# Applied Statistics Graduate Student Handbook

*On this page:*

- Program Description and Requirements
- Suggested Review Materials
- Second Master's Degree
- Comprehensive Examination Guidelines
- Comprehensive Examination Topics
- Financial Aid
- Employment Opportunities and Information
- Useful Links

## Program Description and Requirements

View Master of Science in Applied Statistics program information and degree requirements in the Academic Catalog.

## Suggested Review Materials

There are several specific prerequisites for entry into the Applied Statistics M.S. program at Wright State University. When a student applies for admission to the program, the graduate advisor reviews the student's transcript for evidence of completion of these prerequisite courses and can refuse (or postpone) admission if one or more prerequisites are missing. There are, however, students who technically have the prerequisites for admission, but whose coursework is out of date or was possibly weak to begin with. Often students entering the M.S. program are returning to school after spending some time in the work force. They have not necessarily used the mathematics they learned as undergraduates (and may not have done particularly well in math at the time they took it). Usually these students are now highly motivated and willing to do some serious review before beginning their graduate course work. If you are one of these students, we recommend the following material for review work prior to entry into the M.S. in Applied Statistics program.

### Calculus

Admission prerequisite: "a calculus sequence that includes multivariable calculus". Such a sequence usually lasts at least a year and ordinarily is offered for mathematics majors, engineering majors, and other mathematics-intensive undergraduate programs. At Wright State, MTH 2300-2310-2320, which consists of three 4-semester-credit-hour courses, is the appropriate sequence.

Although not all of the topics taught in a typical math/engineering calculus sequence are necessary background for the M.S. in Applied Statistics, a solid foundation in differential and integral calculus is crucial preparation for several important courses, especially for the sequence of STT 6610 and STT 6620 as a part of the core curriculum.

*Suggested review text: *Calculus: Concepts And Contexts, by James Stewart, 4th Edition, 2010, ISBN: 9780495557425. This text can be found athe WSU Bookstore, at retail bookstores like Barnes & Noble, or online.

Proficiency and understanding of the following chapters and topics are crucial:

- Functions and Models
- Limits and Derivatives
- Differentiation and Rules
- Applications of Differentiation
- Integrals
- Applications of Integration: Sections 6.1 and 6.2
- Infinite Sequences and Series (except Sections 8.9 and 8.10)
- Vectors and the Geometry of Space
- Partial Derivatives (except Section 11.8)
- Multiple Integrals (except Section 12.8)

*Additional Material:* A handout is available from Department of Mathematics and Statistics on Partial Differentiation and Multiple Integrals.

### Linear or Matrix Algebra

The recommended way to get the appropriate linear algebra material is to audit (or actually take for credit) MTH 253 or MTH 255.

### Computer Programming

Most incoming students have an adequate computer background to be able to meet the programming requirements of the degree program. If an applicant is genuinely deficient in this area because they have never learned a programming language, they should confer with the graduate advisor regarding appropriate courses (currently CS 1160), especially the contents of the second volume.

### Statistics

If an applicant has never taken a statistics course, they will need to take at least two courses before being admitted to the program (STT 3600 and 3610 are preferred).If it has been some time since the applicant has taken any statisticscourses, has never had an applied statistics course, or feels that their background is otherwise shaky, the deficiency may be made up by a thorough review of the following materials. If an applicant has already taken a statistics course they should revisit the textbook used in it, paying special attention to the material on confidence intervals and hypothesis testing. Applicants who have not taken an applied statistics course should review the material in the following textbooks,

- Statistics I: Descriptive Statistics and Probability, College Outline Series, by Elliot A. Tanis, 1987, ISBN: 9780156016162
- Statistics II: Estimation and Tests of Hypotheses,College Outline Series, by Elliot A. Tanis, 1987, ISBN: 9780156016179

## Second Master's Degree

Wright State allows students who already have a master's degree in some area to earn a second master's degree with fewer than the usual number of credits. The catalog requirements for a second Master's degree are a minimum of 22 hours (vs 30), but the catalog also says that "Departments or programs may specify additional requirements depending on the length of the program, prerequisites for the individual student, and/or the nature of the first degree." The Statistics Program faculty have approved the following policy regarding a second M.S. degree in Applied Statistics.

Because of the specialized nature of statistics, students who already have a Master's degree in some other subject and who wish to pursue the M.S. in Applied Statistics as a second Master's degree ordinarily must complete the regular program of study in statistics. An exception to this rule may be granted by the Graduate Advisor if he/she determines that the student has completed statistics courses at the graduate level which are comparable to courses in the program. In this case, the required number of hours for the program may be reduced by up to 9 hours. A proposed program of study for such a student must be approved by the Graduate Advisor in advance of admission. All other requirements of the program (e.g. admission requirements, GPA, comprehensive exam, 700-level courses) must be satisfied.

## Comprehensive Examination Guidelines

The comprehensive examination for the M.S. degree in Applied Statistics is generally given in the second and third weeks of the Fall semester according to the following guidelines.

The time that the student takes the examination is subject to the approval of Program Director and must be no earlier than the completion of sixteen (16) credit hours in the Program. These sixteen (16) credit hours must usually be the courses listed in Part I and Part II below. Exceptions must be approved by the Program Director.

For each student, the Examination Committee consists of three or more program faculty members as appointed by the Program Director. The subjects to be examined are:

**Part I Theory.**Theory of Statistics (STT 6610-6620)**Part II Method.**Statistical Methods (STT 6660-6670)**Part III Applications.**A take-home project, which is designed to be applied in nature, is given at the end of Part II of the exam. One week will be allowed for completion of the project.

The time allowed for each of Parts I and II is three hours.

The examination for Part II is scheduled approximately one week later than that of Part I.

Copies of two previous exams are available upon request.

For your study and a guideline for the exam, see the page of core topics of the required courses. However, the students should consult their exam committee members for the effective list of topics for their exams.

The examination committee will make the decision on the outcome of the examination subject to the following:

"The student must pass all three parts of the Examination. Students must attempt all three parts in the same semester. If a student fails one or more parts of the Examination on the initial attempt, the student may re-take all failed parts the next time the exams are offered (typically in the next semester)."

*(Approved by the Statistics Program Committee on April 18, 2012)*

## Comprehensive Examination Topics

The comprehensive exam covers the topics listed below (see also Comprehensive Exam Guide). The list of topics are maintained by the Statistics Program Committee and should be used as guidelines by instructors of the courses. Students preparing to take the comprehensive exam should consult with their examination committee members for more refined guidelines for their exams.

**Part I. Theory.** Theory of Statistics (STT 6610/6620)

**Part II. Methods. **Statistical Methods (STT 6660/6670)

**Part III. Applications. **A take-home project, which is designed to be applied in nature, is given at the end of Part II of the exam. One week will be allowed for completion of the project.

**Core Topics for Theory of Statistics (STT 6610-6620) **

- Definition of Probability: properties (sample space, events, compound events, mutually exclusive, independence, Additive Rule, Multiplication Rule, Bayes Rule), counting techniques, conditional probability
- Random Variables and Distributions: discrete (Binomial, Multinomial, Hypergeometric, Negative Binomial, Poisson, Geometric), continuous (uniform, normal, exponential, gamma, beta, Weibull, t, F, chi-square), expected values, MGF, location and scale parameters
- Joint Distributions: independence, conditional distributions, correlation, conditional expectation
- Functions of Random Vectors: transformation methods, sums of random variables, order statistics
- Limiting Distributions: convergence in distribution, CLT, asymptotically normal distributions, properties of weak convergence (Slutsky)
- Statistics: sampling distributions, point estimation and confidence intervals, evaluation of estimators-UMVUE, Cramer-Rao lower bound, sufficiency and completeness, exponential class
- Hypothesis Testing: power, one-sided and two-sided tests, most powerful tests, UMP tests, Neyman-Pearson Lemma, likelihood ratio tests
- Random Vectors and Distributions: covariance matrices, linear and quadratic forms, distribution of AY, where A is a matrix, independence of quadratic forms, Cochran-Fisher theorem
- The Linear Model: least squares estimates, full rank models, less than full rank models (conditional inverse, reparametrization), estimability in full and less than full rank models, Gauss-Markov theorem, BLUE
- Hypothesis Testing: EY in a linear subspace, A*b = C for a matrix A and vector C, power of test (definition and sample size considerations)
- Interval Estimation: confidence intervals, prediction intervals, simultaneous confidence intervals (Scheffe, Bonferroni, Tukey)
- Examples: multiple regression, one-way ANOVA, two-way ANOVA

**Core Topics for Statistical Methods (STT 6660-6670) **

- Graphical Display of Data: Interpretation of histograms, stem-and-leaf plots, scatterplots, boxplots.
- One- and Two-Sample Inference: z and t tests and confidence intervals for two independent samples and paired data. Wilcoxon signed-rank test and Mann-Whitney/Wilcoxon rank test; power, sample size.
- Categorical Data Analysis: One- and Two-dimensional tables; chi-squared tests and Fisher’s exact test.
- Simple Linear Regression: Least squares, inference regarding slope and intercept, confidence and prediction intervals.
- Diagnostic and Remedial Measures: Residual plots, residual diagnostics, transformations.
- Multiple Regression Model: Parameter estimation, overall F-test, tests for a single parameter and for subsets of parameters, coefficient of determination, general linear test approach, multicollinearity, lack of fit test, qualitative predictor variables, interaction regression models, residual analysis.
- Matrix Approach to Linear Regression: Random vectors and matrices; matrix notation for regression, general linear regression model; matrix results for least squares estimators, residuals, and fitted values; hat matrix.
- Basic design principles: randomization, replication, blocking, factorial design, randomized complete block designs.
- Single Factor ANOVA: Relation between ANOVA and regression, assumptions (e.g., homoscedasticity), fitting ANOVA model, F test for equality of factor levels, ANOVA table, analysis of factor levels and multiple comparisons (Tukey, Scheffé, and Bonferroni), residual analysis, transformations, nonparametric rank test.
- Multi0factor experiments: Interpreting interaction terms and main effects, ANOVA table, F tests, residual analysis, regression approach to two-factor ANOVA, analysis of factor effects in two-factor studies (Tukey, Scheffé, and Bonferroni), one observation per cell, unequal sample sizes in two-factor studies.
- Analysis Covariance
- Single-factor ANOVA for random effects: estimation and testing of variance components.
- Mixed- and random-effects models,including repeated measures
- Nested factors and split-plot designs
- (Optional) Incomplete block designs: existence, construction, estimability, connectivity, data plot, ANOVA, multiple comparisons
- Confounding and partial confounding for 2k factorial experiments: design, analysis
- 2(k-p) fractional factorial designs: design, analysis
- (Optional) More Recent Methods: Logistic regression, bootstrapping, randomization/permutation tests.

*Note: *Use of SAS and interpreting SAS output is done throughout the course.

## Financial Aid

Several sources of financial aid are available to qualified graduate students:

### Graduate Teaching Assistantships (GTA)

Each year, the Department of Mathematics and Statistics awards several graduate teaching assistantships. The stipend accompanying these GTA awards covers reasonable living expenses for the academic year. In order to qualify for a GTA position , a student must have a very good undergraduate record and good communication skills. A personal interview (possibly by telephone) is part of the review process. The GTA award includes an automatic tuition waiver.

**Graduate Research Assistantships (GRA)**

There are also some graduate research assistantships available through a cooperative arrangement with the Dept. of Family Medicine in the Wright State School of Medicine. These GRA awards carry a slightly higher stipend and are for a period of 12 months. These awards are intended to be renewed in the second year. Successful applicants for these stipends need good communication skills and some background in the biological sciences is preferred. The GRA award includes an automatic tuition waiver.

On occasion, there are graduate assistantships available on various grants and contracts or through other sources. These cannot always be anticipated in advance, but will be as widely publicized as possible when they are funded. There are also opportunities of various kinds available through Student Employment Services. If students are in need of financial support, it is a recommended that they check the Student Employment bulletin board in the Student Union, as new postings occur frequently. Student may also check with the School of Graduate Studies for other opportunities.

The graduate school periodically publishes announcements of fellowship programs with varying requirements and qualifications. The Statistics Graduate Advisor publicizes these to all current graduate students via email and attempts to circulate them to prospective students as well.

## Employment Opportunities and Information

As students reach the end of their work in our program, they may be looking for employment upon graduation. If so, there are several resources available. The most important of these are the faculty; we are usually happy to serve as references for you while you are applying for positions. Please use common courtesy and ask permission before using a faculty member as a reference. When you ask permission, please supply some details about hte position so that we can tailor our letters to suit the situation. If possible, please give the faculty member at least a week's notice when requesting a written reference.

Faculty are often notified of job opportunities via email, letter, and telephone. The Statistics Consulting Center maintains a job notebook that contains these notices for your use. The notebook may be perused any time that the SCC is open (8:30 - 5:00 weekdays). You are welcome to make copies of information in the notebook. Also included in the notebook are pages from the Occupational Outlook Handbook, which is published electronically by the Bureau of Labor Statistics. These pages (which were downloaded from the Worldwide Web) describe the types of jobs, educational background, etc. for Actuaries, Statisticians, and Operations Research Analysts, which are possible career choices dor someone with an M.S. in Applied Statistics.

Students may also use campus computers to search the World Wide Web for job opportunities. Several prior students have found excellent opportunities at ASA WebPages or http://jobs.statistics.com or http://www.sas.com/. Other employment websites may be found using an Internet search engine.

Also please note that some of our graduates continued their study to earn Ph.D. degrees at various other universities. Additionally, several are faculty members at various colleges and universities.