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## Multiple Correspondence Analysis and Geometric Data Analysis

This chapter focuses on multiple correspondence analysis (MCA), which is a factor analysis statistical method used to analyse relations between a large set of categorical variables. Developed by Jean-Paul Benzécri in the early 1970s, MCA is one of the principal methods of geometric data analysis (GDA). Three different statistical methods can be identified as GDA: correspondence analysis (CA), which enables the cross-tabulation of two categorical variables; MCA for the analysis of a matrix of individuals and categorical variables; and principal component analysis (PCA), which uses numerical variables. In GDA, data is represented as a cloud of points to allow statistical interpretations. Although MCA is a relational method, it differs from social network analysis (SNA) as it focuses on the objective relations that characterize actors or groups, rather than the effective relations.

## Statistical Significance

This chapter highlights statistical significance. The key question in quantitative analysis is whether a pattern observed in a sample also holds for the population from which the sample was drawn. A positive answer to this question implies that the result is ‘statistically significant’ — i.e. it was not produced by a random variation from sample to sample, but, instead, reflects the pattern that exists in the population. The null hypothesis statistical test (NHST) has been a widely used approach for testing whether inference from a sample to the population is valid. Seeking to test whether valid inferences about the population could be made based on the results from a single sample, a researcher should consider a wide variety of approaches and take into the account not only p-values, but also sampling process, sample size, the quality of measurement, and other factors that may influence the reliability of estimates.

## Covariance

### A First Step in the Analysis of the Relationship between Two Variables

This chapter examines the covariance, which is either a comprehensive qualitative approach or the first step of a quantitative approach to the analysis of the relationship between two variables. On the one hand, in qualitative studies, and in particular in case study methods, covariation is an analytical approach used alongside causal process-tracing and congruence analysis. In the co-variational approach, causal inferences are drawn based on observed covariation between causal factors (independent variables) and causal effects (dependent variables). On the other hand, when the type of data allows a quantitative approach, looking at the covariance constitutes a first step in the statistical analysis. The covariance is then a measure of linear association between two variables.

## Time Series

### A Statistical Method for Longitudinal Analysis

This chapter focuses on time series analysis, a statistical method of longitudinal analysis which is suitable if researchers are interested in the temporality of social phenomena and want to analyse social change and patterns of recurrence over time. In contrast to other statistical methods of longitudinal analysis, time series analysis can be applied even if researchers have only a few cases (maybe even only one) and only a few (maybe even only one) variables. Time series can be built for any level of analysis, as cases can be persons, but are usually organizations or countries. In order to build a time series, the variables need to have been measured several times over a given period, and for each measurement one needs to know the measurement date. There are different goals when doing time series analysis, which can be used in descriptive, explanatory, and interpretive approaches.

## 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.