRE to get in to top places. However, your math background needs to be decent. As the above person has correctly pointed out , it will help if you list the courses you have taken, the topics covered, texts used .

[lonelymonk]

I see you haven't taken any Real Analysis courses nor any Abstract Algebra. The courses that you mentioned are offered in an engineering program as well. I suggest you apply for Masters. I am of the opinion that a Phd program requires more background esp a truly advanced Calculus course along with an introductory analysis course .

[prospectivestudent89]

I see you haven't taken any Real Analysis courses nor any Abstract Algebra. The courses that you mentioned are offered in an engineering program as well. I suggest you apply for Masters. I am of the opinion that a Phd program requires more background esp a truly advanced Calculus course along with an introductory analysis course .

I was actually of the opinion that Analysis and Advanced Calculus are the same. Do you think I'm qualified for a top masters program though?

Edited April 26, 2012 by prospectivestudent89

[lonelymonk]

Yes. The master's program at the top universities is very competetive. You will have to very well in your GRE

[prospectivestudent89]

Measure Theory and Functional Analysis? Those are PhD level math courses. I guess the School Statistics websites aren't telling the truth when they say all you need is Cal 1-3 and Linear Algebra. Thanks for the help.

Edited April 26, 2012 by prospectivestudent89

[lonelymonk]

Apologies. I thought you wanted to apply to a Math Phd Program. I see that you are currently pursuing a masters degree. What all courses are you taking?

Edited April 27, 2012 by lonelymonk

[wine in coffee cups]

Definitely take advanced calculus/real analysis (whatever the first proof-based calculus course is called at Fairfield). Though I don't think it's needed for masters programs, it won't hurt, and you'll need it if you do apply for PhD programs. An analysis course covering measure theory would be a plus for PhD admissions but not necessary. Abstract algebra and functional analysis are not necessary even for PhD admissions. If there is an advanced linear algebra course, that would be helpful but not necessary.

I notice a conspicuous lack of actual statistics courses, though! Isn't an introductory stats course usually a prerequisite for econometrics (which would have been required for your major)? I'm a little puzzled, a more complete academic history would be helpful here.

But stepping back even more: why statistics? Tell me the gist of what you think you'll say in your statement of purpose. How'd you get from economics to the math MS to statistics? How do you know you want to do research in statistics? What are you hoping to do with a masters or PhD in statistics?

[prospectivestudent89]

Definitely take advanced calculus/real analysis (whatever the first proof-based calculus course is called at Fairfield). Though I don't think it's needed for masters programs, it won't hurt, and you'll need it if you do apply for PhD programs. An analysis course covering measure theory would be a plus for PhD admissions but not necessary. Abstract algebra and functional analysis are not necessary even for PhD admissions. If there is an advanced linear algebra course, that would be helpful but not necessary.

I notice a conspicuous lack of actual statistics courses, though! Isn't an introductory stats course usually a prerequisite for econometrics (which would have been required for your major)? I'm a little puzzled, a more complete academic history would be helpful here.

But stepping back even more: why statistics? Tell me the gist of what you think you'll say in your statement of purpose. How'd you get from economics to the math MS to statistics? How do you know you want to do research in statistics? What are you hoping to do with a masters or PhD in statistics?

I'm very interested in applied statistics. I am most interested in statistical trading and sports statistics, particularly baseball. I could see myself working for a baseball organization one day. I think I have some new ideas that haven't been implemented yet. I also love basketball, but haven't thought of any unique evaluation ideas yet. If I cannot go into sports statistics I'd like to go into trading. I need a much firmer understanding of advanced statistics first though. A PhD is probably the best way for me to work and learn from the best statisticians. It would also provide me with the best research experience. To be honest I think I made a mistake going for economics. I was actually doing economics and premed for a while, but then I learned I didn't want to be a doctor junior year and was lost. I'm going for my Math MS to make up for my lack of math background right now. If I could do it all over again I would have double majored in Applied Math and Statistics. Then I might have gotten a minor in Economics.

Edited April 27, 2012 by prospectivestudent89

[prospectivestudent89]

Apologies. I thought you wanted to apply to a Math Phd Program. I see that you are currently pursuing a masters degree. What all courses are you taking?

PDE and Complex Analysis. Sometimes the tougher Complex Analysis problems go over my head, because it follows the Real Analysis course which I never took. I also never had a course in writing Mathematical Proofs which I want to take.

[lonelymonk]

I suggest that you take a course in proof based Mathematical Analysis. That will give you a strong foundation which will be very helpful in your chosen career. If possible, after the introductory Real Analysis, go for a Measure Theory course. It will also give you an edge over other people applying for Phd positions. As for the GRE, it is not that difficult. Some of the questions in Sub GRE are from Analysis, Topology( of Metric Spaces) and algebra. However, 50 % of the paper is calculus(one/multi variable) and a fair amount comes from Linear Algebra. So I don't think you should face major problems

[wine in coffee cups]

Okay, thanks for the additional information. I've got some more thoughts and questions for you. Long post warning: I'm wordy, I used to work as a career advisor, and I just went through the grad school application process myself so I'm bursting with advice to inflict on others.

First, how sure are you that it's statistics you want to study and not one of your specific areas of application? I think it's a question that everyone with applied leanings should consider. You didn't mention taking any actual statistics classes which makes me wonder how much you've engaged with the subject beyond liking some of the areas it is used in. You might find that a masters in mathematical finance or applied math is more appropriate to your preparation, interests, and career plans than statistics.

Sports statistics is niche and I suspect PhD programs might not likely take you seriously if that's what you say you want to study. Maybe there are some academic researchers engaging with the topic (at Wharton maybe?), but you should figure out whether this is the case or not. I also would guess they are more likely to be in economics or business departments than in statistics departments. My impression is that it's more a hobbyist area and that professional sports analysts/Nate Silver types are largely self-taught. I doubt you'd need a PhD if that's what you wanted to do professionally and that a master's in stats would be a better idea if only to get more stat training. Here is a place to start researching this path: http://www.amstat.org/sections/SIS/

While financial statistics is certainly an active area of research in many statistics departments (e.g. time series, high frequency data), that particular application might not be well represented everywhere, so you'd want to do more careful research than just getting fixated on the big names. I think you'll find that some of those turn out not to be such a good fit.

Spend this spring and summer doing due diligence. As you look at different programs, think about what you would specifically say in your essays if you applied. Try even starting some outlines with bullet points of what you would bring up. Beefing up your math preparation won't overcome a fit issue and I think people going into math-related fields underestimate how much this matters.

Don't forget that getting a job in finance after finishing your master's might be a much better idea than more grad school right away! If that's what you want to do and you don't need additional training -- and I don't think you do -- then may as well try that out. You do have fairly easy access to NYC and Boston for interviews, after all.

About the GRE math subject test: do not underestimate how much of a pain in the ass this is and how little reward you will probably get from it. Yes, if you do well on it and apply to PhD programs, it will help with any doubts about your mathematical preparation. But that is such a big "if" that I think you won't want to bother with all the effort needed to perform at a level that will work in your favor, and very few places require it. Given that the population who takes the math subject GRE is a very self-selected group -- mostly pure math majors who like the subject enough to want to pursue a PhD in it and have more advanced classes than you and competitive math experience -- it's just really hard to get a good percentile relative to them even with lots of prep.

[lonelymonk]

@ Wine in Coffee cups:

Your advice is spot on and excellent. I concur with you. Although I still feel that Sub GRE is not that difficult. With a bit of practice, it is easy to get a competitive percentile. 75 % of the paper is linear algebra/calculus. It is imperative that one takes timed tests to gauge the preparations.

[prospectivestudent89]

Okay, thanks for the additional information. I've got some more thoughts and questions for you. Long post warning: I'm wordy, I used to work as a career advisor, and I just went through the grad school application process myself so I'm bursting with advice to inflict on others.

First, how sure are you that it's statistics you want to study and not one of your specific areas of application? I think it's a question that everyone with applied leanings should consider. You didn't mention taking any actual statistics classes which makes me wonder how much you've engaged with the subject beyond liking some of the areas it is used in. You might find that a masters in mathematical finance or applied math is more appropriate to your preparation, interests, and career plans than statistics.

Sports statistics is niche and I suspect PhD programs might not likely take you seriously if that's what you say you want to study. Maybe there are some academic researchers engaging with the topic (at Wharton maybe?), but you should figure out whether this is the case or not. I also would guess they are more likely to be in economics or business departments than in statistics departments. My impression is that it's more a hobbyist area and that professional sports analysts/Nate Silver types are largely self-taught. I doubt you'd need a PhD if that's what you wanted to do professionally and that a master's in stats would be a better idea if only to get more stat training. Here is a place to start researching this path: http://www.amstat.org/sections/SIS/

While financial statistics is certainly an active area of research in many statistics departments (e.g. time series, high frequency data), that particular application might not be well represented everywhere, so you'd want to do more careful research than just getting fixated on the big names. I think you'll find that some of those turn out not to be such a good fit.

Spend this spring and summer doing due diligence. As you look at different programs, think about what you would specifically say in your essays if you applied. Try even starting some outlines with bullet points of what you would bring up. Beefing up your math preparation won't overcome a fit issue and I think people going into math-related fields underestimate how much this matters.

Don't forget that getting a job in finance after finishing your master's might be a much better idea than more grad school right away! If that's what you want to do and you don't need additional training -- and I don't think you do -- then may as well try that out. You do have fairly easy access to NYC and Boston for interviews, after all.

About the GRE math subject test: do not underestimate how much of a pain in the ass this is and how little reward you will probably get from it. Yes, if you do well on it and apply to PhD programs, it will help with any doubts about your mathematical preparation. But that is such a big "if" that I think you won't want to bother with all the effort needed to perform at a level that will work in your favor, and very few places require it. Given that the population who takes the math subject GRE is a very self-selected group -- mostly pure math majors who like the subject enough to want to pursue a PhD in it and have more advanced classes than you and competitive math experience -- it's just really hard to get a good percentile relative to them even with lots of prep.

Wow, thanks for the advice. One of things I have done is look at the research interests of the faculty on the school's website. There's one professor at Berkeley who says he's interested in soccer statistics and another professor at UPenn who labels one of his interests as baseball statistics. So I know that there are definitely professors out there interested in sports. I'm hopeful that I'd catch the eye of a passionate sports fan who is also a statistics professor.

I think that sports statistics can be very complex. It's not just data collecting like some think. I want to develop new statistical measures to get an edge on other teams. With baseball statistics I'd have to deal with finite data, correlation, distribution theory, optimization, and logic. There would also be game theory involved. I'd have to know if what a player accomplishes is statistically significant. I don't know how familiar you are with baseball, but I'm a Yankees fan and one of the things that caught my eye was last year I heard General Manager Brian Cashman explain why he went after Outfielder Nick Swisher. The year before the Yankees traded for Swisher he hit .219/.332/.410. However, the Yankees went after him, because they used statistics to determine that he was the second unluckiest hitter in baseball in 2008. They robbed the White Sox blind in that trade. In the 3 years he's been a Yankee his worst year was 2011 where he hit .260/.374/.449.

However, I'm interested in studying statistics more generally so I can apply the methods I learn. I think it's important for me to get a broader perspective. I know that there's simply a lot of statistical techniques I just don't know about right now. However, we used a lot of the statistical methods (correlation, hypothesis testing, dummy variables) in econometrics. I also became more interested in studying distributions after take probability theory and I'm curious as to how I can tackle more advanced problems involving distributions of data. I know that with sports that there will often be several variables and I'll have to find the optimal solution looking at multi-dimensional data where some data will have more weight than others based on correlation and other statistical reasons.

Thinking deeper about my future, I think I want to start with a Masters and can definitely see myself moving onto a PhD. I think a PhD gives an even more in depth understanding as well as serious research experience that a Masters doesn't offer. If I were in a PhD program I could definitely see myself studying statistics more generally. However, the most beautiful thing about math/statistics to me is the application. To combine it with my passion for sports would be a dream come true.

Edited April 29, 2012 by prospectivestudent89

[ANDS!]

Sports statistics is niche and I suspect PhD programs might not likely take you seriously if that's what you say you want to study.

I don't agree with this at all. There are several instructors at top universities who have written papers on sports statistics; it's all application. If this is truly what the OP wants to do, and they realize they need a strong background in Statistics Theory, it will hardly be counted against their application.

So I know that there are definitely professors out there interested in sports. I'm hopeful that I'd catch the eye of a passionate sports fan who is also a statistics professor.

Of course there are. Sports is no different than politics is no different than industrial machining is no different than. . .blah blah blah. You are simplying honing in what you want your focus to be. Your potential advisors don't have to be Mets fans to be able to understand the metrics underneath what you are trying to study (so long as you clearly define them).

As for your courses, you want to - if at all possible - get upper division linear algebra under your belt. Lay is "fine" to a point, but that point arrives pretty quick. Most folks feel the prereq for an upper division Linear Algebra course would be one semester of Abstract Algebra (up to groups/rings), but I think thats ridiculous. All you really need (especially if you've done some light analysis) is knowledge on how to write a proof.

Seeing as you are in a Math Masters program, you'll of course have to get at least a semester of Analysis, so you should be fine there. I would also take the graduate (not doctoral) level Probability/Statistics sequence to make up for your lack of statistics exposure. Plus it will get you a headstart.

As for your continued prep, you don't need Abstract Algebra or DE though I'm sure you'll have to take graduate Algebra for your degree. Just take as minimal an amount as you have to.

You don't need a perfect Quant GRE score; you will need to bring up your Vocab, and if you plan on applying straight to a PhD program in Stats - some schools are going to want the subject. Don't get a misinformed opinion about what your score NEEDS to be. . .people get into places scoring in the 30th percentile on that thing (but thats if the program even requires you to take it).

[prospectivestudent89]

I don't agree with this at all. There are several instructors at top universities who have written papers on sports statistics; it's all application. If this is truly what the OP wants to do, and they realize they need a strong background in Statistics Theory, it will hardly be counted against their application.

Of course there are. Sports is no different than politics is no different than industrial machining is no different than. . .blah blah blah. You are simplying honing in what you want your focus to be. Your potential advisors don't have to be Mets fans to be able to understand the metrics underneath what you are trying to study (so long as you clearly define them).

As for your courses, you want to - if at all possible - get upper division linear algebra under your belt. Lay is "fine" to a point, but that point arrives pretty quick. Most folks feel the prereq for an upper division Linear Algebra course would be one semester of Abstract Algebra (up to groups/rings), but I think thats ridiculous. All you really need (especially if you've done some light analysis) is knowledge on how to write a proof.

Seeing as you are in a Math Masters program, you'll of course have to get at least a semester of Analysis, so you should be fine there. I would also take the graduate (not doctoral) level Probability/Statistics sequence to make up for your lack of statistics exposure. Plus it will get you a headstart.

As for your continued prep, you don't need Abstract Algebra or DE though I'm sure you'll have to take graduate Algebra for your degree. Just take as minimal an amount as you have to.

You don't need a perfect Quant GRE score; you will need to bring up your Vocab, and if you plan on applying straight to a PhD program in Stats - some schools are going to want the subject. Don't get a misinformed opinion about what your score NEEDS to be. . .people get into places scoring in the 30th percentile on that thing (but thats if the program even requires you to take it).

Thanks for the advice. Is the GRE Verbal really taken that seriously? Many of schools websites say you should aim for a certain score, because it implies "good communication skills". I just don't get how anybody could feel this way. To me it implies wasting months studying words that I'll never see again. Maybe somebody could convince me otherwise.

[ANDS!]

I found the NEW GRE Vocab to be far easier than the old one. The old one (at least the practice exams) had those ridiculous "which words most is like the other" garbage. . .I do not remember much of that on the revised GRE I took. There were a lot of sentence completion and quite a fair bit of reading comprehension. The sentence completion didn't contain too many foreign words, but you could still eliminate most of the easy words.

As for what they look for - I dunno. I really don't think a GRE is going to sink someone; especially not the Verbal. A poor Quant and Analytical yes. If you can finagle taking the next subject GRE, that I think would look a lot better than any regular GRE.

If you're looking for a Masters, disregard above and just finish strong in your current studies and save yourself the 160 bucks retaking it.

Edited April 29, 2012 by ANDS!

[wine in coffee cups]

prospectivestudent89, thanks for the added information! I'm feeling more optimistic about your fit in statistics with these details.

Wow, thanks for the advice. One of things I have done is look at the research interests of the faculty on the school's website. There's one professor at Berkeley who says he's interested in soccer statistics and another professor at UPenn who labels one of his interests as baseball statistics. So I know that there are definitely professors out there interested in sports. I'm hopeful that I'd catch the eye of a passionate sports fan who is also a statistics professor.

Good start! I'd keep on researching to try to select a set of at least a half dozen programs (you probably want more) that are good matches research-wise with a range of selectivities. Said Berkeley prof, if it's who I'm thinking of, seems somewhat likely to retire in the near future (DOB in the 1930s, you do the math...), so keep that in mind. I think Wharton a good fit for your interests, though very hard to get into. Cultivate a balanced mix of programs since it's so hard to predict how your application will be received.

I think that sports statistics can be very complex. It's not just data collecting like some think. I want to develop new statistical measures to get an edge on other teams. With baseball statistics I'd have to deal with finite data, correlation, distribution theory, optimization, and logic. There would also be game theory involved. I'd have to know if what a player accomplishes is statistically significant. I don't know how familiar you are with baseball, but I'm a Yankees fan and one of the things that caught my eye was last year I heard General Manager Brian Cashman explain why he went after Outfielder Nick Swisher. The year before the Yankees traded for Swisher he hit .219/.332/.410. However, the Yankees went after him, because they used statistics to determine that he was the second unluckiest hitter in baseball in 2008. They robbed the White Sox blind in that trade. In the 3 years he's been a Yankee his worst year was 2011 where he hit .260/.374/.449.

However, I'm interested in studying statistics more generally so I can apply the methods I learn. I think it's important for me to get a broader perspective. I know that there's simply a lot of statistical techniques I just don't know about right now. However, we used a lot of the statistical methods (correlation, hypothesis testing, dummy variables) in econometrics. I also became more interested in studying distributions after take probability theory and I'm curious as to how I can tackle more advanced problems involving distributions of data. I know that with sports that there will often be several variables and I'll have to find the optimal solution looking at multi-dimensional data where some data will have more weight than others based on correlation and other statistical reasons.

Thinking deeper about my future, I think I want to start with a Masters and can definitely see myself moving onto a PhD. I think a PhD gives an even more in depth understanding as well as serious research experience that a Masters doesn't offer. If I were in a PhD program I could definitely see myself studying statistics more generally. However, the most beautiful thing about math/statistics to me is the application. To combine it with my passion for sports would be a dream come true.

These are great points to formalize and include in your statements. Showing your enthusiasm for statistics as expressed through the lens of baseball should help you connect with your readers.

As for your courses, you want to - if at all possible - get upper division linear algebra under your belt. Lay is "fine" to a point, but that point arrives pretty quick. Most folks feel the prereq for an upper division Linear Algebra course would be one semester of Abstract Algebra (up to groups/rings), but I think thats ridiculous. All you really need (especially if you've done some light analysis) is knowledge on how to write a proof.

Seeing as you are in a Math Masters program, you'll of course have to get at least a semester of Analysis, so you should be fine there. I would also take the graduate (not doctoral) level Probability/Statistics sequence to make up for your lack of statistics exposure. Plus it will get you a headstart.

As for your continued prep, you don't need Abstract Algebra or DE though I'm sure you'll have to take graduate Algebra for your degree. Just take as minimal an amount as you have to.

Completely agree with this course advice.

You don't need a perfect Quant GRE score; you will need to bring up your Vocab, and if you plan on applying straight to a PhD program in Stats - some schools are going to want the subject. Don't get a misinformed opinion about what your score NEEDS to be. . .people get into places scoring in the 30th percentile on that thing (but thats if the program even requires you to take it).

I still feel that the subject test is not worth the effort unless he is definitely going to apply to a program that requires it. I had a 58th percentile from back in college and was told by my former prof that it wasn't going to help my applications. Besides, looking at how others' stat PhD apps turned out this year (here and at mathematicsgre.com), even a very good subject score doesn't seem to help that much and not submitting one doesn't actually seem to hurt. Everything else seems to matter so much more: your recommendations (above all), your grades, and your statements. Say you go through all the effort to prep and take it and get, like, 35th percentile. What do you do with that? That's not a bad score per se (given the population who takes the test, as I said before), but that's probably not going to open doors for you that weren't already open without it, you know?

[mathgeek282]

ANDS while i agree with you about sports being important and there being professors who are interested in it, i also think wine in coffee cups is right insofar as i think that in your statement of purpose you might want to generalize and say you interested in the social sciences, with particular interest in sports and how you experiences with sports (in particular the statistical element of it) is what has excited you and let you know that statistics is what you want to pursue. That is, i dont think you statement of purpose should be too sports oriented (definitely mention it as a passion but dont say its your sole interest....)

Thats just my read. I can see how it could come off to some universities as someone who doesn't exactly know what they are getting themselves into with a statistics phD. So just make sure you are careful when writing your statement of purpose. Those and recommendations are very important. Good luck

[cyberwulf]

mathgeek is right. For better or worse, sports statistics is not viewed as a "serious" sub-discipline of statistics (as opposed to polisci stat or industrial stat, say) by the vast majority of academics. True, a number of well-known faculty members have written about sports, but these are mostly "hobby" papers that don't enhance their academic reputation.

[ANDS!]

I'm not suggesting the OP tailor their personal statement or their interest in post-graduate work solely around finding academics who are doing hardcore research in sports-statistics; simply that their focus in theoretical stats can be informed by their interest in sports.

[prospectivestudent89]

It sounds like it will come down to how open minded the professors are in the program. If the professors are stuck in the mindset that applied statistics are only worth being seriously studied in more important areas then I don't think I'd want to work with those professors anyways. If they are into sports and want to try something different then I could be a potential fit for the program. Who knows? Maybe something found in the area of sports statistics could lead to advancements in more important things...crazier things have happened.

[wine in coffee cups]

It sounds like it will come down to how open minded the professors are in the program. If the professors are stuck in the mindset that applied statistics are only worth being seriously studied in more important areas then I don't think I'd want to work with those professors anyways. If they are into sports and want to try something different then I could be a potential fit for the program. Who knows? Maybe something found in the area of sports statistics could lead to advancements in more important things...crazier things have happened.

Crazy things happen but you've got to be realistic going into this. Google homework for you: has anyone written a statistics dissertation in the past, say, 10 years with an emphasis on sports applications? If so, read what comes up and see if that gives you some better perspective on what you're potentially getting into. (And if not, then you need to re-think stats PhDs.)