# 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 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. Prerequisites: 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. Prerequisite(s): MATH 19520 or 20000 with a grade of B or better, or MATH 16300 or 20250 or 20300 or 20700 or STAT 24300 or PHYS 22100.

**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. Prerequisite(s): Linear algebra (MATH 19620 or 20250 or STAT 24300 or equivalent) and STAT 24400 or STAT 24410.

**BUSN 41901: Probability and Statistics.** This is a PhD course that introduces fundamental statistical methods for academic research in business and economics. It covers basic concepts in probability and statistics, including conditional probability, limit theorems, estimation and inference, and linear regression. Prerequisites: Real analysis and linear algebra. 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. Asymptotic Theory for Econometricians (revised edition) by White provides a useful and concise reference on asymptotic results. Prerequisites: BUSN 41901.

**MAPS 30000: Perspectives in Social Science Analysis. **This course is an introduction to interdisciplinary social theory which aims to teach students how to read social science research at the graduate level and develop their ability to formulate and execute a successful master’s thesis. It is required of all MAPSS students, regardless of concentration.

**SOSC 36007: Overview of Quantitative Methods in the Social and Behavioral Sciences.** This course is designed to 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. Students will also develop an understanding of the connections between different statistical methods, and become aware of the strengths and limitations of each. This course provides a gateway to the numerous offerings of advanced quantitative methods courses.

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