**QMSA Required Courses**

In consultation with the Senior Instructional Professor, a QMSA student must select a sequence of two courses in statistical theory.

SOSC 26006/36006: Foundations for Statistical Theory

STAT 24400: Statistical Theory and Methods I

Or

STAT 24400: Statistical Theory and Methods I

STAT 24500: Statistical Theory and Methods II

Or

BUSN 41901: Probability and Statistics

BUSN 41902: Inference in Econometrics and Statistics

QMSA students must additionally take two required overview courses:

MAPS 30000: Perspectives in Social Science Analysis

SOSC 26007/36007: Overview of Quantitative Methods in the Social and Behavioral Sciences

COURSE DESCRIPTIONS:

**SOSC 26006/36006: Foundations for Statistical Theory**. This course is designed for graduate and advanced undergraduate students who aim to develop conceptual understanding of the fundamentals of statistical theory underlying a wide array of quantitative research methods. The course introduces students to probability and statistical theory and emphasizes the connection between statistical theory and the routine practice of statistical applications in quantitative research. Students will gain basic understanding of the concepts of joint, marginal, and conditional probability, Bayes rule, probability distributions of random variables, principles of statistical inference, sampling distributions, and estimation strategies. The course can serve as a preparation for mathematical statistics courses such as STAT 244 (Statistical Theory and Methods 1) and as a theoretical foundation for various advanced quantitative methods courses in the social, behavioral, and health sciences. Prerequisite: Basic knowledge of linear algebra and calculus, specifically differentiation and integration, is necessary to understand the material on continuous distributions, multivariate distributions and functions of random variables.

**STAT 24400: Statistical Theory and Methods I.** This course is the first quarter of a two-quarter systematic introduction to the principles and techniques of statistics, as well as to practical considerations in the analysis of data, with emphasis on the analysis of experimental data. This course covers tools from probability and the elements of statistical theory. Topics include the definitions of probability and random variables, binomial and other discrete probability distributions, normal and other continuous probability distributions, joint probability distributions and the transformation of random variables, principles of inference (including Bayesian inference), maximum likelihood estimation, hypothesis testing and confidence intervals, likelihood ratio tests, multinomial distributions, and chi-square tests. Examples are drawn from the social, physical, and biological sciences. The coverage of topics in probability is limited and brief, so students who have taken a course in probability find reinforcement rather than redundancy.

**STAT 24500: Statistical Theory and Methods II. **This course is the second quarter of a two-quarter systematic introduction to the principles and techniques of statistics, as well as to practical considerations in the analysis of data, with emphasis on the analysis of experimental data. This course continues from STAT 24400 and covers statistical methodology, including the analysis of variance, regression, correlation, and some multivariate analysis. Some principles of data analysis are introduced, and an attempt is made to present the analysis of variance and regression in a unified framework. Statistical software is used.

**BUSN 4****1901: Probability and Statistics. **The central topics of BUSN 41901 are probability, martingales and stochastic processes. Basic concepts in probability are also covered. Prerequisites: One year of calculus. The text for the course is DeGroot and Schervish, *Probability and Statistics.* BUSN 41901 is cross-listed as STAT 32400.

**BUSN 41902: Inference in Econometrics and Statistics. **The focus of this course is methods to draw inferences in econometric models. The course covers linear regression models, generalized methods of moments, nonlinear models, and time series models. The majority of the discussion covers frequentist methods focusing on the use of approximations to finite-sample sampling distributions as a means for obtaining inference. It covers methods that are appropriate for independent data as well as dependent data. We will discuss intuition for how and when to use the econometric tools developed in the class in addition to deriving some of the relevant theoretical properties. Three recommended texts are *Econometrics* by Hayashi, *Econometric Analysis of Cross Section and Panel Data* by Wooldridge, and *Time Series Analysis* by Hamilton. A*symptotic Theory for Econometricians* (revised edition) by White provides a useful and concise reference on asymptotic results. BUSN 41901 is cross-listed as STAT 32900.

**MAPS 30000: Perspectives in Social Science Analysis**. Perspectives are stances from which social thinkers see the world and explain the world; they are not just ways of “looking” but also starting points for “acting” in doing research. Different perspectives may complement or contradict one another. This course presents some of the main traditions of theoretical argument in the social sciences today about the nature of social life and individual behavior. The course readings draw upon foundational works representing diverse theoretical perspectives or deemed to be exemplary of the perspectives as applied in empirical research. It will show that some of the most important work in the social sciences derives from scholars who were willing to think beyond the confines of a single perspective.

**SOSC 26007/36007: Overview of Quantitative Methods in the Social and Behavioral Sciences**. The course is designed to offer an overview of and present the common logic underlying a wide range of methods developed for rigorous quantitative inquiry in the social and behavioral sciences. Students will become familiar with various research designs, measurement, and advanced analytic strategies broadly applicable to theory-driven and data-informed quantitative research in many disciplines. Moreover, they will understand the inherent connections between different statistical methods, and will become aware of the strengths and limitations of each. In addition, this course will provide a gateway to the numerous offerings of advanced quantitative methods courses. It is suitable for undergraduate and graduate students at any stage of their respective programs. Prerequisite: Introductory level statistics

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