**100(300). Introduction to Statistical Reasoning. *** (4). (NS). *

This course is designed to provide an overview of the field of statistics. Course topics include methods of collecting, analyzing and summarizing data (with special emphasis on graphical techniques), statistical reasoning as a means of learning from observations, and techniques for dealing with uncertainty in drawing conclusions from collected data. Basic fallacies in common statistical analyses and reasoning are discussed. 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. The course format is lecture, with a weekly one-hour laboratory. Evaluation is based on three evening midterms and a final examination. [Cost:2] [WL:3]

**311/I.O.E. 365. Engineering Statistics. *** Math. 215 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 computer for problem solving. [Cost:2] [WL:3]

**402. Introduction to Statistics and Data Analysis. *** No credit granted
to those who have completed 412. (4). (NS). *

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 and some attention is given to statistical process control methods. 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.

**403. Introduction to Statistics and Data Analysis II. *** Stat. 402.
(4). (Excl). *

APPLIED REGRESSION. The course will also cover various topics associated with the general linear model emphasizing applications. Topics include: multiple regression, variable selection, stepwise regression, residual analysis, analysis of variance models, covariance analysis and principal components. OTHER TOPICS. As time allows, the course may cover some aspects of probit and logit analyses, analysis of time series data, reliability analysis, and topics in experimental design. Three hours of lecture and one and one-half hours of lab per week. [Cost:2] [WL:None, course does not close]

**404. Problem Solving in Medical Statistics. *** Enrollment in Inteflex
or permission of instructor. (3). (Excl). *

This course is intended to introduce students in the medical sciences to the measurement and interpretation of clinically relevant variables. Applications to the design and analysis of clinical trials and diagnosis are presented. The methodology includes some probability theory, classical inference, and curve fitting. Many of the topics are illustrated through current problems in medicine. [Cost:2]

**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). (Excl). *

See Economics 405. (Kmenta)

**412. Introduction to Probability and Statistics. *** Prior or concurrent
enrollment in Math. 215 and CS 283. No credit granted to those who have
completed 311 or 402. (3). (Excl). *

An introduction to probability theory; statistical models, especially sampling models; estimation and confidence intervals; testing statistical hypotheses; important applications, including the analysis of variance and regression. [Cost:3] [WL:3]

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

See Mathematics 425.

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

Basic concepts of statistics: experimental models, including sampling; estimation of parameters, including maximum likelihood estimation; sampling distributions; properties of estimators, including bias and variance; confidence intervals; tests of hypotheses, including UMP tests and likelihood ratio tests. Introductions to non-parametric statistics and Bayesian inference will also be included. Applications may include simple linear regression, elementary analysis of variance, and the analysis of variance, and the analysis of categorical data. Credit given for only one of Statistics 426 and 575.

**466/IOE 466. Statistical Quality Control. *** Statistics 311 or IOE
365. (3). (Excl). *

Design and analysis of procedures for forecasting and control of production processes. Topics include: attribute and variables; sampling plans; sequential sampling plans; rectifying control procedures; charting, smoothing, forecasting, and prediction of discrete time series. [Cost:2] [WL:3]

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

Course outline. Linear Models: Definition, fitting, identifiability, multicollinearity, Gauss-Markov theorem, variable selection, diagnostics transformations, influential observations, robust procedures, ANOVA and analysis of covariance, interpretation of results, meaning of regression coefficients, dangers of data ransacking etc. Randomized block, factorial designs. Discrete and categorical data: Logit and probit, loglinear and logistic models, contingency tables. [Cost:2] [WL:3]

**502. Analysis of Categorical Data. *** Stat. 426. (3). (Excl). *

Models for categorical data, including contingency tables of three or more dimensions, based on Poisson, multinomial and product multinomial models forced frequencies. The course will concentrate on loglinear models. Significance tests, estimation and exploratory data analyses will be stressed. [Cost:2] [WL:1]

**505/Econ. 673. Econometric Analysis. *** Permission of instructor.
(3). (Excl). *

This course is designed for first-year graduate students in economics, business, and related subjects. It involves a fairly rigorous development of statistical reasoning and methods relating to hypothesis testing, estimation, and regression analysis. Students are supposed to have had a course in calculus and in introductory statistics. Knowledge of matrix algebra is recommended but not required. Evaluation of students is based on midterm and final examinations and weekly assignments. Students taking this course are expected to take Economics 674 – Econometric Analysis II in the following term. [Cost:2] [WL:3] (Kmenta)

**510. Mathematical Statistics I. *** Math. 450 or 451, and a course
in probability or statistics; or permission of instructor. (3). (Excl). *

Review of probability theory including: probability, conditioning, independence, random variables, standard distributions, exponential families, inequalities and a central limit theorem. Introduction to decision theory including: models, parameter spaces, decision rules, risk functions, Bayes versus classical approaches, admissibility, minimax rules, likelihood functions and sufficiency. Estimation theory including unbiasedness, complete sufficient statistics, Lehmann-Scheffe and Rao-Blackwell theorems, and various types of estimators.

**525(510)/Math. 525. Probability Theory. *** Math. 450 or 451; or permission
of instructor. Students with credit for Math. 425/Stat. 425 can elect Math.
525/Stat. 525 for only 1 credit. (3). (Excl). *

See Mathematics 525.

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

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. [Cost:3] [WL:3]

**575/Econ. 775. Econometric Theory I. *** Math. 417 and 425 or Econ.
653, 654, 673, and 674. (3). (Excl). *

This course involves a derivation of the required theory in mathematical statistics, and of the main results needed for statistical inference associated with the linear model. The emphasis is on the asymptotic distribution theory as it is applied to the methods of estimation used in econometrics. The course is a prerequisite for Statistics 576 (Econometric Theory II). [Cost:2 or 3] (Genius)

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