When we see data on a spreadsheet, concepts and methods associated with standard quantitative techniques inevitably come to mind. Usually and by default, we try to make sense of the data by deriving the summary statistics to understand what has gone up or down, we explore associations between factors by identifying correlations, and administer technical tests to see if the results confirm, reinterpret, or nullify our research questions and hypotheses.

But is it possible to look at a dataset “qualitatively”? And what would that imply? Is it possible to look at columns and rows and identify relations and configurations between them that are more than associational? At first glance, the possibility of this approach seems incongruous because we usually associate qualitative methods with text and quantitative methods with numbers.

This chapter introduces the reader to a qualitative approach by providing an overview of the set theoretic methodology and the QCA method. An introduction to the methodology and the method is important not just because it is mostly an unfamiliar method to many social scientists, particularly those who work in the Indian context, but also because, as a methodology, its philosophical and conceptual roots are somewhat distinct from standard social science approaches. And, equally important, because QCA relies on numbers and software codes for analysis, it misconstrues expectations since the use of numbers can inadvertently lead to interpretations based on quantitative reasoning.

Over the past 75 years, there have been at least 800 state government terms ruled by around 375 political leaders as chief ministers and counting. Populist leaders are a small but pivotal subset among these leaders. Scholarship on such leaders has necessarily been long on descriptive accounts because of their exceptional rise to and stay in political office. Such accounts are the basis upon which this comparative account is built.

The unit of analysis in this study is not a populist personality over a period of time, but a personality in a particular year that corresponds with either an assembly or a national election year. For example, a single case would not be “Kejriwal,” but would instead be cases like “Kejriwal 2015” or “Kejriwal 2020.” This chapter, therefore, does not aim to provide elaborate accounts of the leaders, but tries to strike a balance with the details and their relevance and, in doing so, provide a narrative of each that is tenable for comparative analysis.

This “case by year” approach seems justified for a couple of reasons. First, while almost all populist leaders come to power riding a wave, they inevitably routinize into the mainstream over successive elections. The fever breaks. Second, it may appear that the period of such long-term leaders is linear, that is, from the heights of riding a wave to come to power, and subsequently routinizing into a banal steady but sustained popularity over time. Breaking this narrative into multiple periods provides space for curvilinear possibilities because it allows for a closer look into the ups and downs of political life in that declining trajectory.

This chapter provides a focused examination of spatio-temporal analysis using multilayer networks in which each layer represents the instantiation of a spatial network at a particular time of observation. The nodes in all layers may be the same with the only differences being of edges among layers (a multiplex network) or the nodes may change or move between layers and times. Multilayer characteristics such as versatility (multilayer centrality) and spectral properties are introduced. Several examples are described and reviewed as model studies for future ecological applications.

In this chapter, we describe how to jointly model continuous quantities, by representing them as multiple continuous random variables within the same probability space. We define the joint cumulative distribution function and the joint probability density function and explain how to estimate the latter from data using a multivariate generalization of kernel density estimation. Next, we introduce marginal and conditional distributions of continuous variables and also discuss independence and conditional independence. Throughout, we model real-world temperature data as a running example. Then, we explain how to jointly simulate multiple random variables, in order to correctly account for the dependence between them. Finally, we define Gaussian random vectors which are the most popular multidimensional parametric model for continuous data, and apply them to model anthropometric data.

Some of the key messages of this book are reviewed here in the format of ’reminders’ to clarify the concerns of past misunderstandings and to emphasize solutions to perceived challenges. The importance of basic fundamentals, such as visual assessment, awareness of assumptions and potential numerical solutions is described and then the complementarity of the many statistics and their bases is reviewed. The exciting potential of ongoing developments is summarized, featuring hierarchical Bayesian analysis, spatial causal inference, applications of artificial intelligence (AI), knowledge graphs (KG), literature-based discovery (LBD) and geometric algebra. A quick review of future directions concludes this chapter and the book.

This chapter focuses on correlation, a key metric in data science that quantifies to what extent two quantities are linearly related. We begin by defining correlation between normalized and centered random variables. Then, we generalize the definition to all random variables and introduce the concept of covariance, which measures the average joint variation of two random variables. Next, we explain how to estimate correlation from data and analyze the correlation between the height of NBA players and different basketball stats.In addition, we study the connection between correlation and simple linear regression. We then discuss the differences between uncorrelation and independence. In order to gain better intuition about the properties of correlation, we provide a geometric interpretation of correlation, where the covariance is an inner product between random variables. Finally, we show that correlation does not imply causation, as illustrated by the spurious correlation between temperature and unemployment in Spain.

Sets of points can be analysed from their positions in space and line segments can be studied separately for their own spatial arrangements and relationships. Combining points and lines as the nodes and edges of a spatial graph provides a flexible and powerful approach to spatial analysis. Such graphs and their network versions are studied by Graph Theory, a branch of mathematics that quantifies their properties, with or without additional features such as labels, weights and functions associated with the nodes and edges. Some relevant graph theory terms are introduced, including connectivity, connectedness, modularity and centrality. Networks are graphs with additional features, usually representing an observed system of interest, whether aspatial like a food web or spatial like a metacommunity. Key concepts for the latter example are connectivity, migration and network flow.

The spatial patterns of point events in the plane can exist at several different scales in a single data set. The assessment of point patterns can be based on the distances between neighbour events, on the counts of events in quadrats or on counts of events in point-centred circles of changing size. Ripley’s K function evaluates simple point patterns and can be modified for different spatial dimensions, for bi- and multi-variate variables and for non-homogeneous data. Quadrat-based quantitative data are usually analysed by one of many related ’quadrat variance’ methods that assess variance or covariance as a function of spatial scale and which can also be modified for different conditions, such as bi- or multi-variate data. There are related methods from other traditions to be considered, including spectral analysis and wavelets. These approaches share a conceptual basis of comparing the data with spatial templates and we provide a summary of their relationships and differences.

Spatial structure is key to understanding diversity in ecological systems, being affected by both location and scale. The effects of scale are often dealt with as the hierarchy of alpha (local area), beta (between areas) and gamma (largest areas) diversity. All have spatial aspects, but beta diversity may be most interesting for spatial analysis because it involves complex responses such as intermediate-scale nestedness and species turnover with or without environmental gradients. In addition to species diversity within communities, the diversity of species composition or combinations as a function of location is an important characteristic of ecological assemblages. Many aspects of spatial diversity are best understood by spatial graphs, with sites as nodes and edges quantifying inter-site relationships. Temporal information, when available, can provide crucial insights about spatial diversity through understanding the dynamics of the system.

Spatial analysis originated in a broad range of disciplines, producing a diverse set of concepts and terminologies. Ecological processes take place in space and time, and the spatio-temporal structure that results takes different forms that produce spatial dependence at all scales. That dependence has major effects, even when ecological data are abstracted from the spatial context. Not all dependence exhibits a smooth decay with increasing separation, but it can vary with scale, stationarity or its absence and direction (anisotropy versus isotropy). A key factor in spatial analysis is the ability to determine neighbour events for points or patches and we present various algorithms to create networks of neighbours. We discuss a range of spatial statistics and related randomization tests, including a ’Markov and Monte Carlo’ approach. The chapter provides a detailed conceptual background for the technical aspects presented in subsequent chapters.