This chapter considers the multivariate case, extending the univariate concepts to the vector time series case. We consider vector autoregressions from different points of view.

The first chapter contains an overview of what is accepted as good practice. We review several general ethical guidelines. These can be used to appreciate good research and to indicate where and how research does not adhere to them. Good practice is “what we all say we (should) adhere to.” In the second part of this chapter, the focus is more on specific ethical guidelines for statistical analysis. Of course, there is overlap with the more general guidelines, but there are also a few specifically relevant to statistics: Examples are misinterpreting p values and malpractice such as p hacking and harking.

Chapter 10 examines correlation, the statistical procedure used to measure the degree of association or relationship between variables. It is bivariate, since we typically apply this statistical technique to measure or describe the association between two variables or groups. The correlation coefficient, which measures the degree and direction of an association, is discussed, as are some of the issues regarding the application and interpretation of correlations. The chapter also outlines the many different measures of association but focuses on Pearson’s r. It emphasizes the definitional formula and z-scores for understanding and computing the correlation coefficient.

This is a translation of the excerpts published in Naturwissenschaften of Grete Hermann’s 1935 essay on philosophy of quantum mechanics, recently translated into English. Her main thesis, in line with her natural-philosophical training and neo-Kantian commitments, is to argue that quantum mechanics does not refute the principle of causality. Quantum mechanics cannot be completed by, hidden variables, because it is already causally complete (albeit retroductively). In establishing this provocative thesis, she makes important use of Bohr’s principles of correspondence and complementarity and of Weizsäcker's version of the gamma-ray microscope, arguing that the lesson of quantum mechanics is the impossibility of an absolute description of nature independent of the context of observation.

The chapter begins with the observation that global history has an ambivalent attitude towards explanation. In many cases, the mere presentation of sources and voices from many different parts of the world seems sufficient to justify a global approach. The need for explanation is ignored or even denied. In other cases, global explanation is eagerly pursued, but often at the expense of more complex explanatory models that incorporate factors at different scales. In this perspective, global explanations are claimed to be inherently superior and a privileged way of explaining historical phenomena. After a cursory survey of current positions on causality and explanation in general methodology and ‘formal’ historical theory, the chapter proposes a brief typology of explanatory strategies. It goes on to discuss the peculiarities of explanation within a framework of connections across great distances and cultural boundaries. The much-exclaimed concept of narrative explanation is found to be of limited value, as it underestimates the difficulties of producing coherent narratives on a global scale. Concepts offered in the social science literature, such as the analysis of mechanisms and temporal sequences, could be helpful in refining purely narrative approaches to explanation.

Sociology is a science concerning itself with the interpretive understanding of social action and thereby with a causal explanation of its course and consequences. Empirically, a key goal is to find relations between variables. This is often done using naturally occurring data, survey data, or in-depth interviews. With such data, the challenge is to establish whether a relation between variables is causal or merely a correlation. One approach is to address the causality issue by applying proper statistical or econometric techniques, which is possible under certain conditions for some research questions. Alternatively, one can generate new data with experimental control in a laboratory or the field. It is precisely through this control via randomization and the manipulation of the causal factors of interest that the experimental method ensures – with a high degree of confidence – tests of causal explanations. In this chapter, the canonical approach to causality in randomized experiments (the Neyman–Rubin causal model) is first introduced. This model formalizes the idea of causality using the "potential outcomes" or "counterfactual" approach. The chapter then discusses the limits of the counterfactual approach and the key role of theory in establishing causal explanations in experimental sociology.

This chapter addresses the often-misunderstood concept of validity. Much of the methodological discussion around sociological experiments is framed in terms of internal and external validity. The standard view is that the more we ensure that the experimental treatment is isolated from potential confounds (internal validity), the more unlikely it is that the experimental results can be representative of phenomena of the outside world (external validity). However, other accounts describe internal validity as a prerequisite of external validity: Unless we ensure internal validity of an experiment, little can be said of the outside world. We contend in this chapter that problems of either external or internal validity do not necessarily depend on the artificiality of experimental settings or on the laboratory–field distinction between experimental designs. We discuss the internal–external distinction and propose instead a list of potential threats to the validity of experiments that includes "usual suspects" like selection, history, attrition, and experimenter demand effects and elaborate on how these threats can be productively handled in experimental work. Moreover, in light of the different types of experiments, we also discuss the strengths and weaknesses of each regarding threats to internal and external validity.

Chapter 2 covers the basics of research design.It is written so that students without any research design experience or coursework can learn common research designs to enable them to conduct statistical analyses in the text.Hypotheses development with variable construction (dependent and independent variables) are covered and applied to experimental and non-experimental designs.Survey methods including question construction and implementation of surveys is presented.

This chapter follows the definition of ‘empirical legal studies’ as research which applies quantitative methods to questions about the relationship between law and society, in particular with the aim of drawing conclusions about causal connections between variables. Comparative law does not typically phrase its research as being interested in questions of causal inference. Yet, implicitly, it is very much interested in such topics as it explores, for example, the determinants of legal differences between countries or when it evaluates how far it may be said that one of the legal solutions is preferable. It is thus valuable that significant progress has been made in empirical approaches to comparative law that may be able to show robust causal links about the relationship between law and society. This chapter outlines the main types of such studies: experiments, cross-sectional studies, panel data analysis and quasi-experiments. However, it also shows that such studies face a number of methodological problems. This chapter concludes that often it may be most promising to combine different methods in order to reach a valid empirical result.

We provide a lay-language primer on the counterfactual model of causal inference and the logic of causal models. Topics include the representation of causal models with causal graphs and using causal graphs to read off relations of conditional independence among variables in a causal domain.

The chapter explores the nature of narrative, the various definitions that are used and how we should define narrative in relation to applied research. We need to make a distinction between narratives – the stories – and narrative processes – the means by which we are able to construct and use stories. The chapter also explores the key characteristics of narratives, such as temporality and meaning. All narratives have certain key characteristics, though researchers and theoreticians do not agree on precisely what these characteristics are. Narratives must be rule-based, or we wouldn't understand each other. They must relate to characters and actions, cause and effect and occur over time. They are also changeable. For instance, we have science stories that are about current theory, but we accept that theory changes over time. This is similar to our life stories, that change as new events and new interpretations are created.