### Statistics

**Head:** E. P. Smith

**Professors:** J. B. Birch, I. Hoeschele, S. Keller, J.P. Morgan, E. P. Smith, G.G. Vining, and W.H. Woodall

**Associate Professors:** P. Du, M. Ferreira, F. Guo, Y. Hong, I. Kim, S. Leman, and G. R. Terrell

**Assistant Professors:** X. Deng, F. Guo, Y. Hong, L. House, J. Li, R. Tang, X. Wu, and H. Zhu

**Assistant Research Professors:** C. Franck, J. Li, and E. Vance

**Professor of Practice:** A. Driscoll and J. Robertson Evia

**Instructors:** C. Tavera

Web: www.stat.vt.edu

### Overview

Statistics courses are offered at both the undergraduate and the graduate levels for students preparing for professions in statistics, for students who need statistical tools to engage in scientific research, and for students who want to acquire knowledge of the important concepts of probability and statistical inference.

Statistics courses for graduate students and programs leading to the M.S. and Ph.D. degrees in statistics are described in the Graduate Catalog and in a special bulletin available from the department.

### Bachelor of Science in Statistics

All statistics majors are required to own specified personal computers and software. Consult the department for details.

A special brochure describing the department and the B.S. program, intended for prospective entering freshmen, is available from the department upon request.

Cooperative Education and Internship positions are available in industry and government, offering valuable practical experience. Students participating in such an experience can receive academic credit which will count towards graduation requirements.

#### Degree Requirements

The graduation requirements in effect at the time of graduation apply. When choosing the degree requirements information, always choose the year of your expected date of graduation. Requirements for graduation are referred to via university publications as "Checksheets". The number of credit hours required for degree completion varies among curricula. Students must satisfactorily complete all requirements and university obligations for degree completion.

The university reserves the right to modify requirements in a degree program. However, the university will not alter degree requirements less than two years from the expected graduation year unless there is a transition plan for students already in the degree program.

Please visit the University Registrar website at http://www.registrar.vt.edu/graduation/checksheets/index.html for degree requirements.

### Minor in Statistics

Please visit the University Registrar website at http://www.registrar.vt.edu/graduation/checksheets/index.html to view requirements for the minor.

The department reserves the right to withhold credit if a student takes a course, the content of which is partially duplicated in a course already taken (see "Course Duplications" below).

### Laboratory for Interdisciplinary Statistical Analysis (LISA)

Associated with the statistics department, the Laboratory for Interdisciplinary Statistical Analysis (LISA) provides statistical assistance for research projects throughout the university community. Faculty members, staff, and students are available to aid in statistical design and analysis for any authorized research study here at the university and at other state agencies.

### Satisfactory Progress

University policy requires that students who are making satisfactory progress toward a degree meet minimum criteria toward the General Education (Curriculum for Liberal Education) (see "Academics") and toward the degree.

Satisfactory progress requirements toward the B.S. in Statistics can be found on the major checksheet by visiting the University Registrar website at http://www.registrar.vt.edu/graduation/checksheets/index.html.

### Course Duplications

- No credit will be given for 2004 if taken with or after any other statistics course
- For non-majors, all of the following are partial duplications: 3005, 3604, 3615, 4604, and 4705.
- For majors, 4604 and 4705 may replace 3005 if taken before becoming a major.
- All the following are partial duplications: 3006, 3616, and 4706.
- No credit will be given for 3704 if taken after any of the following: 3005, 3615, 4604, and 4705.
- BIT 2405 may not be used as a substitute for credit as a statistics course unless the student was officially registered as a Business major at the time BIT 2405 was taken.

### Computer Literacy

Many statistics courses involve the use of statistics software, primarily MINITAB, SAS, JMP or R. Experience with the software is not expected, but students should have familiarity with either the Windows or Macintosh operating system and have access to a computer.

### Course Projects

Many of the upper-division courses include a project, generally to be completed in small groups. These projects are designed to give students the kind of insight and experience in realistic statistical practice that cannot be obtained in classroom lectures or short-term homework assignments.

### Undergraduate Course Descriptions (STAT)

1004: THE FIRST YEAR EXPERIENCE IN LEARNING FROM DATA

Introduction to the field of statistics and aspects of
college life for first year students. Topics included:
history of the statistics; key roles of statisticians in
field, such as actuarial sciences, pharmaceutical,
medical, and bioinformatics industries, governmental
agencies, academia; fundamental principles of
statistical fields of study and applications;
exploring data sets; and aspects of college life
for first-year students.
(2H,2C)

2004: INTRODUCTORY STATISTICS

Fundamental concepts and methods of statistics with
emphasis on interpretation of statistical arguments.
An introduction to design of experiments, data analysis,
correlation and regression, concepts of probability
theory, sampling errors, confidence intervals, and
hypothesis tests. (See also Course Duplications).
Pre: MATH 1015 or MATH 1014.
(4H,3C)

2524: DATA SCIENCE

Organize, summarize, and visualize large-scale datasets from
web studies. Interpret visualizations and communicate
information discovered by data explorations. Program in R or
comparable statistics programming language. Not intended for
statistics majors.
Pre: (3005 or 3615), (MATH 1114, MATH 1206 or MATH 2015), (CS 1054 or CS 1064).
(3H,3C)

2964: FIELD STUDY

Pass/Fail only. Variable credit course.

2974H: INDEPENDENT STUDY

Honors section.
Variable credit course.

2984: SPECIAL STUDY

Variable credit course.

3005-3006: STATISTICAL METHODS

3005: Basic statistical methodology: exploratory data
techniques, estimation, inference, comparative analysis
by parametric, nonparametric, and robust procedures.
Analysis of variance (one-way), multiple comparisons, and
categorical data. 3006: Analysis of variance, simple and
multiple, linear and nonlinear regression, analysis of
covariance. Use of MINITAB.
STAT 3005 duplicates STAT 3615 and STAT 4604, only one
may be taken for credit.
STAT 3006 duplicates STAT 3616, STAT 4604 and STAT 4706,
only one may be taken for credit.
Pre: MATH 1206 or MATH 1226 for 3005; 3005 for 3006.
(3H,3C)

3094: SAS PROGRAMMING

Introduction to basic programming techniques: creating DATA
and PROC statements, libraries, functions, programming
syntax and formats. Other topics include loops, SAS Macros
and PROC IML. Emphasis is placed on using these tools for
statistical analyses. The pre-requisite may be substituted
for an equivalent course.
Pre: 3005.
(3H,3C)

3104: PROBABILITY AND DISTRIBUTIONS

Probability theory, including set theoretic and
combinatorial concepts; in-depth treatment of discrete
random variables and distributions, with some introduction
to continuous random variables; introduction to estimation
and hypothesis testing.
Pre: (MATH 1206 or MATH 1226 or MATH 2015 or MATH 1026 or MATH 1526), (STAT 3005 or S
TAT 3615).
(3H,3C)

3424: INTRODUCTION TO STATISTICAL NEUROSCIENCE AND IMAGE ANALYSIS

Analysis of data arising in studies in neuroscience and
from fMRI neuroimaging. Topics include background on
neuroscience and the brain, overview of structural and
functional MRI data, introduction to MATLAB, overview of
linear models, contrasts, and statistical parametric
mapping, experimental design, and Bayesian analysis.
Pre: 3006 or 3616.
(3H,3C)

3504: NONPARAMETRIC STATISTICS

Statistical methodology based on ranks, empirical
distributions, and runs. One and two sample tests, ANOVA,
correlation, goodness of fit, and rank regression,
R-estimates and confidence intervals. Comparisons with
classical parametric methods. Emphasis on assumptions and
interpretation.
Pre: 3006 or 3616 or 4106 or 4604 or 4706.
(3H,3C)

3604: STATISTICS FOR THE SOCIAL SCIENCES

Statistical methods for nominal, ordinal, and interval
levels of measurement. Topics include descriptive
statistics, elements of probability, discrete and continuous
distributions, one and two sample tests, measures of
association. Emphasis on comparison of methods and
interpretations at different measurement levels.
(See also Course Duplications).
Pre: MATH 1015 or MATH 1014.
(3H,3C)

3615-3616: BIOLOGICAL STATISTICS

Descriptive and inferential statistics in a biological
context. 3615: Fundamental principles, one- and two-sample
parametric inference, simple linear regression, frequency
data. 3616: One- and two-way ANOVA, multiple
regression, correlation, nonparametrics, using the MINITAB
computer package.
STAT 3615 partially duplicates STAT 3005 and STAT 4604,
only one may be taken for credit.
STAT 3616 partially duplicate STAT 3006, 4604 and 4706,
only one may be taken for credit.
(3H,3C)

3654 (CMDA 3654) (CS 3654): INTRODUCTORY DATA ANALYTICS & VISUALIZATION

Basic principles and techniques in data analytics;
methods for the collection of, storing, accessing,
and manipulating standard-size and large datasets;
data visualization; and identifying sources of bias.
Pre: CMDA 2006.
(3H,3C)

3704: STATISTICS FOR ENGINEERING APPLICATIONS

Introduction to statistical methodology with emphasis on
engineering experimentation: probability distributions,
estimation, hypothesis testing, regression, and analysis of
variance. Only one of the courses 3704, 4604, 4705, and
4714 may be taken for credit.
Pre: MATH 2224 or MATH 2204 or MATH 2204H.
(2H,2C)

4004: METHODS OF STATISTICAL COMPUTING

Computationally intensive computer methods used in
statistical analyses. Statistical univariate and
multivariate graphics; resampling methods including
bootstrap estimation and hypothesis testing and
simulations; classification and regression trees;
scatterplot smoothing and
splines.
Pre: (4105, 4214).
(4H,3C)

4024: COMMUNICATION IN STATISTICAL COLLABORATIONS

Theory and examples of effective communication in the
context of statistical collaborations. Practice developing
the communication skills necessary to be effective
statisticians using peer feedback and self-reflection.
Topics include helping scientists answer their research
questions, writing about and presenting statistical concepts
to a non-statistical audience, and managing an effective
statistical collaboration meeting.
Pre-requisite: Senior standing in the Department of
Statistics
Pre: 4105, 4204.
Co: 4214.
(3H,3C)

4094: INTRODUCTION TO PROGRAMMING IN R

Introduction to R programming techniques with an emphasis
on statistical analyses. Topics include: data objects,
loops, importing/exporting datasets, graphics, functions,
t-tests, ANOVA, linear regression, nonparametric tests, and
logistic regression.
Pre: 3615.
(1H,1C)

4105-4106: THEORETICAL STATISTICS

4105: Probability theory, counting techniques, conditional
probability; random variables, moments; moment generating
functions; multivariate distributions; transformations of
random variables; order statistics. 4106: Convergence of
sequences of random variables; central limit theorem;
methods of estimation; hypothesis testing; linear models;
analysis of variance.
STAT 4105 partially duplicates STAT 4705, STAT 4714, and
STAT 4724, only one may be taken for credit.
Pre: MATH 2224 for 4105; 4105 for 4106.
(3H,3C)

4204: EXPERIMENTAL DESIGNS

Fundamental principles of designing and analyzing
experiments with application to problems in various subject
matter areas. Discussion of completely randomized,
randomized complete block, and Latin square designs,
analysis of covariance, split--plot designs, factorial and
fractional designs, incomplete block designs.
Pre: 3006 or 3616 or 4106 or 4706 or 5605 or 5615.
(3H,3C)

4214: METHODS OF REGRESSION ANALYSIS

Multiple regression including variable selection procedures;
detection and effects of multicollinearity; identification
and effects of influential observations; residual analysis;
use of transformations. Non-linear regression, the use of
indicator variables, and logistic regression. Use of SAS.
Pre: 3006 or 3616 or 4106 or 4706 or 5606 or 5616.
(3H,3C)

4364: INTRODUCTION TO STATISTICAL GENOMICS

Statistical methods for bioinformatics and genetic studies,
with an emphasis on statistical analysis, assumptions, and
problem-solving. Topics include: commonly used statistical
methods for gene identification, association mapping and
other related problems. Focus on statistical tools for gene
expression studies and association studies, muliple
comparison procedures, likelihood inference and
preparation for advanced study in the areas of
bioinformatics and statistical genetics.
Pre: (3006, MATH 1206, CS 1044) or (STAT 3006, MATH 1206, CS 1054) or (STAT 3006, MATH 1206, CS 1114).
(3H,3C)

4444: APPLIED BAYESIAN STATISTICS

Introduction to Bayesian methodology with emphasis
on applied statistical problems: data displaying, prior
distribution elicitation, posterior analysis, models for
proportions, means and regression.
Pre: MATH 2224, (STAT 3104 or STAT 4105 or STAT 4705), (STAT 3006 or STAT 3616 or STAT 4706).
(3H,3C)

4504: APPLIED MULTIVARIATE ANALYSIS

Non-mathematical study of multivariate analysis.
Multivariate analogs of univariate test and estimation
procedures. Simultaneous inference procedures.
Multivariate analysis of variance, repeated measures,
inference for dispersion and association parameters,
principal components analysis, discriminate analysis,
cluster analysis. Use of SAS.
Pre: 3006 or 4706 or 5606 or 5616.
(3H,3C)

4514: CONTINGENCY TABLE ANALYSIS

Statistical techniques for frequency data. Goodness-of-fit.
Tests and measures of association for two-way tables.
Log-linear models for multidimensional tables. Parameter
estimation, model selection, incomplete tables, ordinal
categories, logistic regression. Use of SAS and SPSSx.
Pre: 3006 or 3616 or 4106 or 4706 or 5606 or 5616.
(3H,3C)

4524: SAMPLE SURVEY METHODS

Statistical methods for the design and analysis of survey
sampling. Fundamental survey designs. Methods of
randomization specific to various survey designs.
Estimation of population means, proportions, totals,
variances, and mean squared errors. Design of questionnaires
and organization of a survey.
Pre: 3006 or 3616 or 4106 or 4706 or 5606 or 5616.
(3H,3C)

4534: APPLIED STATISTICAL TIME SERIES ANALYSIS

Applied course in time series analysis methods. Topics
include regression analysis, detecting and address
autocorrelation, modeling seasonal or cyclical trends,
creating stationary time series, smoothing techniques,
forecasting and forecast errors, and fitting autoregressive
integrated moving average models.
Pre: 3006 or 4104 or 4706 or 4714 or 3616 or BIT 2406.
(3H,3C)

4584 (MATH 4584): ADVANCED CALCULUS FOR STATISTICS

Introduction to those topics in advanced calculus and
linear algebra needed by statistics majors. Infinite
sequences and series. Orthogonal matrices, projections,
quadratic forms. Extrema of functions of several variables.
Multiple integrals, including convolution and nonlinear
coordinate changes.
Pre: (MATH 1114 or MATH 2114 or MATH 2114H), (MATH 1205 or MATH 1225), (MATH 1206 or
MATH 1226), (MATH 2224 or MATH 2204 or MATH 2204H).
(3H,3C)

4604: STATISTICAL METHODS FOR ENGINEERS

Introduction to statistical methodology with emphasis on
engineering applications: probability distributions,
estimation, hypothesis testing, regression, analysis of
variance, quality control. Only one of the courses 4604,
4705, and 4714 may be taken for credit.
STAT 4604 partially duplicates STAT 3005, STAT 3615,
STAT 3006, STAT 3616 and STAT 4706. Only one may be taken
for credit.
Pre: MATH 1206 or MATH 1226.
(3H,3C)

4654 (CMDA 4654) (CS 4654): INTERMEDIATE DATA ANALYTICS AND MACHINE LEARNING

A technical analytics course. Covers supervised and
unsupervised learning strategies, including regression,
generalized linear models, regularization, dimension
reduction methods, tree-based methods for classification,
and clustering. Upper-level analytical methods shown in
practice: e.g, advanced naive Bayes and neural networks.
Pre: CMDA 2006.
(3H,3C)

4664 (CMDA 4664): COMPUTATIONAL INTENSIVE STOCHASTIC MODLEING

Stochastic modeling methods with an emphasis in
computing are taught. Select concepts from the
classical and Bayesian paradigms are explored to
provide multiple perspectives for how to learn from
complex, datasets. There is particular focus on nested,
spatial, and time series models.
Pre: CMDA 2006.
(3H,3C)

4705-4706: PROBABILITY AND STATISTICS FOR ENGINEERS

Basic concepts of probability and statistics with emphasis
on engineering applications. 4705: Probability, random
variables, sampling distributions, estimation, hypothesis
testing, simple linear regression correlation, one-way
analysis of variance. 4706: Multiple regression, analysis
of variance, factorial and fractional experiments. Only
one of the courses 3704, 4604, 4705, 4714, and 4724 may be
taken for credit.
Pre: MATH 2224 or MATH 2204 or MATH 2204H for 4705; 4705 or 4105 for 4706.
(3H,3C)

4714: PROBABILITY AND STATISTICS FOR ELECTRICAL ENGINEERS

Introduction to the concepts of probability, random
variables, estimation, hypothesis testing, regression, and
analysis of variance with emphasis on application in
electrical engineering. Only one of the courses 3704,
4604, 4705, 4714 and 4724 may be taken for credit.
Pre: MATH 2224 or MATH 2204 or MATH 2204H.
(3H,3C)

4804 (AAEC 4804): ELEMENTARY ECONOMETRICS

Economic applications of mathematical and statistical
techniques: regression, estimators, hypothesis testing,
lagged variables, discrete variables, violations of
assumptions, simultaneous equations.
Pre: (3005 or 3604), (AAEC 1006).
(3H,3C)

4964: FIELD STUDY

Pass/Fail only. Variable credit course.

4974: INDEPENDENT STUDY

Variable credit course.

4974H: INDEPENDENT STUDY

Honors section.
Variable credit course.

4984: SPECIAL STUDY

Variable credit course.

4994: UNDERGRADUATE RESEARCH

Variable credit course.

4994H: UNDERGRADUATE RESEARCH

Honors section.
Variable credit course.