With an undergraduate degree in Statistics, you can get a job, go to graduate school in Statistics, go to graduate school in a field other than Statistics, or do something else. The last alternative is possibly the most interesting, but beyond the scope of this document. Statistics students who plan on graduate study in a non-statistical discipline probably know how Statistics fits into their plans. Here, we will deal with the first two options.


With an undergraduate degree in Statistics, you are a more attractive candidate for jobs that require understanding of statistical information. For example, in an industrial setting you will be able to readily understand information based on statistical quality control, even though you probably will not have a course in it. In a management or sales position in an insurance company, you will be able to understand actuarial data, even though you are not an actuary. In a marketing or market research setting, lots of the data come from sample surveys and are subjected to standard statistical analyses. You will be able to understand and use these data, even though you may not be crunching the numbers yourself.

A degree in Statistics is also an advantage to Computer Science students. In many companies, statistical analysis is an important category of computing; a programmer/analyst who knows what the software is trying to accomplish is more valuable than someone who just knows the hardware and the operating system. All other things being equal, job applicants who appear to know some statistics have an advantage in almost every field.

On the other hand, an undergraduate degree in Statistics -- even a specialist degree -- does not qualify you as a professional statistician. You may wind up doing statistical analyses for a living, depending on the type of company or organization you're in, but you probably will not be hired in that capacity initially. It happens, but in our experience it is rare.

Let's face it; with a degree in History, are you qualified as a professional historian? With a degree in Mathematics, are you going to be hired as a mathematician? With a degree in Physics, are you going to get a job as a physicist? With a bachelor's degree in Statistics, you should not count on being employed as a statistician. You will probably be hired as something else.

In fields like History, Mathematics and Physics you need a Ph. D. in order to be taken seriously as a professional. In fields like Engineering and Computer Science, an undergraduate degree is just fine. Statistics is in a sort of intermediate category. A Master's degree qualifies you to do applied statistics for a living in a medical, business or government setting. A Ph. D. is an extremely powerful credential for applied jobs, and also allows you to seek university faculty positions. It is possible to be a university teacher with a master's degree, but it's becoming rare.


So if you're a good student, you really like Statistics and you're sure that's what you want to do for a living, you should consider graduate study. Even if your ultimate goal is a Ph.D., you generally get a Master's degree first, and then seek admission to Ph.D. programmes.

Preparation and requirements

The Statistics specialist program gives you all the undergraduate Statistics courses you will need for graduate study -- maybe more. In addition, you should have MAT236 (Vector Calculus) and especially MAT378 (Introduction to Analysis) at UTM or MAT257/337 on the St. George campus. Many graduate courses in Statistics assume the tools and mindset of MAT378. Without it, students will be very uncomfortable at best.

An overall grade average of B+ should be good enough for admission to most graduate schools in Canada; the University of Toronto is a special case. Many U of T students think of applying to graduate school at U of T because it is familiar, and they see it as the path of least resistance. But the Statistics department at U of T is widely believed to be the best in Canada. It is not a place where you apply as insurance against not finding a job. You should not think of applying to U of T with a cumulative GPA less than 3.75. Even with this, any mark less than A- in a Math or Statistics class is cause for concern. UTM students without MAT378 have been admitted in the past, but they had trouble. Professor Brunner will no longer write letters of recommendation to U of T for students without an excellent mark in MAT378 at UTM or MAT257/337 on the St. George campus. He is tired of seeing his favourite students get hammered.

If you are a foreign student, there is more bad news. All Arts and Science grad students at U of T must receive full financial support, and tuition for foreign students is very expensive. Departments get a small quota. We can admit as many international students as we wish, but we must find the tuition money for all those beyond the quota. And even if an applicant is able to pay his or her own tuition, this is not allowed; we have to pay. The result is that only a small number of foreign students are admitted each year to the Statistical Sciences department. Here's what I mean by small. In a recent year, we had around 200 international applicants to the Masters program, many of them highly qualified. We admitted zero. I believe that only 2 out of several hundred were accepted into the Ph.D. programme. The moral of this sad story is that unless you're a domestic student, applying to the U of T Statistical Sciences department is probably a waste of the application fee, not to mention everybody's time. U ot T Biostatistics (see below) is not subject to these rules, and may be a better choice for international students with money who want to pursue graduate study in Statistics at U of T.


Let's be clear about one point. We are not talking here about what you know, or what you are truly qualified to do. We are talking about the perceptions of potential employers. The topics taught in our Specialist and Major programs has a large overlap with the topics in Master's level courses, both here and in other schools. The topics may be covered at a more advanced level in graduate school, but in terms of what you would do on the job there's not much difference. At least, you will learn the material better than you did the first time, and after you finish your career earnings should be significantly higher. You will get more respect, and the work will be rewarding, if you like analyzing data. You'll need about a year of on-the-job experience before you are actually as qualified as you appear to be, but that's no problem. It's true in any field. In any respectable master's degree program, there will be at least a one year course in mathematical statistics (same material as STA256/257 and STA260/261 but deeper and faster), in which your brains are pulverized and poured back into your ear. This is thought to be a beneficial experience.

At the University of Toronto, there are M. Sc. and Ph. D. programs in both the departments of Statistics and Biostatistics. The Biostatistics department is really a Statistics department (and a good one), but it is affiliated with the medical school, it does not offer any undergraduate courses, and it tends to focus on statistical problems that appear in biomedical research. The Biostatistics department often send their students to the Statistics department to take basic courses. So apart from courses in survival analysis and categorical data analysis, they tend to offer mostly research seminars in specialized topics. This statement was accurate a few years ago. Things may be changing.


Many Ph. D.s in Statistics go into the private, public and medical sectors as applied statisticians on the fast track. Their training, however, is in statistical research. In Statistics, as in all other disciplines, Ph. D. students learn to create new knowledge in their field, to formulate important new questions and answer them. Every theorem and statistical technique you learn is the result of somebody's research. Researchers in Statistics mostly are professors at universities, and their students tend to view them exclusively as teachers. In fact, at U of T the typical professor's job description consists of 40% teaching, 40% research, and 20% administrative duties and community service. This is true in most fields, not just Statistics.

For a Ph. D. in Statistics, what you need more than anything else is a solid mathematical background. Basic Calculus is certainly not enough. Multivariable calculus, Real Analysis, Complex Variables and Topology are very helpful content areas. Learn how to do proofs! This is the main way that knowledge is created in the mathematical disciplines, and what a Ph. D. says is that you know how to create new knowledge.

One other thing you should be aware of is that after the first year or so, taking courses and doing well is not the main point. Research training is primarily a process of apprenticeship. You find somebody who is doing something interesting (or he/she finds you), and the person trains you one on one. Probably the most important choice a Ph. D. student makes is whom to work with. Almost any professor will tell you more than you want to know on this topic, if given half a chance.