Within the Dept. of Department of Mathematics and Statistics, students may choose options which concentrate in Statistics. This page summarizes the main features of the Statistics options and overlaps considerably with the material in the Axioms, which contains full detail of all program requirements.

The M.S. option provides students with training in statistical applications, statistical computing and theory, preparing them for jobs in industry or government, or for moving on to a Ph.D. in Statistics of Biostatistics. The Ph.D. option provides a combination of theory and application preparing students for positions in academia, industry or government. Each of these programs is described in more detail below.

**On this page:**

M.S. in Statistics

The Fifth Year M.S. in Statistics

Ph.D. in Statistics

General Info

Courses

## M.S. in Statistics

The M.S. option in statistics is designed to prepare students for positions in industry or government. It also serves as a basis for future work towards a Ph.D. in Statistics or Biostatistics. This program is designed to provide the student with a background in basic theory along with experience in various applications, including computational aspects. As part of their training, students will receive comprehensive exposure to the use of SAS, one of the more popular statistical software packages. In addition to courses offered within the department, the program allows room for the students to take statistics courses in other departments on campus.

Students entering the M.S. are expected to have had Linear Algebra and Calculus up through Multivariate Calculus (this is typically covered by a three semester sequence in U.S. schools). Students with a weak background in these areas will be required to take appropriate courses at an early stage of their graduate study here.

The requirements for the M.S. degree involve coursework, a project and qualifying exams.

### Courses

The student must complete 30 hours of coursework with grades of C or better, including at least 24 hours with grades of B or better. In addition, the student must have at least an overall B average. The required 30 hours must include:

- Stat 697R: Applied Regression
- Stat 526: Applied Experimental Design
- Stat 607-608: Probability and Mathematical Statistics I, II
- Stat 705: Linear Models I
- At least three other courses which are either Statistics courses numbered 600 or above, from within the Department. Some graduate courses from outside the department can be used as one of these three courses, subject to prior approval by the Statistics coordinator.

Some, 500 level courses (e.g., S526 or 511) may be counted towards the 30 hours but other 500 level courses (such as S501, 515 or 516) would not count towards the 30 hours. Students may take, and in fact are often encouraged to take, courses from other departments. Students should consult with their advisor or other members of the faculty regarding outside courses.

### Basic Exam

Students doing the M.S. in Statistics are required to pass two basic exams, one in Probability and one in Statistics, which are based primarily on ST607-608. The Basic Exam is given twice a year, in January and in August. A student seeking only a Master's degree will normally take the Basic Exam at the beginning of the second year.

### Project

The project is completed under the guidance of a faculty member. This project must have prior approval of the Graduate Program Director and involves 3 credit hours which may be used to satisfy the 30 hour coursework requirement. The project can take many forms; an expository report on a particular area, an examination of methods through simulations or a detailed statistical analysis of real data. A final report is required.

## The Fifth Year M.S. in Statistics

This section explains how a Five College student can earn a Masters degree in statistics in a fifth year.

### The MS Degree

This is a brief description of the MS degree. Consult the Coordinator of the Statistics Program for details or see here for details.

### Prerequisites

- linear algebra
- multivariable calculus
- a course in statistics
- computing experience

### Requirements

- 30 units of credit (10 3-credit courses)
- exams in probability and statistics
- required courses
- Stat 697R regression
- Stat 526 design
- Stat 607/608 two semesters of probability and statistical theory
- Stat 691 project
- Stat 705 linear models

### Five Year Plan

A student can earn the MS in five years by attending to the following two points.

**Earning enough credits.**If a student takes seven courses at UMass in the fifth year, that is a total of only 21 credits. Therefore, nine credits must be transferred from the student's undergraduate program. Up to nine credits of graduate work taken while enrolled as an undergraduate may be counted toward both the Master's degree and the baccalaureate degree for students in the fifth year MS degree program. Total credits taken across both programs must equal at least 30 plus the minimum required for the baccalaureate degree (typically 120).**Taking the right courses.**Some courses taken as an undergraduate can satisfy the MS requirement for specific courses. In particular, undergraduate courses at the Five Colleges in linear regression and experimental design can satisfy the requirement for Stat 697R and 526. Undergraduate courses in probability and statistics might satisfy the requirement for Stat 607/608, depending on their level. Courses taught from texts such as Casella & Berger, DeGroot & Schervish, or Lavine do satisfy the requirement, while courses from texts such as Larsen & Marx or Mendenhall, Wackerly & Schaeffer are more similar to Stat 515/516 and do not satisfy the requirement for 607/608. When in doubt, check with the coordinator of the statistics program at UMass. Note: to complete the MS in one year, the student must take Stat 705 in the first semester. Because 607/608 is a prerequisite for 705, the student must take the equivalent of 607/608 as an undergraduate.

Please note that if students are interested in The Fifth Year MS in Statistics, students should contact the Coordinator of the Statistics Program during the fall of the their junior year.

## Ph.D. in Statistics

The Ph.D. option in statistics prepares students for academic positions or positions in Academia, applied statisticians in industry or government. Entering students are expected to have had Linear Algebra, Calculus and Advanced Calculus. Typically an incoming Ph.D. student will have had an introductory course or two in Statistics at the undergraduate level. Student seeking a Ph.D. in statistics must complete the following: coursework, qualifying exams, language requirement and dissertation.

### Coursework

The student must complete successfully 36 hours of coursework, including:Stat 607-608 (Mathematical Statistics I, II), Stat 605 (Probability Theory), Stat 705-706 (Linear Models I, II), Stat 725 (Theory of Estimation and Statistical Inference), two additional graduate courses in Statistics numbered 600 or above, and Math 623 (Real Analysis I).

Additional courses may be required by the student's dissertation Committee.

Any course outside the Department or numbered less than 600 must have the Graduate Program Director's approval if it is to be counted towards the 36 hours. While the required courses focus primarily on theory, all students are strongly encouraged to develop some expertise in applied statistics and statistical computing.

### Qualifying Exams

There are two tiers of written exams, Basic and Advanced, which are intended to measure a student's overall mastery of standard material. The exams are administered during the week preceding each semester (August and January).

**Basic Exams:** All prospective Ph.D. candidates must pass the Basic Exam at the "Ph.D. level". The student must take these exams no later than the beginning of the third semester of graduate study and pass them no later than the start of the fourth semester. If a student fails on an attempt, he or she has to re-take all three parts. The basic exam consists of three parts: Probability, Statistics and Advanced Calculus/Linear Algebra.

**Advanced Exams:** The advanced exams must be passed in order to proceed to the dissertation level. The student must take these exams no later than the start of the fifth semester and pass both exams no later than the start of the sixth semester. If the student fails, he or she has to re-take both parts.The advanced exam has two parts: Mathematical Statistics (based on Stat 725, and 605) and Linear Models (based on Stat 705 and 706).

### Oral Presentation

By completing the required coursework and passing the Advanced Exam, a student becomes a Ph.D. candidate. All students are expected to acquire experience in preparing and presenting high-level material. After passing the Advanced Exam but before registering for any dissertation credits, each Ph.D. candidate must give a public presentation of some topic beyond the textbook level which is relevant to the student's proposed area of specialization. This would typically have the format of a one-hour seminar (either regularly scheduled or ad hoc). It might be coordinated with the forming of the dissertation committee and preparation of the prospectus. The topic presented is to be chosen in consultation with a faculty advisor and might for example be drawn from a recent research paper.

### Dissertation

After passing the Advanced Exam, the student becomes a Ph.D. candidate. The student must write a satisfactory dissertation under the direction of a faculty member and pass a final oral examination (primarily a defense of the dissertation).

## General Information

### Financial Aid

Most graduate students are supported by Teaching Assistantships which provide a stipend and a waiver of tuition and most fees. Students in the M.S. program have a smaller stipend (approximately 2/3rds) than Ph.D. students with a proportional reduction in duties. Some students are supported through research assistantships in the Statistical Consulting Center which also carry a tuition waiver and stipend.

There are also opportunities for summer teaching, Graduate School fellowships and grants from various government and private agencies.

The renewal of support depends on the student's academic and teaching performance. The department does not normally support a Master's student longer than two years, and does not normally support any student beyond the fifth year.

### Research/Seminar

There is a weekly seminar series in statistics and probability which features a wide variety of speakers, both from within and from outside the university.

The faculty in statistics have a broad range of research interests in both theoretical and applied areas.

### Statistical Consulting Center

The Statistical Consulting Center offers a full range of statistical services for clients inside and outside the university. The center provides an opportunity for graduate students to complement traditional studies with exposure to real world problems involving the statistical analysis of data.

### Computing Facilities

The Department of Mathematics and Statistics maintains a research computing facility equipped with a "mainframes", workstations and PC's supporting basic computing including Fortran, C, Mathematica, SAS, SPlus, Latex, email, etc.

## Courses

### Statistics Courses

Stat 511 Multivariate Statistical Methods

Stat 515-516 Introduction to Statistics I, II

Stat 526 Design of Experiments

Stat 597BCD Statistical Computing with SAS

Stat 697R Topics in Regression

Stat 605 Probability Theory (Advanced)

Stat 607-608 Mathematical Statistics I, II

Stat 640 Sampling Theory

Stat 697R Applied Regression Analyis

Stat 705-706 Linear Models I, II

Stat 708 Applied Stochastic Models and Methods

Stat 712 Multivariate Analysis

Stat 725 Advanced Statistical Theory

Additional topics courses are offered on a regular basis including (but not limited to) Time Series, Reliability, and Mathematical and Statistical Methods in Imaging.

As noted earlier there are additional Statistics courses offered by other departments on campus.

### Related Mathematics Courses

Math 425 Advanced Multivariate Calculus

Math 523 Real Variables

Math 545 Linear Algebra for Applied Mathematics

Math 611 Algebra I

Math 621 Complex Analysis

Math 623-624 Real Analysis I, II

Math 645-646 Applied Mathematics I, II

Math 705 Topics in Analysis

Math 725 Introduction to Functional Analysis