**Statistics
Courses**

Statistics courses are offered from the Statistics department, the Teachers'
College, the Quantitative Methods program (courses beginning with QMSS), and
the departments of economics, sociology, and political science. In general,
courses from the statistics department are more difficult, require a stronger
math background, and are more theoretically focused than the other courses.

Some possible courses have been listed below (the names of any current grad
students who have taken these courses are mentioned in italics at the end of
the descriptions, in case you would like to contact them for their opinion). As
you consider your options, you should be in contact with David Krantz ( __dhk@psych.columbia.edu__ ). This is a good idea because 1) he can tell you
exactly which courses suit your needs and 2) he must approve your final choices
before they "count".

In the list below, courses have been grouped by the headings:

Please note that we have not described every statistics course available at the
university. For a more complete listing, visit the web pages of the respective
schools and departments.

__QMSS 4015 Quantitative methods.__

(Prerequisite:
undergraduate statistics course) The elements of a statistical computing
language and the use of standard statistical programs to explore and
characterize social data from archival sources, field observations, surveys,
and controlled experiments. Material covered includes linear regression,
analysis of variance, probability models, and statistical graphics. Students study
how to use a statistical package and learn to solve data analytic problems in
the social sciences. This is a non-calculus introductory course. *This course
is taught by David Krantz, a professor in our department.*

__Statistics W4150 Introduction to
probability and statistics__

(Prerequisite: a working knowledge of calculus). Fundamentals of probability theory and statistical inference. Probabilistic models, random variables, useful distributions, expectations, laws of large numbers, central limit theorem. Statistical inference: point and confidence interval estimation, hypothesis tests, linear regression.

__Statistics W3000 Introduction to
Statistics: Probability Models __

(Prerequisite: one year of calculus) An introduction to the main ideas and tools of probability emphasizing conceptual understanding and problem solving rather than theory. The topics covered include: conditional probability and expectation, independence, Bayes's rule, important distributions, random variables, joint distributions variance, control limit theorem, law of large numbers, some of independent random variables, Markov's inequality, Chebychev's inequality. Examples are drawn from several areas of human knowledge including: genetics, biology, meteorology, engineering, reliability, medical studies, sports, elections, sampling, finance.

__Statistics W4105-W4107
Probability & Statistical Inference __

(Prerequisite:
one year of calculus) W4105 studies fundamentals, random variables, and
distribution functions in one or more dimensions; moments, conditional
probabilities, and densities; Laplace transforms and characteristic functions.
Infinite sequences of random variables; weak and strong laws of large numbers;
central limit theorem. W4107 covers principles of statistical inference.
Population parameters, sufficient statistics. Basic distribution theory. Point
and interval estimation. Method of maximum likelihood. Method of least squares,
regression. Introduction to the theory of hypothesis testing. Likelihood ratio
tests. Nonparametric procedures. Statistical decision theory. Applications to
engineering, medicine, and natural and social sciences. *The 4105-4107
sequence has been taken by Lara Kammrath, in our department.*

__Economics G6411-G6412 Introduction to econometrics, I & II.__

(Prerequisite: background in the calculus of several variables and linear algebra.) Designed to provide students with the statistical and econometric methods necessary for quantitative research in economics. G6411: introduction to probability theory and statistical inference. G6412: introduction to the general linear model and its use in econometrics, including the consequences of departures from the standard assumptions.

__Political Science W4910X
Quantitative political resarch__

Introduction to the use quantitative techniques in political science and public policy. Topics include descriptive statistics and principles of statistical inference and probability through analysis of variance and ordinary least-stquares regression. Computer applications are emphasized.

__Sociology G4025 Mathematical
models for social science exploration.__

Exposure to the mathematical modeling of social processes, including choice of strategic position in production markets, alliance formation in political movements, diffusion through large-scale social and biological networks, and conversational turn-taking among bankers. Formal models draw on combinatorial analysis, ordinary differential equations, Galois lattices and computer simulation.

__Sociology G4074-G4075 Introductory social data analysis. __

Basic techniques for analyzing quantitative social science data. Emphasis on conceptual understanding as well as practical mastery of probability and probability distributions, inference, hypotheses testing, analysis of variance, simple regression, and multiple regression.

__TM5122 Applied Regression
Analysis__

(Prerequisite: TM4122 or equivalent) Least squares estimation theory. Traditional simple and multiple regression models, polynomial regression models with grouping variables including one-way ANOVA, two-way ANOVA and analysis of covariance. Lab devoted to applications of SPSS-X regression program.

__W4315 Linear regression models __

(Prerequisites: a calculus-based first course in statistics, linear algebra, and calculus.) Theory and practice of regression analysis. Simple and multiple regression including testing, estimation and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, fixed effects ANOVA and ANCOVA models, non-linear regression, multiple comparisons, co-linearity and confounding, model selection. Geometric approach to the theory and use of the computer to analyze data are both emphasized.

__TM5123 Experimental Design__

(Prerequisite: TM5122 or equivalent) Analysis of variance models including within subject designs, mixed models, blocking, Latin Square, and models with categorical dependent variables. Lab devoted to computer applications.

__W4327 Design of experiments __

Principles in the design and analysis of controlled experiments: Latin squares, incomplete block designs, crossover designs, fractional factorial designs, confounding.

__TM6122-3 Multivariate Analysis I-II__

(Prerequisite:
TM 5122 or equivalent) An introduction to multivariate statistical analysis,
including matrix algebra, general linear hypothesis and application, profile
analysis, principle components analysis, discriminant analysis, classification
methods, canonical analysis, MANOVA, and factor analysis. Use of SPSS-X
programs. *The TM6122-3 sequence has been taken by Dan Molden, in our
department.*

__W4415 Multivariate statistical inference __

(Prerequisite: STAT W4315 or the equivalent.) Multivariate normal distribution, multivariate regression and analysis of variance; canonical correlation and tests of

independence. Principal components and other models for factor analysis. Discriminant functions and the classification problem; cluster analysis.

__W4220 Analysis of categorical data __

(Prerequisites: a calculus-based first course in statistics) A thorough study of the fourfold table, with applications to survey and clinical studies. Significance

versus magnitude of association; relative risk; matching cases and controls; effects, measurement, and control of misclassification errors; combining evidence from many studies. Extension to m x 2 tables; elements of logistic regression.

__W4201 Advanced data analysis __

(Prerequisite: undergraduate statistics course) Data analysis using a

computer statistical package and selected exploratory data analysis subroutines. Topics include editing of data for errors, exploratory and standard techniques for one-way analysis of variance, linear regression, and two-way analysis of variance.

Material is presented in case-study format.

__G6101 Statistical Modeling and
Data Analysis I__

(Prerequisite: Stat W4107 and familiarity with Matrix Algebra) Intensive survey of the use of statistical models and of statistical data analyses within an interactive computing environment, with emphasis on acquiring the ability to apply and interpret statistical models and to understand the theoretical distinctions and commonalities among different modeling framework. Assignments requiring computer analysis of scientific data will be due approximately every week, including topics from the subjects of least squares regression, ANOVA, design of experiments, random effects, variance component estimation, and survival analysis.

__G6102 Statistical Modeling and
Data Analysis II__

(Prerequisite:
Stat G6101) Following a review of basic statistical methods (statistical
graphics and model checking, linear and generalized linear models, analysis of
variance, analysis of data from experiments, surveys, and observational
studies), we will cover model-based data analysis: likelihood and Bayesian
methods, hierarchical models, computer simulation of probability models.
Regular homework assignments will involve data analysis from medical/biological
sciences, physical sciences, social sciences, engineering, and business
applications. *The G6101-2 sequence has been taken by Rahul Dodhia, in our
department.*

__W4911Y Analysis of Political Data__

(Prerequisite: Poli Sci W4910 or knowledge of ordinary least squares regression.) Multivariate and time-series analysis of political data. Topics include lime-series regession, structural equation models, factor analysis, and other special topics. Computer applications are emphasized

__Sociology G6225 Models of categorical data. __

(Prerequisite: Sociology G4074-G4075, or the equivalent.) Standard multiple regression techniques, and a variety of log-linear models with intention of acquiring both an understanding of these techniques and an ability to use them for research, as demonstrated by an analysis of a data set provided in the course.

__Sociology G6500 Issues of measurement and causal inference in sociological
research.__

(Prerequisites: Sociology G4074-G4075, or the equivalent). Introduction to the concepts of reliability and validity; methods of assessing them in sociological research. The effects of unreliability and invalidity on causal inference addressed in detail.

__Sociology G9513. Methods of temporal analysis. __

(Prerequisite: Sociology G4025, or the equivalent) Dynamic models of change using panel data, time-series and event histories; parametric and non-parametric models, estimation and interpretation.

*content last updated 7/14/99*