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## V. Variables

### A Matter of Kind and Degree

This chapter explores variables, which are measurable representations. As such, they are located at the interface between theoretical constructs and empirical observations. Deductive research identifies variables by operationalizing abstract concepts, while inductive research typically constructs variables from the observation of units. Irrespective of whether the research is deductive and theory-driven or inductive and empirically driven, variables occupy a central position in research methodology. One of the key features of variables is that they vary across units; any variable can have at least two distinct values (also called attributes). The chapter distinguishes dependent and independent variables before introducing other types of variables and presenting different types of values. It also discusses the epistemological assumptions underlying the notion of variables.

## Comparative Analysis

This chapter illustrates comparative analysis, which is simply defined as comparing and contrasting two or more phenomena in order to better understand them. Comparative analysis plays an important role in both academic and policy-related circles and can be useful in many different ways. While in the hard sciences it is possible to conduct experiments under controlled laboratory conditions, this is often impossible in social science. Social scientists must therefore find other ways of isolating and testing the impact of variables and understanding the relationships between them. Accordingly, the goal of comparative analysis is the comparison of phenomena — whether that means comparison within individual cases, among a small group of cases, or the analysis of large amounts of data — to identify key independent variable(s) and establish what link, if any, exists between them and the dependent variable(s). Comparative analysis can also be useful in establishing the nature of that relationship, assessing whether it is necessary, sufficient, or both. Moreover, cross-case comparison allows social scientists to build broad theories that are applicable in different contexts.

## 17. A Guide to Multivariate Analysis

This chapter extends the principles of bivariate analysis to multivariate analysis, which takes into account more than one independent variable and the dependent variable. With multivariate analysis, it is possible to investigate the impact of multiple factors on a dependent variable of interest, and to compare the explanatory power of rival hypotheses. Multivariate analysis can also be used to develop and test multi-causal explanations of political phenomena. After providing an overview of the principles of multivariate analysis, and the different types of analytical question to which they can be applied, the chapter shows how multivariate analysis is carried out for statistical control purposes. More specifically, it explains the use of ordinary least squares (OLS) regression and logistic regression, the latter of which builds on cross-tabulation, to carry out multivariate analysis. It also discusses the use of multivariate analysis to debunk spurious relationships and to illustrate indirect causality.

## 17. A Guide to Multivariate Analysis

This chapter extends the principles of bivariate analysis to multivariate analysis, which takes into account more than one independent variable and the dependent variable. With multivariate analysis, it is possible to investigate the impact of multiple factors on a dependent variable of interest, and to compare the explanatory power of rival hypotheses. Multivariate analysis can also be used to develop and test multi-causal explanations of political phenomena. After providing an overview of the principles of multivariate analysis, and the different types of analytical question to which they can be applied, the chapter shows how multivariate analysis is carried out for statistical control purposes. More specifically, it explains the use of OLS regression and logistic regression, the latter of which builds on cross-tabulation, to carry out multivariate analysis. It also discusses the use of multivariate analysis to debunk spurious relationships and to illustrate indirect causality.

## 16. Patterns of Association: Bivariate Analysis

This chapter discusses the principles of bivariate analysis as a tool for helping researchers get to know their data and identify patterns of association between two variables. Bivariate analysis offers a way of establishing whether or not there is a relationship between two variables, a dependent variable and an independent variable. With bivariate analysis, theoretical expectations can be compared against evidence from the real world to see if the theory is supported by what is observed. The chapter examines the pattern of association between dependent and independent variables, with particular emphasis on hypothesis testing and significance tests. It discusses ordinary least squares (OLS) regression and cross-tabulation, two of the most widely used statistical analysis techniques in political research. Finally, it explains how to state the null hypothesis, calculate the chi square, and establishing the correlation between the dependent and independent variables.

## 16. Patterns of Association

### Bivariate Analysis

This chapter discusses the principles of bivariate analysis as a tool for helping researchers get to know their data and identify patterns of association between two variables. Bivariate analysis offers a way of establishing whether or not there is a relationship between two variables, a dependent variable and an independent variable. With bivariate analysis, theoretical expectations can be compared against evidence from the real world to see if the theory is supported by what is observed. The chapter examines the pattern of association between dependent and independent variables, with particular emphasis on hypothesis testing and significance tests. It discusses ordinary least squares (OLS) regression and cross-tabulation, two of the most widely used statistical analysis techniques in political research. Finally, it explains how to state the null hypothesis, calculate the chi square, and establishing the correlation between the dependent and independent variables.