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An introduction to the methods of scientific inquiry, research planning, and techniques of making observations and analyzing and presenting data.

An introduction to basic concepts and issues in measurement. Descriptive statistics, scales of measurement, norms, reliability, validity. Advantages and limitations of measurement techniques are discussed and illustrated.

Designed as a one‑semester introduction to statistical concepts and methods. An overview of data analysis techniques, including organizing, graphing, analyzing, reporting, and interpreting data. Both descriptive and inferential techniques will be introduced. Use of statistical software is discussed.

An introduction to statistical theory, including elementary probability theory; random variables and probability distributions; sampling distributions; estimation theory and hypothesis testing using binomial, normal, T, chi square, and F distributions. Calculus not required.

Prerequisite: Course in Calculus. Calculus-based introduction to mathematical statistics. Topics include an introduction to calculus-based probability; continuous and discrete distributions; point estimation; method of moments and maximum likelihood estimation; properties of estimators including bias and mean squared error; large sample properties of estimators; hypothesis testing including the likelihood ratio test; and interval estimation.

Permission required.

Permission required.

Students in this lab must also be enrolled in HUDM 5122 or HUDM 5123.

Prerequisite: HUDM 4122 or HUDM 4125. This course provides an introduction to the R language and environment for statistical computing with an emphasis on the application of fundamental graphical and statistical techniques. While some theory will be presented (for example, when discussing regression models), the focus will be on implementation and interpretation as opposed to study of the statistical properties of the methods.

Prerequisite: HUDM 4122 or equivalent. Surveys quantitative models of individual decision making, from the introduction of the notion of "utility" by Daniel Bernoulli through current models such as Tversky and Kahneman's "Prospect Theory." The focus is on psychological or descriptive models of how people make decisions, although methods of rational decision analysis are briefly discussed.

A previous course in statistics or measurement is recommended. An in-depth examination of measurement and associated techniques, norms, classical test theory, reliability, validity, item response theory, issues, and applications.

Least squares estimation theory. Traditional simple and multiple regression models and polynomial regression models, including use of categorical predictors. Logistic regression for dichotomous outcome variables is also covered. Lab meetings devoted to applications of SPSS regression program. Prerequisite: HUDM 4120 or HUDM 4122. Students may also contact Amina Abdelaziz (aa3915@tc.columbia.edu) to request a prerequisite override. Class time includes time for lab.

Prerequisite: HUDM 5122 or HUDM 5126. This course provides an overview of experimental design and analysis from the perspective of the general linear modeling framework. Topics include the incremental F test for model comparisons, dummy and effect coding, single and multiple factor ANOVA and ANCOVA, analysis of categorical outcome data via generalized linear models, and repeated measures. The course includes lab time devoted to computer applications.

Prerequisites: HUDM 4122 and HUDM 5122 or equivalent. Familiarity with R recommended. Methods of analyzing proximity data (similarities, correlations, etc.), including multidimensional scaling, which represents similarities among items by plotting the items into a geometric space, and cluster analysis for grouping items. Graph and network models will also be discussed.

Introduction to the theory and application of linear regression using calculus and matrix algebra. Focus on multiple regression models including dummy variables and polynomial models, regression diagnostics, and advanced methods such as weighted least squares, multilevel models, and an introduction to the generalized linear model.

Prerequisite: 24 points completed towards MS Applied Statistics degree. This is a capstone course to the M.S. in Applied Statistics degree. In it students will discuss best practices in statistical analyses, including the role of a consultant and ethical issues encountered in analyses. Students will also study best practices for effective communication of statistics, including verbal, written, and graphical. Students will produce a capstone paper integrating the methods and skills they have learned across the M.S. degree.

Permission required. Students enrolled are expected to spend a semester involved in a research project, either assisting a faculty member or in an applied setting. A formal report will be submitted.

Prerequisite: HUDM 4125 and either HUDM 5122 or HUDM 5126. Provides an introduction to computationally intense methods in applied statistics, taught in R. Topics include methods of evaluating statistical estimators; design, implementation, and reporting of Monte Carlo simulation studies; resampling and reordering methods; and nonparametric and data mining approaches to regression.

Prerequisite: HUDM 5122. Multilevel models include a broad range of models called by various names, such as random effects models, multi-level models, and growth curve models. This course introduces the background and computer skills needed to understand and utilize these models.

Permission required. Prerequisites: Both HUDM 5059 and HUDM 5122 or 5126. Classical test theory, and test/instrument development and validation.

Permission required. Prerequisites: HUDM 6051 or equivalents. Item response theory & applications, and cognitive diagnostic models.

Prerequisite: HUDM 5122. Recommended: HUDM 6122. Study of latent structure analysis, including measurement models for latent traits and latent classes, path analysis, factor analysis, structural equations, and categorical data analysis.

Prerequisite: HUDM 5122 or HUDM 5126; HUDM 5123 is recommended. An introduction to multivariate statistical analysis, including matrix algebra, general linear hypothesis and application, profile analysis, principal components analysis, discriminant analysis, and classification methods.

Permission required.

Permission required. Development of doctoral dissertations and presentation of plans for approval. Registration limited to two terms. Ph.D & Ed.D students must complete 3 points over 2 semesters prior to proposing their dissertation.

Individual advisement on doctoral dissertation. Fee to equal 3 points at current tuition rate for each term. See section in catalog on Continuous Registration for Ed.D./ Ph.D. degrees. Ed.D & Ph.D students must register for this every semester while completing their dissertation.

*Program Director:* Dr. Bryan Keller (Applied Statistics); Dr. Young-Sun Lee (Measurement and Eval)