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220. Statistical Methods and Their Applications. PQ: Math 152 or
equivalent and completion of one of the Common Core sequences in the
biological, physical, or social sciences. This is an introduction to
statistical techniques and methods of data analysis, including the use of
computers. Examples are drawn from the biological, physical, and social
sciences. Students are required to apply the techniques discussed to data drawn
from actual research. Topics include data description, graphical techniques,
exploratory data analyses, random variation and sampling, one- and two-sample
problems, the analysis of variance, linear regression, and analysis of discrete
data. One or more sections of Stat 220 in the autumn and spring quarters use
examples drawn from economics and business and a selection of texts and topics
that are more appropriate for concentrators in economics. Staff. Summer,
Autumn, Winter, Spring.
222. Linear Models and Experimental Design. PQ: Stat 220 or equivalent.
This course covers principles and techniques for the analysis of
experimental data and the planning of the statistical aspects of experiments,
surveys, and observational programs. Topics may include linear and nonlinear
models; analysis of variance and response surface analysis; randomization,
blocking, and factorial designs; fractional replication and confounding;
incorporation of covariate information; design and analysis of sample surveys;
designs subject to constraints; split-plot and nested experiments; and
components of variance. Staff. Spring.
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224. Applied Regression Analysis. PQ: Stat 220 or equivalent. This
course is an introduction to the methods and applications of fitting and
interpreting multiple regression models. The primary emphasis is on the method
of least squares and its many varieties. Topics include the examination of
residuals, the transformation of data, strategies and criteria for the
selection of a regression equation, the use of dummy variables, tests of fit,
nonlinear models, biases due to excluded variables and measurement error, and
the use and interpretation of computer package regression programs. The
techniques discussed are illustrated by many real examples involving data from
both the physical and social sciences. Matrix notation is introduced as needed.
Staff. Autumn.
226. Analysis of Qualitative Data. PQ: Stat 220 or equivalent. This
course covers statistical methods for the analysis of structured, counted data.
Topics discussed may include Poisson, multinomial, and product-multinomial
sampling models; chi-square and likelihood ratio tests; log-linear models for
cross-classified counted data, including models for data with ordinal
categories and log-multiplicative models; logistic regression and logit linear
models; and measures of association. Applications in the social and biological
sciences are considered, and the interpretation of models and fits, rather than
mathematical details of computational procedures, is emphasized. The computer
is used throughout the course. Staff. Winter.
227. Biostatistical Methods. PQ: Stat 220 or 244, MedBio 315, or consent
of instructor. This course builds on the statistical methods introduced in
Stat 220 and deals with methods frequently required in biology and medicine.
Topics include an overview of biostatistics, linear regression and correlation,
adjustment for covariates, contingency table analysis emphasizing 2 by 2
tables, logistic regression, and survival data analysis. Additional topics may
include Poisson regression and statistical methods in epidemiology, such as
relative risk, attributable risk, and assessment of screening and diagnostic
tests. R. Thisted. Autumn.
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230/251. Introduction to Mathematical Probability. PQ: Math 200, 203, or
consent of instructor. This course covers fundamentals and axioms;
combinatorial probability; conditional probability and independence; binomial,
Poisson, and normal distributions; the law of large numbers and the central
limit theorem; and random variables and generating functions. Staff.
Spring.
240. Probability and Statistics for the Natural Sciences. PQ: Math 201
or 196; and Chem 113 or 123, or Phys 123, 133, or 143. This course is an
introduction to those topics in probability and statistics most relevant to
experimental sciences, particularly the physical sciences. Probability topics
include the central limit theorem and rules of probability, random variables,
means, variances, and correlations. Statistics topics include propagation of
errors, inference for means, and regression analysis for experimental data. In
addition, topics in linear algebra such as vector spaces, projection and
eigenvalues and eigenvectors are studied within the context of regression.
Connections of statistical methods to Fourier series and other mathematical
methods commonly used in the physical sciences may also be made. M. Stein.
Spring.
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242. Applied Probability and Elementary Stochastic Models. PQ: Math 133,
153, or consent of instructor. This course is an introduction to
probability and stochastic processes at an elementary level. Emphasis is on
topics that have applications in the natural and social sciences. Topics
include conditional probability, independence, random variables and
expectations, standard distributions such as the binomial and Poisson
distributions, and random processes, including Poisson processes and Markov
chains. This course covers more material but in considerably less depth than
Stat 230, with more emphasis on applications and less on rigorous proofs.
Staff. Autumn.
244-245. Statistical Theory and Methods. PQ: Math 153 or equivalent.
A systematic introduction to the principles and techniques of statistics,
with emphasis on the analysis of experimental data. Topics include theoretical
and empirical frequency distributions; binomial, Poisson, normal, and other
standard distributions; random variables and probability distributions;
principles of inference including Bayesian inference, maximum likelihood
estimation, hypothesis testing, and confidence intervals; and analysis of
counted data, analysis of variance, least squares, and multiple and logistic
regression. Computers are used throughout the sequence. Staff. Autumn,
Winter.
299. Undergraduate Research. PQ: Consent of faculty adviser and
departmental counselor. Students are required to submit the College Reading and
Research Course Form. Open to students concentrating in statistics and to
nonconcentrators. Students may take this course either for a P/F grade
or for a quality grade. This course consists of reading and research in an
area of statistics or probability under the guidance of a faculty member. A
written report must be submitted at the end of the quarter. Staff. Autumn,
Winter, Spring.
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301-302. Mathematical Statistics. PQ: Math 205, and Stat 230 and 245; or
equivalent. This course surveys the mathematical structure of modern
statistics. Topics include statistical models, methods for parameter
estimation, comparison of estimators, efficiency, confidence sets, theory of
hypothesis tests, elements of linear hypothesis theory, analysis of discrete
data, and an introduction to Bayesian analysis. Staff. Autumn,
Winter.
312. Introduction to Stochastic Processes. PQ: Stat 230, and Math 201 or
204. This course is an introduction to stochastic processes not requiring
measure theory. Topics covered include branching processes, recurrent events,
renewal theory, random walks, Markov chains, Poisson, and birth-and-death
processes. Staff. Autumn.
321. Applied Multivariate Analysis (=Bus 423). PQ: Stat 220 or
equivalent. This course is an introduction to multivariate analysis. Topics
include principal component analysis, multidimensional scaling, discriminant
analysis, canonical correlation analysis, and cluster analysis. Staff.
Spring.
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Statistics Courses
200. Elementary Statistics. PQ: Math 102, 106, placement into Math
131 or higher, or satisfactory performance on a special elementary diagnostic
mathematics examination, and completion of one of the Common Core sequences in
the biological, physical, or social sciences. This course fulfills one of the
Common Core requirements in the mathematical sciences. This course is an
introduction to statistical concepts and methods for the collection,
presentation, analysis, and interpretation of data. Elements of sampling,
simple techniques for analysis of means, proportions, and linear association
are used to illustrate both effective and fallacious uses of statistics.
Staff. Autumn, Winter, Spring.
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