## Undergraduate Courses

### 100-Level Statistics Courses

**Statistics 100: Introduction to Statistics, Probability and Mathematical Modeling**

Statistical reasoning for learning from observations; continuous and discrete mathematical approaches for modeling a variety of scientific phenomena. Emphasis is on the interplay between data, statistical and mathematical principles and the human activity of modeling, as opposed to specific methods or theories. *(4 credits)*

*No credit granted to those who have completed or are enrolled in SOC 210, STATS 280, 250, 400, 405 or 412, IOE 265, or ECON 404 or 405.*

**Statistics 125: Games, Gambling and Coincidences**

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. *(First Year Seminar) (3 Credits)*

**Statistics 150: Making Sense of Data**

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. *(3 Credits)*

*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.*

**STATS 180: AP Statistics**

Credit is assigned for a score of 4 or 5 on the AP Statistics test. Those with STATS 180 credit may proceed to STATS 280 (while keeping full credit for STATS 180) or may take STATS 250, in which case they receive full credit for STATS 250 but lose their credit for STATS 180.

Students with STATS 180 may also bypass both STATS 250 and STATS 280 and take any Statistics class for which STATS 250 is prerequisite. It is an individual choice which Statistics course to take following AP Statistics, but here is some guidance.

Those who took AP Statistics several years ago, or do not feel ready to proceed to a more advanced course, are encouraged to take STATS 250. Otherwise, STATS 280 may be a suitable choice, particularly for those considering a Statistics major. Those considering a Statistics or Applied Statistics minor can take either STATS 280 or STATS 401.

### 200-Level Statistics Courses

**Statistics 206: Introduction to Data Science**

Data science combines mathematical and computational skills, together with statistical and ethical reasoning, to draw conclusions from data. Programming is introduced with an emphasis on data analysis. Probability and algorithms are developed as tools for formal statistical modeling and inference, and for exploratory analysis and visualization of data.

*Advisory pre-req: high school algebra*

**Statistics 250: Introduction to Statistics and Data Analysis**

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. *(4 Credits)*

*No credit granted to those who have completed or are enrolled in ECON 451, IOE 265, or STATS 280, or STATS 412. Those with credit for STATS 250 receive no credit for STATS 180.*

**Statistics 251 – Introductory Statistics Supplement for Mathematics Education**

This course is a supplemental Lab section to Stats 250. It follows the content trajectory of Stats 250, providing discussion and coursework assignments on (1) statistical knowledge needed for future elementary, middle, and high school teachers who will teach statistics; and (2) pedagogical practices of teaching statistics throughout the K-12 curriculum. (*1 credit.)*

*Enforced prerequisites: Prior or concurrent enrollment in STATS 250.*

**Statistics 280: Honors Introduction to Statistics & Data Analysis**

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.* *Definition and summary of univariate and bivariate data, distributions, correlation, and associated visualization techniques; randomization in comparative studies and in survey sampling; basic probability calculus, including conditional probabilities, concept of random variable and their properties; sampling distributions and the central limit theorem; statistical inference, including hypothesis test, confidence intervals; one sample and two sample problems with binary and continuous data, including nonparametric procedures; analysis of variance; simple and bivariate regression; simple design of experiments; chi-square and rank-based tests for association and independence.* (4 Credits)*

*No credit granted to those who have completed or are enrolled in ECON 451, IOE 265, SOC 210, STATS 250 or STATS 412.*

**STATS 299 - Workplace Internship for Undergraduate Statistics Majors**

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. *(1 credit.)*

*Consent of department required. (EXPERIENTIAL). May be elected twice for credit. Offered mandatory credit/no credit. *

### 300-Level Statistics Courses

**Statistics 306: Introduction to Statistical Computing (DATASCI 306)**

This course introduces basic concepts in computer programming and statistical computing techniques as they are applied to data extraction and manipulation, statistical processing and visualization. It is aimed primarily at undergraduate majors and minors in Statistics.

*Enforced Pre-requisite: [STATS 206 or STATS 250 OR STATS 280 OR STATS 412 or IOE 265] and [MATH 116 or MATH 121 or MATH 156 or MATH 186].*

### 400-Level Statistics Courses

**Statistics 401: Applied Statistical Methods II**

An intermediate course in applied statistics, covering 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. *(4 Credits)*

*Advisory Pre-requisite: MATH 115, one of STATS 180, STATS 250, STATS 280 or STATS 412, or ECON 451, or NRE 438. No credit granted if completed or enrolled in STATS 413.*

**Statistics 403: Introduction to Quantitative Research Methods**

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. *(4 Credits)*

*Advisory Pre-requisite: STATS 401 or (STATS 250 and [MATH 214 or MATH 217]). May not be repeated for credit.*

**Statistics 404: Effective Communication in Statistics**

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. *(2 Credits)*

*Advisory Pre-requisite: STATS 470 or STATS 480*

**Statistics 406: Computational Methods in Statistics and Data Science (DATASCI 406)**

This course introduces basic computational methods as needed in statistics. It is aimed primarily at undergraduate majors in Statistics and Data Science.

*Enforced Pre-requisite: [MATH 214 OR MATH 217 OR MATH 417] AND [(STATS 250 AND MATH /STATS 425) OR STATS 412 OR STATS 426] AND [Stat 306 OR EECS 183 OR ENGR 101 OR EECS 280].*

**Statistics 408: Statistical Principles for Problem Solving: A Systems Approach**

Our purpose is to help students 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. *(4 Credits)*

*Advisory Pre-requisite: High school algebra.*

**Statistics 412: Introduction to Probability & Statistics**

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. *(3 Credits)*

*Enforced Pre-requisite: MATH 215 or MATH 285.*

*No credit granted to those who have completed or are enrolled in ECON 451 or 453, STATS 250 or 280, or IOE 265. *

**Statistics 413: Applied Regression Analysis (DATASCI 413)**

The following topics will be covered: a) models and methods of inference for simple and multiple regression, regression splines; b) dignostics, multicollinearity, influence, outliers, transformation, model selection, and dimension reduction; c) principal component regression, ridge and robust regression, non-linear regression, non-parametric regression and Lasso; d) generalized linear models, binary and Poisson regression.

*Enforced Pre-requisites: [Math 214 OR Math 217 OR Math 417] AND [(STATS 250 AND MATH/STATS 425) OR STATS 412 OR STATS 426]*

*No credit granted for those who have completed or enrolled in STATS 500.*

**Statistics 414: Topics Course**

Selected topics in Applied Statistics.

Examples of previous Stats 414 topics:

"Introduction to Bayesian Data Analysis"

"Applied Survival Analysis"

**Statistics 415: Data Mining and Statistical Learning (DATASCI 415)**

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. *(4 Credits)*

*Advisory Pre-requisite: MATH 215 and 217, and one of STATS 401, 406, 412 or 426*

**Statistics 425: Introduction to Probability (Math 425)**

This course introduces students to both useful and interesting ideas from the mathematical theory of probability and to a number of application of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of Math 116 and 215.* (3 Credits)*

*Advisory Pre-requisite*: *MATH 215.*

**Statistics 426: Introduction to Theoretical Statistics**

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. *(3 Credits)*

*Effiective W20 - Enforced prerequisites: (MATH/STATS 425 or STATS 412) and (MATH 214 or MATH 217).*

**Statistics 430: Applied Probability**

Review of probability theory; introduction to random walks; counting and Poisson processes; Markov chains in discrete and continuous time; equations for stationary distribution 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. *(3 Credits)*

*Advisory Pre-requisite: STATS 425 or equivalent.*

**Statistics 449: Topics in Biostatistics (Biostat 449)**

Introduction to biostatistical topics: clinical trials, cohort and case-control studies; experimental versus observational data; 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.* (3 Credits)*

*Advisory Pre-requisite: STATS 401, 403, or 425.*

**Statistics 451: Bayesian Data Analysis (DATASCI 451)**

The course is an introduction to both principles and practice of Bayesian inference for data analysis. At the end of this course students will be familiar with the Bayesian paradigm, and will be able to analyze different classes of statistical models. The course gives an introduction to the computational tools needed for Bayesian data analysis and developes statistical modeling skills through a hands-on data analysis approach. Topics include: prior/posterior distributions, Bates rule, Markov Chain Monte Carlo computations, linear and generalized linear models, mixed effect models, hierarchical models, analysis of spatial data, model selection and comparison, model checking. *(3 credits)*

*Enforced Prerequisites: (STATS 412 or STATS 425) and (STATS 306 or EECS 280).*

**Statistics 470: Introduction to the Design of Experiments**

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; fractional factorial designs, blocked designs, and split-plot designs. *(4 Credits)*

*Enforced Pre-requisites:* *One of STATS 401, 412, or 425, or MATH 425.*

**Statistics 480: Survey Sampling Techniques**

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, systematics, multiple stage), various errors and biases, special topics. *(4 Credits)*

*Enforced Pre-requisites:* *One of STATS 401, 412, 425, or MATH 425.*

**Statistics 485: Capstone Seminar (DATASCI 485)**

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. *(3 Credits)*

*Prior or concurrent enrollment in STATS 426 and STATS 413. Restricted to Statistics or Data Science majors in their final year of study, or Statistics honors students in their junior year.*

**Statistics 489: Independent Study in Statistics**

Individual study of advanced topics in statistics, reading and/or research in applied or theoretical statistics.* (1-4 Credits)*

*Permission of instructor required.*

**Statistics 499: Honors Seminar**

Advanced topics, reading and/or research in applied or theoretical statistics. (2-3 Credits)

This may be offered as a group seminar or as an individually supervised project. Discuss available options with an undergraduate advisor.

Effective F19: STATS 499-003 in Fall semesters will also fulfill Upper Level Writing (ULWR).

*Permission of Departmental Honors advisor required: statsugradprogram@umich.edu.*

**Please send permission requests to statsugradprogram@umich.edu**