PhD In Statistics Programs

Many people are looking for the right Doctor of Philosophy in Statistics program. But it’s not easy to find one that really meets your needs and expectations. One of the useful tips is to find out which are the colleges offering PhD in statistics that have a strong reputation in this specific field, taking into account all the other criteria that you’re interested in. This guide lists some of them.

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A Short Guide for Students Interested in a Statistics PhD Program

This summer I had several conversations with undergraduate students seeking career advice. All were interested in data analysis and were considering graduate school. I also frequently receive requests for advice via email. We have posted on this topic before, for example here and here, but I thought it would be useful to share this short guide I put together based on my recent interactions.

It’s OK to be confused

When I was a college senior I didn’t really understand what Applied Statistics was nor did I understand what one does as a researcher in academia. Now I love being an academic doing research in applied statistics. But it is hard to understand what being a researcher is like until you do it for a while. Things become clearer as you gain more experience. One important piece of advice is to carefully consider advice from those with more experience than you. It might not make sense at first, but I can tell today that I knew much less than I thought I did when I was 22.

Should I even go to graduate school?

Yes. An undergraduate degree in mathematics, statistics, engineering, or computer science provides a great background, but some more training greatly increases your career options. You may be able to learn on the job, but note that a masters can be as short as a year.

A masters or a PhD?

If you want a career in academia or as a researcher in industry or government you need a PhD. In general, a PhD will give you more career options. If you want to become a data analyst or research assistant, a masters may be enough. A masters is also a good way to test out if this career is a good match for you. Many people do a masters before applying to PhD Programs. The rest of this guide focuses on those interested in a PhD.

What discipline?

There are many disciplines that can lead you to a career in data science: Statistics, Biostatistics, Astronomy, Economics, Machine Learning, Computational Biology, and Ecology are examples that come to mind. I did my PhD in Statistics and got a job in a Department of Biostatistics. So this guide focuses on Statistics/Biostatistics.

Note that once you finish your PhD you have a chance to become a postdoctoral fellow and further focus your training. By then you will have a much better idea of what you want to do and will have the opportunity to chose a lab that closely matches your interests.

What is the difference between Statistics and Biostatistics?

Short answer: very little. I treat them as the same in this guide.

How should I prepare during my senior year?

Math

Good grades in math and statistics classes are almost a requirement. Good GRE scores help and you need to get a near perfect score in the Quantitative Reasoning part of the GRE. Get yourself a practice book and start preparing. Note that to survive the first two years of a statistics PhD program you need to prove theorems and derive relatively complicated mathematical results. If you can’t easily handle the math part of the GRE, this will be quite challenging.

When choosing classes note that the area of math most related to your stat PhD courses is Real Analysis. The area of math most used in applied work is Linear Algebra, specifically matrix theory including understanding eigenvalues and eigenvectors. You might not make the connection between what you learn in class and what you use in practice until much later. This is totally normal.

If you don’t feel ready, consider doing a masters first. But also, get a second opinion. You might be being too hard on yourself.

Programming

You will be using a computer to analyze data so knowing some programming is a must these days. At a minimum, take a basic programming class. Other computer science classes will help especially if you go into an area dealing with large datasets. In hindsight, I wish I had taken classes on optimization and algorithm design.

Know that learning to program and learning a computer language are different things. You need to learn to program. The choice of language is up for debate. If you only learn one, learn R. If you learn three, learn R, Python and C++.

Knowing Linux/Unix is an advantage. If you have a Mac try to use the terminal as much as possible. On Windows get an emulator.

Writing and Communicating

My biggest educational regret is that, as a college student, I underestimated the importance of writing. To this day I am correcting that mistake.

Your success as a researcher greatly depends on how well you write and communicate. Your thesis, papers, grant proposals and even emails have to be well written. So practice as much as possible. Take classes, read works by good writers, and practice. Consider starting a blog even if you don’t make it public. Also note that in academia, job interviews will involve a 50 minute talk as well as several conversations about your work and future plans. So communication skills are also a big plus.

But wait, why so much math?

The PhD curriculum is indeed math heavy. Faculty often debate the possibility of changing the curriculum. But regardless of differing opinions on what is the right amount, math is the foundation of our discipline. Although it is true that you will not directly use much of what you learn, I don’t regret learning so much abstract math because I believe it positively shaped the way I think and attack problems.

Note that after the first two years you are pretty much done with courses and you start on your research. If you work with an applied statistician you will learn data analysis via the apprenticeship model. You will learn the most, by far, during this stage. So be patient.

What department should I apply to?

The top 20-30 departments are practically interchangeable in my opinion. If you are interested in applied statistics make sure you pick a department with faculty doing applied research. Note that some professors focus their research on the mathematical aspects of statistics. By reading some of their recent papers you will be able to tell. An applied paper usually shows data (not simulated) and motivates a subject area challenge in the abstract or introduction. A theory paper shows no data at all or uses it only as an example.

Can I take a year off?

Absolutely. Especially if it’s to work in a data related job. In general, maturity and life experiences are an advantage in grad school.

What should I expect when I finish?

You will have many many options. The demand of your expertise is great and growing. As a result there are many high-paying options. If you want to become an academic I recommend doing a postdoc. 

Statistics PhD Program Information and Requirements

Students in PhD in Statistics programs learn to gather, analyze, interpret and apply mathematical data to a wide range of topics. Coursework varies and may be catered to an individual’s career goals.

Essential Information

Doctoral programs in statistics offer students a wide range of classes, among them applied statistics, modern analysis, stochastic processes and nonparametric statistics. Many programs also cover the computer programs used in statistical analysis, enabling students to professionally apply their knowledge.

Programs usually take 4-5 years to complete, and require a bachelor’s degree and an expertise in advanced mathematics for admission. Most programs require students to complete a dissertation and oral examination before they are awarded their degrees.


PhD in Statistics

Candidates in a doctoral statistics program are generally required to complete a number of courses covering theoretical and practical applications of mathematical data analysis. They typically participate in various projects involving applications of probability theory and statistics, and are expected to conduct extensive research. The list below includes subjects often covered in statistics PhD programs:

  • Theoretical statistics
  • Analysis and probability theory
  • Asymptotic analysis
  • Information theory
  • Econometrics
  • Graphical methods

Popular Career Options

People who hold a PhD in statistics are capable of conducting complex research and understanding obscure mathematical data, skills that are useful in a variety of fields. The following are common career options for people who hold a PhD in statistics:

  • University professor
  • Government research analyst
  • Mathematical probability expert

Employment Outlook and Salary Info

PhD holders working as professors were projected to see a 13% employment growth from 2014-2024, stated the U.S. Bureau of Labor Statistics (BLS); however, competition will be keen for those seeking tenure positions. In May 2015, the median salary for mathematical science teachers working at the postsecondary level was $67,170.

People who like playing with statistics and conducting research may want to consider a Ph.D. in statistics. This doctoral program will teach you what you need to know to analyze and report research finding in a professional setting. While you earn your degree you will have plenty hands on experience using statistics and will complete your own dissertation. One of the more common jobs for Ph.D. graduates in statistics is secondary education.

A beginner’s guide to statistics for PhD research

Statistics can be invaluable for adding a level of rigour to your analysis, but they can be extremely technical and difficult for non-specialists.

This is not by any means a comprehensive guide, but I will try to give some basic working principles to help reduce the pain and avoid the most common mistakes.

Plot your data

Before doing statistical analysis, wherever possible create a visual representation of your data.

This will give you a much better intuitive understanding of what is going on.For example, if you have survey data using a Likert scale, where answers to questions are given as;

  1. Strongly disagree
  2. Disagree
  3. Neither agree nor disagree
  4. Agree
  5. Strongly agree

You may want to see how the answers to a specific question are distributed across all respondents. You can do this by plotting a histogram showing the number of responses at each point in the scale.Here are 3 examples of possible distributions:

likert histogram 1
likert histogram 2
likert histogram 3

Without doing any statistics, you can instantly see how the data is distributed, and you can use this as a basis for your analysis

What does the mean mean?

If you take the means of each of the three distributions above, you will get values of 3.7, 3 and 2.8.

But what do these values mean? In the top histogram, 3.7 clearly correlates to the peak at 4. In the second, the distribution is flat, so the mean just represents the middle of the range, and in the third, the mean is the least selected option.It is up to you to then interpret what the mean means, but you can only do that when you can see the distribution of the data.

Standard deviation

The standard deviation is a measure of the spread of data around the mean. It is widely used, but you need to be careful.If you use the standard deviation without plotting your data, then you can end up with a meaningless number.

Standard deviation is best used when you have something approximating a normal distribution of data (the classic “bell curve” below)

from http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg

When you say the standard deviation = x, this indicates that about 68% of the data lies within ± x of the mean.

But what if you have a graph with 2 peaks? Then the standard deviation becomes meaningless, even though a statistical program will still give you an answer.

from http://en.wikipedia.org/wiki/File:Bimodal.png

Don’t include numbers you don’t understand

When you use statistical analysis software, it will spit out countless different results, some will be useful, some not.

Do not include in any report or table of results numbers you don’t understand. Imagine an examiner asking, “what do these numbers mean?” and if you can’t answer, either find out or don’t include them.

How many decimal places?

Another potential hazard is that stats software will often give you numbers to many decimal places.

For example, let’s say you measure the height of every adult human being on earth and look for the mean. With several billion data points, your calculation of the mean might look something like 1.68234597864422 m (I just made this number up as an example). If you copy and paste this number, you are effectively claiming that you can measure the height of a human being to an accuracy of  0.00000000000002 m, which is much smaller than the radius of an atom.

Much better to give the value as 1.68 or 1.682, since this reflects the accuracy with which you can make a single measurement.

Quoting errors

The same is true when giving an estimate of the error on a measurement. Giving an error of ± 2.336598774654654 is ridiculous! You can’t be that precise in an error estimate! Stick to one (or two at the most) significant figures.

Do analysis at a small scale early in your research

If you have 1 month left to submit your thesis, and you are doing analysis for the first time, it’s going to be difficult.

So do some analysis early, on a small scale, so you have some experience before you do the full analysis. You will be able to take your time, while the pressure is still low. Most mistakes happen when doing things in a rush at the last minute, especially if you have never done that type of analysis before.

If you know what methodology you are going to use, do a small trial run and analyse the data you get. Not only will this help you refine your methodology, but it will make the final analysis much, much easier.

PhD Requirements

Learning Goals: Doctor of Philosophy in Statistics

  1. Demonstrate comprehensive understanding of advanced statistical methods and theory, including probability, mathematical statistics, and the construction of probability-based models for complex data structures.
  2. Demonstrate the ability to formulate statistical questions on the basis of objectives in substantive scientific investigations, and the ability to compute the quantities needed to bring statistical theory and methods to bear on those questions.
  3. Conduct original research into one or more specific areas of statistical science that is of sufficient depth to merit publication in a statistical or scientific journal.
  4. Demonstrate understanding of the scholarly literature in the area of dissertation research.
  5. Demonstrate the ability to communicate research results to scientists and other researchers in both written and oral formats.

Core Courses

All students seeking the PhD degree in Statistics are required to know the material in the core courses (Stat 601, 641, 642 and 643). It is assumed that the material in the MS core courses has also been mastered. Many students entering the program with a Bachelor’s degree complete the MS core program in the first year and begin the PhD core in their second year of study. A typical schedule is shown below, and this can be compared to the sample schedule presented for the MS program to see how the PhD core courses would fit into the overall schedule of courses.

Typical Schedule for a Student Entering with a Bachelor’s Degree

Year 1/Fall
Stat 500 (4 cr.) Statistical Methods I
Stat 542 (4 cr.) Theory of Probability and Statistics I.
Stat 579 (1 cr.) Introduction to Statistical Computing.

Year 1/Spring
Stat 510 (3 cr.) Statistical Methods II
Stat 543 (3 cr.) Theory of Probability and Statistics II.
Elective (3 cr.)

Year 2/Fall
Stat 520 (3 cr). Statistical Methods III
Stat 641 (3 cr.) Foundations of Probability Theory
Electives (3 cr.)

Year 2/Spring
Stat 601 (3 cr.) Advanced Statistical Methods
Stat 642 (3 cr.) Advanced Probability Theory
Electives (3 cr.)

Year 3/Fall
Stat 643 (3 cr.) Advanced Theory of Statistical Inference
Electives (3-6 cr.)
 

The Director of Graduate Studies and/or Chair of the Department are available to advise a student entering the program with more experience than typically represented by a Bachelor’s degree on how best to sequence core courses and where to begin in the program. If a student enters the program with a Master’s degree in statistics, he or she may be advised to start directly with the PhD core courses or may be advised to include some MS core courses in the first one or two semesters of study.
 

Typical Schedule for a Student Entering with a Master’s Degree in Statistics
 

Year 1/Fall
Stat 520 (3 cr.) Statistical Methods III (optional)
Stat 641 (3 cr.) Foundations of Probability Theory
Electives (3 cr.)

Year 1/Spring
Stat 642 (3 cr.) Advanced Probability Theory
Stat 601 (3 cr.) Advanced Statistical Methods
Electives (3 cr.)

Year 2/Fall
Stat 643 (3 cr.) Advanced Theory of Statistical Inference
Electives (3-6 cr.)
 

If English is not a student’s native language, he or she will be required to take an English Placement Test at the start of the first semester of graduate study. Based on the results of this exam, the student may be required to take one or more English courses. Other language requirements, if any, will be established by the Program of Study Committee and major professor.

Written Preliminary Examination

All students seeking a PhD degree must pass a written preliminary examination, which is given over two days and covers material from both the MS and PhD core courses. The exam is administered in two parts, one part covering primarily statistical methods and applications (Stat 500, Stat 510, Stat 520, Stat 601) and one part covering primarily statistical theory (Stat 542, Stat 543, Stat 641, Stat 642). Note that Stat 643, “Advanced Theory of Statistical Inference” is a required course but is not included on the written preliminary exam. This is because the exam is typically given during the summer, after a student entering with a Bachelor’s degree has completed two years of study and a student entering with a Master’s degree has completed one year of study. Both parts of the written preliminary exam must be taken at the same time.  The possible outcomes are: a student may pass; fail but be given an invitation to re-take the exam in the next year; or fail and be asked to find another academic program or institution at which to continue study, if that is desired.

The PhD written preliminary examination is intended to provide both the student and the program with a concrete indication of whether pursuit of a PhD in Statistics at Iowa State is a good option for the student. It serves as a solid indication of whether it will be wise for a student to devote the immense amount of time and energy needed to write and defend a dissertation.

Major Professor and Program of Study Committee

The selection of a major professor is an important milestone in most PhD programs, and often occurs after one or two years of study, when a student has gained some familiarity with the research areas of faculty members in the department. The major professor serves as the principal mentor of a PhD student; provides advice on the selection of elective courses; supervises and advises the dissertation research and preparation of the written dissertation; and assists in nearly every other step of the PhD program. Most students reach agreement with a faculty member to serve as their major professor either the semester before or the semester following the written preliminary examination. Before a major professor has been determined, the student can seek advice from the Director of Graduate Education or the Department Chair.

Along with the major professor, the student selects at least four more faculty members to form a Program of Study Committee, and obtains agreement from those faculty members to participate in the committee. At least one member of the committee must have a primary area of research activity that differs substantially from the topic of the dissertation research. It is common, but not required, that one member of the committee is a faculty member in a department other than Statistics.

The Program of Study Committee conducts the oral preliminary examination and the final oral examination, and approves the official Program of Study, which is a list of coursework that the student will apply toward the PhD degree. The Program of Study serves as an official contract between the student, and the university that the courses listed will satisfy the requirements for core courses, suitable electives, research credits. and total credits.  It must be approved by the major professor, committee members, Director of Graduate Education, and the Graduate College.

Dissertation

To be awarded the degree of Doctor of Philosophy in Statistics, a student must complete an original research project that results in a written PhD dissertation. This work will be mentored and directed by the student’s major professor, a faculty member with whom the student reaches a mutual agreement for supervision of the dissertation research project. Although there is no formal requirement for publication, it is typically expected that a dissertation project will result in publishable research, usually in the form of one or more articles in peer-reviewed journals, although such articles need not have been accepted or even submitted for publication at the time a PhD candidate defends his or her dissertation.
Oral Preliminary Examination

After a suitable amount of work has been conducted on the dissertation research project, as mutually determined by the student and his or her major professor, the student requests permission from the Graduate College to take their oral preliminary examination. The oral preliminary exam is conducted by the student’s Program of Study committee, and usually centers on early results from the dissertation research as well as proposed work to be done during the remainder of the student’s program. An important objective of the oral preliminary exam is for the student, the major professor, and the members of the committee to reach agreement on what will constitute an acceptable dissertation for defense at the final oral examination (sometimes called the dissertation defense). When a student passes the oral preliminary exam he or she officially is recognized as a candidate for the PhD degree by the Graduate College.

Maintaining Academic Standing

Students must maintain a 3.0 (B) average to remain a candidate for a degree. Failure to do this can result in being placed on academic probation. Academic probation can have implications for tuition scholarships and require additional permission to allow registration in subsequent semesters. A student cannot receive a graduate degree without removing academic probation by achieving an overall grade point average of 3.0 or higher. Students who fail to reach a 3.0 average during their first semester of graduate study are given a one semester grace period to improve their grades before being placed on academic probation. Failure to raise a grade point average to 3.0 and remove academic probation for two years may be considered failure to make satisfactory academic progress, and result in the termination of an assistantship or membership in an academic program.

Final Oral Examination

When the student and his or her major professor believe the dissertation has reached its final form, and that any concerns or issues raised during the oral preliminary examination have been appropriately addressed, the student schedules and completes the final oral examination or dissertation defense. As part of this examination, the student must present a public seminar concerning the dissertation research. There is then a longer session involving only the student and his or her Program of Study Committee, during which the student presents additional material from the dissertation and answers questions posed by the members of the committee. Passing the final oral exam is the last step in the progression toward completing a PhD degree.

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