# Table of Contents

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The focus of this book is on using quantitative research methods to test hypotheses and build theory in political science, public policy and public administration. It is designed for advanced undergraduate courses, or introductory and intermediate graduate-level courses.

## 1: Theories and Social Science

The focus of this book is on using quantitative empirical research to test hypotheses and build theory in political science and public policy. The book is designed to be used by graduate students in the introductory and intermediate quantitative analysis courses. It is important to note that quantitative analysis is not the only – or even the most important – kind of analysis undertaken in political science and public policy research. Qualitative analysis, including ethnographic studies, systema## 2: Research Design

Research design refers to the plan to collect information to address your research question. It covers the set of procedures that are used to collect your data and explain how your data will be analyzed. Your research plan identifies what type of design you are using. Your plan should make clear what your research question is, what theory or theories will be considered, key concepts, your hypotheses, your independent and dependent variables, their operational definitions, your unit of analysis,## 3: Exploring and Visualizing Data

You have your plan, you carry out your plan by getting out and collecting your data, and then you put your data into a file. You are excited to test your hypothesis, so you immediately run your multiple regression analysis and look at your output. You can do that (and probably will even if we advise against it), but before you can start to make sense of that output you need to look carefully at your data. You will want to know things like “how much spread do I have in my data” and “do I have any## 4: Probability

Probability tells us how likely something is to occur. Probability concepts are also central to inferential statistics - something we will turn to shortly. Probabilities range from 0 (when there is no chance of the event occurring) to 1.0 (when the event will occur with certainty). If you have a probability outside the 0 - 1.0 range, you have made an error! Colloquially we often interchange probabilities and percentages, but probabilities refer to single events while percentages refer to the por## 5: Interference

This chapter considers the role of inference—learning about populations from samples—and the practical and theoretical importance of understanding the characteristics of your data before attempting to undertake statistical analysis. As we noted in the prior chapters, it is a vital first step in empirical analysis to “roll in the data.”## 6: Association of Variables

The last chapter focused on the characterization of distributions of a single variable. We now turn to the associations between two or more variables. This chapter explores ways to measure and visualize associations between variables. We start with how to analyze the relations between nominal and ordinal level variables, using cross-tabulation in R. Then, for interval level variables, we examine the use of the measures of covariance and correlation between pairs of variables. Next, we examine hy## 7: The Logic of Ordinary Least Squares Estimation

This chapter begins the discussion of ordinary least squares (OLS) regression. OLS is the “workhorse” of empirical social science and is a critical tool in hypothesis testing and theory building. This chapter builds on the discussion in Chapter 6 by showing how OLS regression is used to estimate relationships between and among variables.## 8: Linear Estimation and Minimizing Error

As noted in the last chapter, the objective when estimating a linear model is to minimize the aggregate of the squared error. Specifically, when estimating a linear model, Y = A + B X + E , we seek to find the values of ^ α and ^ β that minimize the ∑ ϵ 2 . To accomplish this, we use calculus.## 9: Bi-Variate Hypothesis Testing and Model Fit

The previous chapters discussed the logic of OLS regression and how to derive OLS estimators. Now that simple regression is no longer a mystery, we will shift the focus to bi-variate hypothesis testing and model fit. We recommend that you try the analyses in the chapter as you read.## 10: OLS Assumptions and Simple Regression Diagnostics

Now that you know how to run and interpret simple regression results, we return to the matter of the underlying assumptions of OLS models, and the steps we can take to determine whether those assumptions have been violated. We begin with a quick review of the conceptual use of residuals, then turn to a set of “visual diagnostics” that can help you identify possible problems in your model. We conclude with a set of steps you can take to address model problems, should they be encountered. As with## 11: Introduction to Multiple Regression

In the chapters in Part 3 of this book, we will introduce and develop multiple ordinary least squares regression – that is, linear regression models using two or more independent (or explanatory) variables to predict a dependent variable. Most users simply refer to it as “multiple regression”.20 This chapter will provide the background in matrix algebra that is necessary to understand both the logic of, and notation commonly used for, multiple regression. As we go, we will apply the matrix form## 12: The Logic of Multiple Regression

The logic of multiple regression can be readily extended from our earlier discussion of simple regression. As with simple regression, multiple regression finds the regression line (or regression plane" with multiple independent variables) that minimizes the sum of the squared errors. This chapter discusses the theoretical specification of the multiple regression model, the key assumptions necessary for the model to provide the best linear unbiased estimates (BLUE) of the effects of the X s o## 13: Multiple Regression and Model Building

This book focuses on the use of systematic quantitative analysis for purposes of building, refining and testing theoretical propositions in the policy and social sciences. All of the tools discussed so far – including univariate, bi-variate, and simple regression analysis – provide means to evaluate distributions and test hypotheses concerning simple relationships. Most policy and social theories, however, include multiple explanatory variables. Multiple regression extends the utility of simple## 14: Topics in Multiple Regression

Thus far we have developed the basis for multiple OLS reression using matrix algebra, delved into the meaning of the estimated partial regression coefficient, and revisited the basis for hypothesis testing in OLS. In this chapter we turn to one of the key strengths of OLS: the robust flexibility of OLS for model specification. First we will discuss how to include binary variables (referred to as dummy variables“) as IVs in an OLS model. Next we will show you how to build on dummy variables to## 15: The Art of Regression Diagnostics

The previous chapters have focused on the mathematical bases of multiple OLS regression, the use of partial regression coefficients, and aspects of model design and construction. This chapter returns our focus to the assessment of the statistical adequacy of our models, first by revisiting the key assumptions necessary for OLS to provide the best, linear, unbiased estimates (BLUE) of the relationships between our model X s and Y . We will then discuss the “art” of diagnosing the results o## 16: Logit Regression

Logit regression is a part of a larger class of generalized linear models (GLM). In this chapter we first briefly discuss GLMs, and then move on into a more in-depth discussion of logistic regression.## 17: Appendix- Basic R

This Appendix willl introduce you to the basics of programming languages, such as R, as well as explain why we have chosen to use R in our course and this textbook. Then we will provide you with some basic programming skills in R that are generally unrelated to the use of R as a statistical software such as downloading, reading, manipulating and writing data. In so doing, we will prepare and introduce you to the data used throughout the book and for the accompanying exercises.