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Courses in LSA Statistics
The field of Statistics offers a variety of exciting career opportunities. Statistics deals with methods for the collection, visualization, modeling and analysis of data. Massive amounts of data are now routinely collected in business, health, environment, engineering and social sciences. Statistics is the science that transforms these data into information that is critical for decision making. Statistics has always played a major role in marketing, public policy, social and health sciences through the design and analysis of surveys. More recently, statistical methods have been an important part of advances in medicine and engineering such as genetics, tomography, speech recognition, computational vision, and so on.
Statistics (STATS)
STATS 125. Games, Gambling and Coincidences
Enrollment restricted to first-year students, including those with sophomore standing. (3). (MSA). (BS). (QR/1). May not be repeated for credit.

Students and faculty will work together solving problems related to games, gambling and coincidences, touching on many fundamental ideas in discrete probability, finite Markov chains, dynamic programming and game theory.

STATS 150. Making Sense of Data
(3). (MSA). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in SOC 210, IOE 265, STATS 250(350), 280, 400, 412, or ECON 404, ECON 405.

Can you really make statistics say anything you want? Yes and no. Some common statistical comparisons are susceptible to coercion, but there are others that can be trusted to tell the truth. We explore their differences, using the examples from the social and medical sciences and cutting-edge computing and graphical techniques.

STATS 250. Introduction to Statistics and Data Analysis
(4). (MSA). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in ECON 404 or 405, IOE 265, or STATS 280, 400 or 412.

A one term course in applied statistical methodology from an analysis-of-data viewpoint. Frequency distributions; measures of location; mean, median, mode; measures of dispersion; variance; graphic presentation; elementary probability; populations and samples; sampling distributions; one sample univariate inference problems, and two sample problems; categorical data; regression and correlation; and analysis of variance. Use of computers in data analysis.

STATS 280. Honors Introduction to Statistics and Data Analysis
Pre-calculus. (4). (MSA). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in ECON 404 or 405, or IOE 265, or SOC 210, or STATS 250 (350), 400, or 412.

This course is an introduction to statistical methods and data analysis at the honors level, targeting advanced undergraduate students who are interested in a challenging introductory course.

STATS 299. Workplace Internship for Undergraduate Statistics Majors
Consent of department required. (1). (EXPERIENTIAL). May be elected twice for credit. Offered mandatory credit/no credit.

This course allows Statistics majors to earn one credit for statistical work they perform as off-campus interns. Students must obtain advance approval from the Statistics Department for internship plans. Upon completion of the internship, the internship's offsite supervisor needs to provide documentation of satisfactory performance. Students also are required to submit a final report describing their internship duties and accomplishments and relating them to studies in Statistics.

STATS 401. Applied Statistical Methods II
MATH 115, and STATS 250 (350) or 400 or 405, or ECON 405, or NRE 438. (4). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in STATS 413.

An intermediate course in applied statistics which assumes knowledge of STAT 350/400-level material. Covers a range of topics in modeling and analysis of data including: review of simple linear regression, two-sample problems, one-way analysis of variance; multiple linear regression, diagnostics and model selection; two-way analysis of variance, multiple comparisons, and other selected topics.

STATS 403. Introduction to Quantitative Research Methods
MATH 115, one of STATS 250 (350), 280, 400, 412. (4). (BS). May not be repeated for credit.

This course introduces methods for planning, executing, and evaluating research studies based on experiments, surveys, and observational datasets. In addition to learning a toolset of methods, students will read and report on recent research papers to learn how study design and data analysis are handled in different fields.

STATS 404. Effective Communication in Statistics
STATS 470 or 480. (2). (BS). May not be repeated for credit. May not be used in the Statistics or Applied Statistics academic minor. Rackham credit requires additional work.

This course will focus on the principles of good written and oral communication of statistical information and data analyses. Participants will study communication principles and apply them in writing assignments and oral presentations of statistical analyses. Topics will include giving constructive feedback and rewriting to improve clarity and technical correctness.

STATS 406. Introduction to Statistical Computing
STATS 401 AND MATH 215; or STATS 403 and MATH 215; or STATS 412; or MATH 425. (Prerequisites enforced at registration.) (4). (BS). May not be repeated for credit. F.

Selected topics in statistical computing, including basic numerical aspects, iterative statistical methods, principles of graphical analyses, simulation and Monte Carlo methods, generation of random variables, stochastic modeling, importance sampling, numerical and Monte Carlo integration.

STATS 408. Statistical Principles for Problem Solving: A Systems Approach
High school algebra. (4). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in STATS 170.

Our purpose is to help you use quantitative reasoning to facilitate learning. Specifically, we introduce statistical and mathematical principles, and then use these as analogues in a variety of real world situations. The notion of a system, a collection of components that come together repeatedly for a purpose, provides an excellent framework to describe many real world phenomena and provides a way to view the quality of an inferential process.

STATS 412. Introduction to Probability and Statistics
Prior or concurrent enrollment in MATH 215. (3). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in ECON 405, STATS 280, 400, or IOE 265. One credit granted to those who have completed or are enrolled in STATS 250. May not be used in the Statistics or Applied Statistics academic minor. F, W, Sp.

An introduction to probability theory; statistical models, especially sampling models; estimation and confidence intervals; testing statistical hypotheses; and important applications, including the analysis of variance and regression.

STATS 414. Special Topics in Statistics
Consent of department required. Varies by term and instructor. (3 - 4). May be elected twice for credit. May be elected more than once in the same term. Rackham credit requires additional work.

A course in exploring topics of current interest in statistics, probability and/or data science. Content varies by term and instructor.

STATS 415. Data Mining and Statistical Learning
MATH 215 and 217, and one of STATS 401, 406, 412 or 426. (4). (BS). May not be repeated for credit.

This course covers the principles of data mining, exploratory analysis and visualization of complex data sets, and predictive modeling. The presentation balances statistical concepts (such as over-fitting data, and interpreting results) and computational issues. Students are exposed to algorithms, computations, and hands-on data analysis in the weekly discussion sessions.

STATS 425 / MATH 425. Introduction to Probability
MATH 215. (3). (BS). May not be repeated for credit. F, W, Sp, Su.

STATS 426. Introduction to Theoretical Statistics
STATS 425 and prior or concurrent enrollment in MATH 217, 412 or 451. (3). (BS). May not be repeated for credit.

An introduction to theoretical statistics for students with a background in probability. Probability models for experimental and observational data, normal sampling theory, likelihood-based and Bayesian approaches to point estimation, confidence intervals, tests of hypotheses, and an introduction to regression and the analysis of variance. This course serves as a prerequisite for many graduate-level statistics courses.

STATS 430. Applied Probability
STATS 425 or equivalent. (3). (BS). May not be repeated for credit.

Review of probability theory; introduction to random walks; counting and Poisson processes; Markov chains in discrete and continuous time; equations for stationary distributions; introduction to Brownian motion. Selected applications such as branching processes, financial modeling, genetic models, the inspection paradox, inventory and queuing problems, prediction, and/or risk analysis.

STATS 449 / BIOSTAT 449. Topics in Biostatistics
STATS 401, 403, or 425 or permission of instructor. (3). (BS). May not be repeated for credit.

Introduction to biostatistical topics: clinical trials, cohort and case-control studies; experimental versus observational date; issues of causation, randomization, placebos; case control studies; survival analysis; diagnostic testing; image analysis of PET and MRI scans; statistical genetics; longitudinal studies; and missing data.

STATS 470. Introduction to the Design of Experiments
STATS 401 or 412 or 425, or MATH 425. (Prerequisites enforced at registration.) (4). (BS). May not be repeated for credit. F.

Introduces students to basic concepts for planning experiments and to efficient methods of design and analysis. Topics covered include concepts such as randomization, replication and blocking; analysis of variance and covariance and the general linear model; factorial and fractional factorial designs, blocked designs, and split-plot designs.

STATS 480. Survey Sampling Techniques
STATS 401 or 412 or 425 or MATH 425. (Prerequisites enforced at registration.) (4). (BS). May not be repeated for credit. W.

Introduces students to basic ideas in survey sampling, moving from motivating examples to abstraction to populations, variables, parameters, samples and sample design, statistics, sampling distributions, Horvitz-Thompson estimators, basic sample design (simple random, cluster, systematic, multiple stage), various errors and biases, special topics.

STATS 485. Capstone Seminar
Consent of department required. Prior or concurrent enrollment in STATS 426 and STATS 500. Restricted to Statistics concentrators in their final year of study. (3). (BS). May not be repeated for credit.

This capstone seminar builds on students' substantial statistical backgrounds to reach a broader and deeper understanding of statistical theory and practice. Specific topics vary by instructor, but generally include sophisticated examples of statistical methods being used to address challenging applied research problems. In addition, the seminar explores how statisticians evaluate the strengths and weaknesses of existing statistical methods and develop new ones.

STATS 489. Independent Study in Statistics
Consent of instructor required. (1 - 4). (BS). (INDEPENDENT). May be repeated for a maximum of 4 credits. May not be used in the Statistics or Applied Statistics academic minor.

Individual study of advanced topics in statistics, reading and/or research in applied or theoretical statistics.

STATS 499. Honors Seminar
Consent of instructor required. Permission of departmental Honors advisor. (2 - 3). (BS). (INDEPENDENT). May not be repeated for credit. May not be used in the Statistics or Applied Statistics academic minor. Continuing Course. Y grade can be reported at end of the first-term to indicate work in progress. At the end of the second term, the final grade is posted for both term's elections. F, W, Sp.

Advanced topics, reading and/or research in applied or theoretical statistics.

STATS 500. Applied Statistics I
MATH 217, 417, or 513; and STATS 250 (350) or 426. (3). (BS). May not be repeated for credit. F.

Linear models; definitions, fitting, identifiability, collinearity, Gauss-Markov theorem, variable selection, transformation, diagnostics, outliers and influential observations. ANOVA and ANCOVA. Common designs. Applications and real data analysis are stressed, with students using the computer to perform statistical analyses.

STATS 504. Statistical Consulting
STATS 401 or 500. (3). (BS). May be repeated for a maximum of 9 credits.

The goal of this course is to introduce students to key aspects of statistical consulting and data analysis activities. Students will be involved in problem solving and real applications individually or in groups, analyze data, write reports, and make presentations.

STATS 525 / MATH 525. Probability Theory
MATH 451 (strongly recommended). MATH 425/STATS 425 would be helpful. (3). (BS). May not be repeated for credit.

STATS 526 / MATH 526. Discrete State Stochastic Processes
MATH 525 or STATS 525 or EECS 501. (3). (BS). May not be repeated for credit.

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