Department of Statistics
220 Yost Hall
Phone 368-2880; Fax 368-5163
Christopher Cullis
The Department of Statistics offers a variety of programs leading to both undergraduate (Bachelor of Arts and Bachelor of Science in Statistics) and graduate (Master of Science) degrees. A Ph.D. program in statistics is being developed.
Prospects for employment in statistics are very good. Because of the central role of statistics in the physical, life and social sciences, in engineering, in goverment, and in business, the demand for statisticians will continue to grow. More actuaries are needed.
The bachelor's degree in statistics furnishes a strong background for graduate study in many areas (e.g., computer science, medicine, law, economics, etc.). The master's degree is sufficient for many areas of non-academic employment.
The Department of Statistics is being organized this year and the faculty listing will be provided in the next issue of this bulletin.
Christopher A. Cullis, PH.D. (University of East Anglia, United Kingdom)
Professor of Biology, Acting Chairman of Statistics
A Bachelor of Arts degree in statistics and a Bachelor of Science in statistics is available.
The B.A. in statistics requires CMPS 131, MATH 125, 126, and 201 and at least 27 hours of statistics including:
- MATH 125, 126, and 201;
- STAT 285, 286, 403, and 406 (the Statistics Core);
- Two approved statistics electives which may be STAT 381, STAT 382 or a 400-level statistics course.
- Two approved technical electives, which are any approved mathematics or statistics courses or approved technical courses in biometry, computing, econometrics, management, operations research, social science, etc.
The B.S. in Statistics requires at least 50 hours of approved mathematics and statistics courses, including:
- MATH 121, 122, 223, and 224, or an equivalent sequence;
- MATH 201
- STAT 380, 381, 382, 385, 395, 403, 406, and 414 (the Statistics Core);
- Two statistics electives chosen from: STAT 408, 409, 483, 484, 487, 488, 489, 490;
- One approved technical elective, which is any approved mathematics or statistics course in biometry, computing, econometrics, management, operations research, social science, etc.
A minimum of 17 hours including:
- MATH 125, 126 (or equivalent sequence)
- STAT 285 and 286, or STAT 380 and STAT 385
- Any approved STAT course
The following courses cannot be counted toward the Bachelor of Science in Mathematics, the Bachelor of Arts with a major in mathematics, or a minor in mathematics or statistics: MATH 101, 105, 106; STAT 319, 320.
Bachelor of Arts Degree
FRESHMAN
Fall Semester
MATH 125, Mathematics I (4)
CMPS 131, Elementary Computer Programming (3)
Science core course (3-4)
Core Sequence II, III or IV (3)
ENGL 150, Expository Writing (3)
PHED 101, Physical Education Activities (0)
Spring Semster
MATH 126, Mathematics II (4)
MATH 150, Mathematics from a MathematicianŐs Perspective (3)
Core Sequence II, III or IV (3)
Core Sequence II, III or IV (3)
Science core course (3-4)
PHED 102, Physical Education Activities (0)
SOPHOMORE
Fall Semester
STAT 285, Statistics for Business and Management Science I (3)
Core Sequence II, III or IV (3)
Course in selected minor field (3)
Elective (6)
Spring Semster
STAT 286, Statistics for Business and Management Science II (3)
Core Sequence II, III or IV (3)
Course in selected minor field (3)
MATH 201, Linear Algebra (3)
Elective (3)
JUNIOR
Fall Semester
STAT 403, Regression Techniques (3)
Course in selected minor field (3)
Electives (9)
Spring Semster
STAT 406, Methods of Experimental Design (3)
Course in selected minor field (3)
Electives (9)
SENIOR
Fall Semester
Course in selected minor field (3)
Approved elective in statistics (3)
Approved Technical Elective (3)
Electives (6)
Spring Semster
Course in selected minor field (3)
Approved elective in statistics (3)
Approved Technical Elective (3)
Electives (6)
FRESHMAN
Fall Semester
Open elective or humanities/social science (3-0-3)b, c
CHEM 105, Principles of Chemistry I (3-0-3) or
CHEM 107, Properties and Structure of Matter I (3-0-3)
CHEM 113, Principles of Chemistry Laboratory (1-3-2)
MATH 121, Calculus for Science and Engineering I (4-0-4)
ENGL 150, Expository Writing (3-0-3)
PHED 100, Physical Education Activities (0-3-0)
Total (14-6-15)
Spring Semester
Humanities/social science or open elective (3-0-3)a,b
CHEM 106, Principles of Chemistry II (3-0-3) or
CHEM 108, Properties and Structure of Matter II (3-0-3)
CMPS 131, Elementary Computer Programming (2-2-3)
MATH 122, Calculus for Science and Engineering II (4-0-4)
PHYS 120, General Physics I (4-0-4)d
PHED 100, Physical Education Activities (0-3-0)
Total (17-3-17)
SOPHOMORE
Fall Semester
Humanities or Social Science Sequence I (3-0-3)
PHYS 219, General Physics II (4-0-4)
MATH 223, Calculus for Science and Engineering III (3-0-3)
STAT 385, Statistical Methods (3-0-3)
Open elective (3-0-3)
Total (16-0-16)
Spring Semester
Humanities or Social Science Sequence II (3-0-3)
PHYS 220, General Physics III (3-0-3)
MATH 224, Elementary Differential Equations (3-0-3)
MATH 201, Linear Algebra (3-0-3)
STAT 380, Intro to Probability (3-0-3)
Total (15-0-15)
JUNIOR
Fall Semester
Humanities or Social Science Sequence III (3-0-3)
STAT 403, Regression (3-0-3)
Statistics elective (3-0-3)d
Open elective (3-0-3)
Open elective (3-0-3)
Total (15-0-15)
Spring Semester
Humanities or Social Science Sequence IV (3-0-3)
STAT 406, Experimental Design (3-0-3)
Statistics elective (3-0-3)d
Open elective (3-0-3)
Open elective (3-0-3)
Total (15-0-15)
SENIOR
Fall Semester
Humanities or social science elective (3-0-3)
STAT 381, Theoretical Stat. I (3-0-3)
STAT 414, Industrial Stat. (3-0-3)
Technical elective (3-0-3)e
Open elective (3-0-3)
Open elective (3-0-3)
Total (18-0-18)
Spring Semester
Humanities or social science elective (3-0-3)
STAT 395, Senior Project (3-0-3)
STAT 382, Theoretical Stat. II (3-0-3)
Open elective (3-0-3)
Open elective (3-0-3)
Total (15-0-15 )
Total hours to graduate 126.
a A suitable open elective is MATH 150 Introduction to Mathematics. This course must be taken during the freshman year to count towards the 50 hours requirement for mathematics courses.
b One of these courses must be a humanities/social science elective.
c Selected students may be invited to take PHYS 125, 126 Physics & Frontiers I, II, Honors (3, 3) in place of an open elective (3) and PHYS 120 (4).
d Statistics electives are to be chosen from: STAT 408, STAT 409, STAT 483, STAT 484, STAT 487, STAT 488, STAT 489, or STAT 490.
e Technical electives are approved mathematics or statistics courses or approved technical courses in biometry, computing, econometrics, management, operations research, social science, etc.
The department offers a program leading to the Master of Science degree.
Doctor of Philosophy program in statistics is being developed.
The Ph.D. program will be designed for students who intend to pursue a career in either theorical or applied statistics. The candidate must pass qualifying exams in approved subjects; demonstrate a reading knowledge of an approved foreign language; and must present a doctoral dissertation representing significant original research.
The M.S. in applied statistics is a professional degree intended for the individual desiring a career in applied statistics. Candidates for the M.S. degree must complete 27 semester hours of approved courses and either successfully pass a comprehensive examination or write a Master's thesis. Throughout the student's graduate career in the department, his or her work will be closely supervised by a faculty adviser.
The Department of Statistics at Case Western Reserve University is being developed to be an active center for theoretical and applied research.
Statistics (STAT)
STAT 285. Statistics for Business and Management Science I (3).
Organizing and summarizing data. Elementary probability. Mean, variance, moments. Conditional probability. Bayes' Theorem. Binomial, negative binomial, Poisson, hypergeometric, uniform, exponential, and normal distributions. Central limit theorem. Empirical distributions: Sample mean, sample variance, proportions. Chi-square, t, and F distributions. Point estimation. Confidence intervals. Hypothesis testing. Uses computer package. Students may take only one of STAT 285 and 385 for credit. Prerequisite: MATH 122 or 126 or consent of instructor.
STAT 286. Statistics for Business and Management Science II (3).
Analysis of variance. Linear regression and correlation. Multiple regression. Analysis of categorical data. Goodness-of-fit tests. Nonparametric statistics; sign, Wilcoxon, Kruskal-Wallis, and runs tests. Introduction to time series analysis and forecasting. Decision theory. Applications in quality control and relitheory. Use of computer in applications. Prerequisite: ability, STAT 285.
STAT 319. Basic Statistics for the Social and Life Sciences I (3) (no credit for students who have taken STAT 385, PSCL 282, or any other introductory statistics course).
Descriptive statistics, probability models, sampling distributions, point and confidence interval estimation, testing hypotheses, elementary regression with accompanying efficient computing procedures and package programs. Designed primarily for students in social and life sciences. Prerequisite: High school algebra.
STAT 320. Basic Statistics for the Social and Life Sciences II (3).
(Continuation of STAT 319.) Basic theory of design of experiments. The analysis of variance - multifactor models. Multiple linear regression models and the multiple correlation analysis of covariance. The analysis of contingency tables - multinomial distributions and large sample chi-square approximation. Tests of goodness of fit. Nonparametric procedure. Accompanying efficient computing procedures and package programs. Prerequisite: STAT 319 or consent of instructor.
STAT 333. Uncertainty in Science and Engineering (3).
(Also listed as MATH 384.) Phenomenon of uncertainty appears in engineering and science for various reasons and can be modeled in different ways. The course will integrate the mainstream ideas in statistical data analysis with models of uncertain phenomena stemming from the three distinct viewpoints: algorithmic/computational complexity; classical probability theory; and chaotic behavior of nonlinear systems. Descriptive statistics, estimation procedures and hypotheses testing (including design of experiments) will be covered in this introductory statistics course. Mathematica notebooks and simulations will be used throughout the course. Prerequisite: MATH 122 or equivalent or consent of instructor.
STAT 380. Introduction to Probability (3).
Random variables. Algebra of sets. Combinatorial methods. Sampling. Conditional probability. Bayes' Theorem. Independent events. Mathematical expectation. Mean, variance, moments. Chebyshev's inequality. Bernoulli, binomial, geometric, negative binomial, and Poisson distributions. Histogram, ogives, sample mean, sample variance. Uniform, exponential, gamma, chi-square, and normal distributions. Central limit theorem. Law of large number. Order statistics. Confidence intervals for percentiles, means, and percentages. Sample size. Prerequisite: MATH 122 or 126 or consent of instructor.
STAT 381. Theoretical Statistics I (3).
Basic probability theory. Estimation techniques for the parameters of the basic distributions: maximum likelihood, method of moments, unbiased estimates, confidence intervals, sufficient statistics, Cramer-Rao inequality. Transformations of random variables. F and t distributions. Order statistics. Prerequisite: MATH 223, STAT 285, or STAT 385.
STAT 382. Theoretical Statistics II (3).
Hypothesis testing: Neyman-Pearson lemma, uniformly most powerful tests, likelihood ratio tests, sequential tests. Exponential families. Rao Blackwell theorem. Linear models. Nonparametric methods. Multivariate normal distributions. Likelihood, repeated sampling, conditionality and other basic principles. Prerequisite: STAT 381.
STAT 385. Statistical Methods (3).
For advanced undergraduate or graduate students in engineering, physical sciences, life sciences, social sciences, etc. Provides comprehensive introduction to probability models and statistical methods for analyzing data. It also discusses available statistical packages for computer applications and applies them to real-life data. General objective is to train students in formulating statistical models and in choosing appropriate methods of data analysis to test the validity of these models. Starts with descriptive statistics and moves to probability theory as a framework for statistical inference. Emphasis on the following statistical techniques: analysis of variance, regression analysis, analysis of categorical data, nonparametric statistical analysis, fitting statistical distributions to data. Prerequisite: MATH 122 or consent of instructor.
STAT 395. Senior Project (3).
An individual project done under faculty supervision involving the investigation and statistical analysis of a real problems encountered in university research or an industrial setting. Written report. Prerequisite consent of instructor.
STAT 403. Regression Techniques (3).
Simple linear regression and various inferences. Lack of fit methods and residuals analysis. Aptness of model and remedial measures. Simple and joint confidence intervals. Multiple linear regression, estimation, testing and confidence limits. General linear hypothesis. Further residuals analysis. Dummy variables and analysis of variance. Multiple comparisons. Polynomial regression and orthogonal polynomials. Multicollinearity and influential observation diagnostics. Elements of non-linear regression. "Best" regression techniques and theory. Prerequisites: MATH 201 and STAT 385 or STAT 485.
STAT 406. Methods of Experimental Design (3).
Basic problems of experimental design. Completely randomized and balanced incomplete block designs. Hierarchical designs and Latin squares. Factoral designs and fractional replications of 2n factorial experiments. Exploration of response surfaces and designs. Optimal designs for regression problems. Sequential designs for life-testing, for maintenance and reliability problems. Course is computer-oriented; emphasis on methods of execution and proper applications. Prerequisite: MATH 201 and STAT 385 or 485.
STAT 408. Survey Sampling (3).
Sampling from finite populations. Simple random, stratified, and systematic sampling. Ratio and regression estimates. One-and two-stage cluster sampling. Use of the computer in applications. Prerequisites: STAT 385 or 485 or consent of instructor.
STAT 409. Methods of Nonparametric Statistics (3).
For graduate (or advanced undergraduate students) in life sciences, physical sciences, social sciences, or engineering. Methodology of nonparametric statistics involving point estimators, confidence intervals, and multiple comparison procedures. Recent advances in nonparametric tests. Non-calculus treatment of: Sign test and Wilcoxon's signed rank test for one sample location problems; Wilcoxon rank sum test and Mann-Whitney U-statistic for two sample location problem; Ansari-Gradley's test for two sample dispersion problems; Kruskal-Wallis test, Jonckheeve-Terpstra test (for ordered alternatives) in two-way layouts: Kendall's test for independence; Theil's test and Hollander's test for regression problems; Kolmogorov-Smirnov test; Chi-squared test for goodness of fit; and some recent developments. Prerequisite: STAT 319 and 320; or STAT 385 or 485 or the equivalent.
STAT 414. Industrial Statistics (3).
Introduces researchers and engineers to statistical methods used to solve problems related to the collection and analysis of data. Case studies illustrate which techniques are applicable and how they are used. Derivations of sampling distributions. Includes one, two, and k-sample test and estimation procedures and methods of multiple comparisons. Prerequisite: STAT 385 or equivalent or consent of instructor.
STAT 433. Uncertainty in Science and Engineering (3) (See STAT 333.) Graduate students are expected to do extra work. Prerequisite: MATH 122 or equivalent or consent of instructor.
STAT 481. Theoretical Statistics I (3).
(See STAT 381.) Graduate students are expected to do extra work. Prerequisite: STAT 385 or equivalent.
STAT 482. Theoretical Statistics II (3).
(See STAT 382.) Graduate students are expected to do extra work. Prerequisite: STAT 481 or equivalent.
STAT 483. Linear Models (3).
General linear model, least squad theory, polynomial and curvilinear models, factorial models, special design models, variance components, and mixed models. Prerequisite: STAT 403 or consent of instructor.
STAT 484. Multivariate Statistical Analysis (3).
The multivariate normal distribution and distributions of quadratic forms. Correlation, regression, classification problems. Principal components, discrimination, factor analysis. Multivariate regression and ANOVA. Clustering techniques, non-parametric methods. Nearest neighbor methods, minimal spanning tree sets. Prerequisites: MATH 201, 223; STAT 385 or 485.
STAT 485. Probability and Statistics in Engineering and Science (3).
A computationally-oriented one-semester course. Graduate level overview of probability and statistics. Descriptive statistics, probability, univariate and multivariate probability distributions, some common discrete and continuous distributions, sampling distributions, point and interval estimation, hypothesis testing, probability plotting, randomization, introduction to time dependent probability models. Prerequisite: MATH 224 or equivalent or consent of instructor.
STAT 487. Stochastic Processes in Engineering and Science (3).
(See OPRE 426.)
STAT 488. Time Series Analysis (3).
Univariate spectral models, sampling, aliasing, and discrete time models, linear filters, digital filters, finite parameter models, linear prediction, real time filtering, statistical problems. Prerequisite: STAT 485 or consent of instructor.
STAT 489. Theory of Queues (3).
(Also listed as OPRE 521.) The mathematical model of queues. The distributions of the queue size and the waiting time, and the stochastic law of the busy periods. Single server queues with (i) Poisson input and exponential service times, (ii) Poisson input and general service times, (iii) recurrent input and exponential service times, and (iv) recurrent input and general service times. Many-server queues with (i) Poisson input and exponential service times and (ii) recurrent input and exponential service times. Queues with infinitely many servers in case of (i) Poisson input and general service times and (ii) recurrent input and exponential service times. Loss systems. Erlang's and Palm's formulas. Queues with a finite number of sources. Processes of serving machines. Prerequisites: STAT 487, or consent of instructor.
STAT 490. Reliability and Life Testing (3).
Failure distributions related to life testing and hazard functions: exponential, Weibull, normal, log-normal, Gamma, extreme value, etc. Distributions of functions of random variables. Static reliability models of systems; series, parallel, and mixed types of systems; component versus system redundance. Coherent systems and system reliability approximations. Dynamic reliability models, maintainability, service ability, availability, and limiting results; redundancy, allocation, and optimization, graphical methods for model identification; probability plotting, hazard plotting, and linear estimation techniques. Maximum likelihood methods, censored data, completing failures models, estimation and accelerated life testing. Prerequisite: STAT 385 or 485, or consent of instructor.
STAT 581. Mathematical Statistics I (3).
Review of distribution theory. Sufficient statistics, completeness, invariance, exponential and group families. Prior and posterior distributions, conjugate prior distributions. Methods of estimation: least squares, minimum variance unbiased estimation, Bayes' estimation procedures, maximum likelihood. Consistency, asymptotic properties of maximum likelihood estimators, asymptotic efficiency. Interval estimation. Special topics. Prerequisite: STAT 482 or equivalent.
STAT 582. Mathematical Statistics II (3).
Basic principles of statistics: conditionality, sufficiency, strong and weak likelihood, repeated sampling, etc. Testing simple and composite hypotheses: Neyman-Pearson theory, uniformly most powerful tests, local power, likelihood ratio tests, sequential procedures. Elements of Decision Theory: estimation and hypothesis testing in a decision theoretic framework, Bayes and minimax rules, admissibility. Separating Hyperplane and complete class theorems. Special topics. Prerequisite: STAT 581.
STAT 589. Seminars in Statistics I (1-3).
Prerequisite: consent of instructor.
STAT 590. Seminars in Statistics II (1-3).
Prerequisite: consent of instructor.
STAT 601. Reading and Research (3).
Individual study and/or project work. Prerequisite: consent of instructor.
STAT 651. Thesis (M.S.) (credit as arranged).
Prerequisite: consent of instructor.
STAT 701. Dissertation (Ph.D.) (credit as arranged).
Prerequisite: consent of instructor.
The following is the listing of statistical courses offered by other CWRU departments.
- ANES 431, Statistical Methods I
- ANES 432, Statistical Methods II
- BIOL 431, Statistical Methods in Biological Sciences I
- BIOL 432, Statistical Methods in Biological Sciences II
- ECON 326, Econometrics
- EPBI 431, Statistical Methods I
- EPBI 432, Statistical Methods II
- EPBI 435, Survival Data Analysis
- EPBI 441, Biostatistics I
- EPBI 442, Biostatistics II
- EPBI 443, Applied Multivariate Analysis
- EPBI 448, Mathematical Statistics I
- EPBI 449, Mathematical Statistics II
- EPBI 491, Statistical Methods in Epidemiology
- MGMT 570, Research Theory and Methods
- MGMT 571, Measurement Theory and Methods
- MGMT 573, Multivariate Data Analysis
- NURS 620, Advanced Statictics for Health Research
- OPRE 425, Probability Theory in Operations Research
- OPRE 426, Stochastic Process in Operations Research
- OPRE 428, Statistical Methods for Operations Research Applications
- QUMM 403, Managerial Statistics
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