## Undergraduate Courses

### 100-Level Statistics Courses

**Statistics 100: Introduction to Statistical Reasoning**

Provides an overview of the field of statistics, including methods of summarizing and analyzing data, statistical reasoning for learning from observations (experimental or sample), and techniques for dealing with uncertainties in drawing conclusions from collected data. Emphasis is on presenting underlying concepts rather than covering a variety of different methodologies.

*No credit to those who have completed or are enrolled in SOC 210, STATS 250/350, 400, 412, IOE 265, ECON 404 or 405 or ENVIRON/NRE 438.*

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

Emphasizes problem solving and modeling 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**

The course establishes techniques for determining whether relationships between variables, particularly intervention and outcome variable, exist in the sense that the appearance of an association can't be explained by chance. The course formalizes and extends the set of phenomena that can be numerically represented in a way as to permit these modes of analysis. This is done in the interest of making predictions and judgments, particularly about what hypotheses are and are not supported by a set of data and to what extent the data support them. It introduces general perspectives from the field of Statistics to a broad audience of lower-division students. 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 examples from the social and medical sciences and cutting-edge computing and graphical techniques.* (First Year Seminar)(3 Credits)*

*May not be repeated for credit. No credit to those who have completed or are enrolled in SOC 210, IOE 265, STATS 250/350, 400, 412, ECON 404, 405, or ENVIRON/NRE 438*

**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 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 280: Honor 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.* (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.*

### 300-Level Statistics Courses

**Statistics 306: Introduction to Statistical Computing**

This course introduces basic concepts in computer programming and statistical computing techniques as they are applied to data extraction and manipulation, statisitcal processing and visualization.

*Enforced Pre-requisite: [STATS 250 OR STATS 280 OR STATS 412] and MATH 116*

### 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. 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: MATH 115, one of STATS 180, STATS 250, STATS 280, or STATS 412, or ECON 451. 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: Introduction to Statistical Computing**

Selected topics in statistical computing including basic numerical aspects, iterative statistical methods, principles of graphical analysis, simulation and Monte Carlo methods, generation of random variables, stochastic modeling, importance sampling, numerical and Monte Carlo integration. *(4 Credits)*

*Enforced Pre-requisite:* *STATS 401 and MATH 215 OR STATS 403 and MATH 215 OR STATS 412 OR MATH 425.*

**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 situation. 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)*

*Advisory Pre-requisite: Prior or concurrent enrollment in MATH 215.*

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

**Stat 413: Applied Regression Analysis**

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.*

**Stat 414: Introduction to Bayesian Data Analysis**

The course is an introduction to both the principles and practice of Bayesian inference for data analysis using the statistical software R. At the end of this course students will be familiar with the Bayesian paradigm, and will be able to use R to analysis different classes of statistical models. The course gives an introduction to the computational tools (Markov Chain Monte Carlo) needed for Bayesian data analysis and develops statistical modeling skills through a hands-on data analysis approach. Topics include: prior/posterior distributions, Bayes 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)*

*Pre-requisites: (STATS 426 and STATS 406) or equivalent courses. Familiarity with R programming*

**Statistics 415: Data Mining and Statistical Learning**

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)**

Basic concepts of probability; expectation, variance, covariance; distribution functions; and bivariate, marginal, and conditional distributions.* (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)*

*Advisory Pre-requisite: STATS 425 and prior or concurrent enrollment in MATH 217, 412, or 451.*

**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: STATA 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 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**

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 500. Restricted to Statistics concentrators in their final year of study.*

**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)

*Permission of Departmental Honors advisor required: stat-ugrad-honors-ad@umich.edu.*