# Courses in Statistics (Division 489)

300. Introduction to Statistical Reasoning. (3). (NS).

This course is designed to provide an overview of the field of statistics. Course topics include approaches to the collection of numerical data, methods of analyzing and summarizing such data, statistical reasoning as a means of learning from observations (experimental or sample), and techniques for dealing with uncertainties in drawing conclusions from collected data. Basic fallacies in common statistical analyses and reasoning are discussed and proper methods indicated. Alternative approaches to statistical inference are also discussed. The course emphasis is on presenting basic underlying concepts rather than on covering a wide variety of different methodologies. Applications are drawn from a wide variety of other disciplines. Evaluation is based upon class examinations, a final examination, and weekly assignments. The course format is lecture with some discussion.

310. Elements of Probability. Prior or concurrent enrollment in Math. 215. (3). (NS).

This course covers the main ideas and uses of probability: expectation, variance, covariance, distribution functions, bivariate, marginal and conditional distributions, the binomial and related distributions, the Poisson process, the exponential and gamma distributions, the normal sample statistics, the law of large numbers, the central limit theorem. There are regularly assigned homework exercises, two in-class examinations, and a final examination. The emphasis is on problem solving and applications.

311/I.O.E. 365. Engineering Statistics. Math. 215 and Eng. 102, or equivalent. No credit granted to those who have completed 412. (4). (Excl).

Analysis of engineering data associated with stochastic industrial processes. Topics include: fundamentals of distribution analyses; process model identification, estimation, testing of hypothesis, validation procedures, and evaluation of models by regression and correlation. Students are required to use the MTS computer system for problem solving. (Herrin)

402. Introduction to Statistics and Data Analysis. No credit granted to those who have completed 412. (4). (NS).
Section 00l.
In this course students are introduced to the concepts and applications of statistical methods and data analysis. Statistics 402 has no prerequisite and has been elected by students whose mathematics background includes only high school algebra. Examples of applications are drawn from virtually all academic areas. The course format includes three lectures and a laboratory (l.5 hours per week). The laboratory section covers some of the data analysis material and introduces the use of interactive computing through the use of MIDAS. Course evaluation is based on a combination of three examinations given Wednesday evenings, a final examination and teaching fellow input. (Rothman)

Section 002. This course is designed for students with an interest in the application of the scientific method and in the use of Michigan Interactive Data Analysis System (MIDAS). Statistics 402 has no prerequisite and has been elected by many students whose mathematics background includes only high school algebra. The course is "applications oriented" and is appropriate for students from all academic areas. The course focuses on the general problems associated with conclusions drawn on the basis of observation. Examples which reflect student interests are chosen, and all concepts are illustrated via these examples. The course format includes three lectures and a laboratory (l.5 hours) each week. The laboratory introduces the use of MIDAS and serves as a recitation section. Course evaluation is based upon a combination of class examinations, a midterm, a final, and class discussion. (Ericson)

403. Introduction to Statistics and Data Analysis II. Stat. 402. (4). (NS).
Applied Regression and Analysis of Variance.
This course surveys some intermediate topics in multiple linear regression and the analysis of variance and covariance, stressing applications rather than theory. We particularly emphasize residual analysis in multiple regression and cover such topics as the least squares estimation and tests of hypotheses, prediction analysis, multicollinearity and variable selection. Fixed, random, and mixed models are all discussed in the analysis of variance. Experimental designs studied include randomized complete block, hierarchial or nested designs and the latin square. Three hours of lecture and one and one-half hours of lab per week.

405/Econ. 405. Introduction to Statistics. Math. 115 or permission of instructor. Juniors and seniors may elect concurrently with Econ. 201 and 202. No credit granted to those who have completed Econ. 404. (4). (SS).

See Economics 405. (Kmenta)

412. Introduction to Probability and Statistics. Prior or concurrent enrollment in Math. 215 and either CCS 274 or Engin. 102. No credit granted to those who have completed 311 or 402. (3). (NS).

The objectives of this course are to introduce students to the basic ideas of probability and statistical inference and to acquaint students with some important data analytic techniques, such as regression and the analysis of variance. Examples will emphasize applications to the natural sciences and engineering. There will be regular homework, including assignments which require the use of MTS, two midterms, and a final exam.

425/Math. 425. Introduction to Probability. Math. 215. (3). (N.Excl).

426. Introduction to Mathematical Statistics. Stat. 425. (3). (NS).

This course covers the basic ideas of statistical inference, including sampling distributions, estimation, confidence intervals, hypothesis testing, regression, analysis of variance, nonparametric test, and Bayesian inference. The sequence of Statistics 425/426 serves as a prerequisite for more advanced Statistics courses. Weekly problem sets, one or two hourly exams, and one final exam.

500. Applied Statistics I. Math. 417 and a course in statistics (Stat. 402 or 426); or permission of instructor. (3). (NS).

Review of matrices, multivariate normal and related distributions. Regression and general least squares theory, Gauss-Markov theorem, estimation of regression coefficients, polynomial regression, step-wise regression, residuals. ANOVA models, multiple comparisons, analysis of covariance, Latin square designs, random and mixed-effect models. Applications and real data analysis will be stressed, with students using the computer to perform statistical analysis. (Ericson)

502. Analysis of Categorical Data. Stat. 426. (3). (NS).

The course will begin with coverage of basic probability models for categorical data such as binomial, multinomial, product multinomial, Poisson, and hypergeometric distributions and parameter estimation techniques, particularly maximum likelihood. The major portion of the course will be devoted to the application of log-linear models to data analysis. The analysis of multi-way contingency tables will be covered, but emphasis will be placed on more general models arising from experimental studies. Grading will be based on two examinations and a series of computer-based data analysis problems. The course will be taught as a lecture with discussion and laboratory problems. It is loosely based on Discrete Multivariate Analysis, Bishop, Fienberg and Holland. M.I.T. Press, l975. (Smith)

550/SMS 576/I.O.E. 560. Bayesian Decision Analysis. Stat. 425 or permission of instructor. (3). (NS).

Axiomatic foundations for personal probability and utility; interpretation and assessment of personal probability and utility; formulation of Bayesian decision problems; risk functions, admissibility; likelihood principle and properties of likelihood functions; natural conjugate prior distributions; improper and finitely additive prior distributions; examples of posterior distributions, including the general regression model and contingency tables; Bayesian credible intervals and hypothesis tests; application to a variety of decision-making situations. There will be assigned homework exercises, a midterm and a final examination.

560/Biostat. 685 (Public Health). Introduction to Nonparametric Statistics. Stat. 426 or permission of instructor. (3). (NS).

The course will cover the basic linear rank statistics for one sample, two sample, one and two way ANOVA, and regression problems. Tests and their power functions, point and interval estimates are covered. Efficiencies of rank and parametric tests are computed.