Let X be the condition ‘soccer player living close to the training site’ and Y the outcome ‘arriving in time for training’. If empirically all players who live close to the training ground also arrive in time for practice, then X implies Y, or X is a subset of Y. This empirical pattern provides support for interpreting X as sufficient for Y.

In this chapter, we introduce the basic logic of sufficiency and introduce various parameters of fit for sufficient conditions. We explain how to allow for causal complexity in terms of conjunctural causation, equifinality, and asymmetry, how to summarize and present data in the form of a truth table, and how to then analyze that truth table via the process of logical minimization.

Learning goals:

- Understanding of the basic logic of sufficiency.

- Assessing deviations from perfect subset relations of sufficiency using parameters of fit.

- Understanding of how to represent data in a truth table.

- Understanding of how to analyze and logically minimize truth tables for detecting set relations.

- Familiarity with the various ways of dealing with limited diversity.

- Ability to implement all of the above in R for both crisp and fuzzy sets.

Being a member state of the European Union is necessary for having the Euro as the official currency: the set of EU member states is a superset of the set of countries with the Euro as a national currency. Generally, if a condition X is necessary for an outcome Y, then X is a superset of Y. In this chapter, we introduce the notion of necessity and discuss the analysis of necessary conditions in R. We explain what necessity is, how to analyze and visualize necessary conditions, how to interpret the results, and how to avoid common pitfalls. We outline the basic protocol for the analysis of necessity in R, both for the analysis of individual necessary conditions and for conditions combined with a logical OR, that is necessary disjunctions composed of so-called SUIN conditions.

Learning goals:

- Understanding of the basic logic of necessity.

- Familiarity with different approaches to analyzing necessity in QCA and the protocol for the analysis of necessity.

- Basic understanding of possible analytic pitfalls when analyzing necessity and ways of avoiding them.

- Ability to implement an analysis of necessity in R and visualize the results.

This last, consolidating chapter has four goals. The first is consolidation: we specify appropriate case selection strategies for research using QCA and summarize an integrated protocol for analyzing set relations in an iterative manner, which bases inferences on cross-case patterns, knowledge of individual cases, and external knowledge. This protocol follows three main steps both for necessary and for sufficient conditions: determining empirical consistency, empirical importance, and substantive importance. The second goal is to broaden the perspective: we discuss the diverse variants, uses, and analytic goals of QCA in different research designs. We argue that for deriving valid inferences with QCA, it is important to coherently choose tools in line with analytic approaches. Third, we summarize and update good practices for conducting QCA and presenting and visualizing its results. Lastly, we map exciting developments that are likely to shape the field in the foreseeable future, including a summary of prominent software functionality.

Learning goals:

- Consolidated knowledge of the analytic protocol of QCA.

- Overview of different uses of QCA, their analytic goals and corresponding tools.

- Overview of recommendations for good practice and transparency before, during, and after the analytic moment.

- Outlook of possible developments in the field.

A solid QCA does not end with the analytic moment. Researchers must make several analytic decisions at various stages in the analysis, some with more confidence than others. Researchers might also be confronted with data that are structured in analytically relevant ways. For example, cases might group into different geographic, substantive, or temporal clusters, or there might be relevant causal dependencies or sequences among conditions.

This chapter introduces the different robustness and diagnostic tools available in R to assess QCA results. It enables the reader to investigate to what extent their QCA results are robust against equally plausible analytic decisions regarding the selection of calibration anchors or consistency and frequency cut-offs. We present possibilities to assess robustness in R. Moreover, we introduce tools for cluster diagnostics and discuss strategies for dealing with timing and temporality, including ‘coincidence analysis’ (CNA).

Learning goals:

- Basic understanding of different approaches to diagnosing and assessing QCA results.

- Familiarity with how the robustness of QCA results to different analytical decisions can be assessed.

- Familiarity with proposals on how to assess QCA results in the presence of clustered data.

- Familiarity with how to model sequences and causal chains in R.

This chapter uses an empirical example to explain what Qualitative Comparative Analysis (QCA) is and how it works. We familiarize the reader with the basic analytic goals and steps of QCA and the results this method produces. We also sketch the empirical spread of QCA and related software. We explain how this book is structured and how the reader can best use it.

QCA identifies necessary and sufficient conditions for an outcome by modeling core aspects of causal complexity. As QCA is a set-theoretic method, we attribute cases to sets that represent the outcome we want to explain, the conditions we assume to be relevant for this outcome, and we analyze necessary and sufficient conditions as set relations. Before the analytic moment, we design our research, conceptualize cases and sets, and transform them into ‘data’ (‘calibration’). The ‘analytic moment’ refers to the actual analyses of necessity and sufficiency. Finally, we interpret the results and check how ‘good’ they are.

Learning goals:

- Familiarity with the general analytic goals and motivations underlying the use of QCA.

- Basic understanding of the main analytic steps involved in doing a QCA.

- Basic understanding and interpretation of QCA results.

When using QCA, we conceive of social phenomena as sets in which the cases have membership, and we look at social phenomena as complex combinations of different sets. For example, to allocate students to the set of ‘good students’, we need to define clear criteria for distinguishing ‘good’ from ‘not good’ students, and think about how different criteria combine to indicate that a student is ‘good’.

We first discuss how to attribute cases to sets: types of sets and ways to measure them, approaches to calibrating sets, and their implementation in R. We introduce good practices, practical tips, and some diagnostic tools for calibration. Second, we discuss how to combine sets with the Boolean operations AND, OR, and NOT. These techniques help us conceptualize social phenomena, including useful rules for combining and presenting set-theoretic expressions.

Learning goals:

- Basic understanding of the notion of calibration and different calibration techniques.

- Familiarity with good practices and diagnostic tools for set calibration.

- Familiarity with basic Boolean operations on sets and the rules for attributing cases to combined sets.

- Familiarity with different techniques of aggregating sets into higher-order concepts.

- Ability to implement these calibration and concept formation tools in R.

It significantly strengthens the inferences drawn based on QCA results if we connect these results to theoretical knowledge and within-case evidence before, during, and after the analysis. In this chapter, we discuss two prominent tools of doing so after the analytic moment – set-theoretic theory evaluation and set-theoretic multi-method research (SMMR) – and demonstrate their implementation within R. Theory evaluation is a form of re-assessing theoretical hunches based on the results generated by QCA. While it can also be used for the identification of interesting cases for follow-up case studies, this task is better achieved with set-theoretic multi-method research. The latter is a tool for identifying typical and deviant cases for comparative or single within-case analysis.

Learning goals:

- Basic understanding of what theory-evaluation and set-theoretic multimethod research are.

- Familiarity with how to apply formal set-theoretic theory evaluation for re-assessing theoretical hunches based on the results generated by QCA.

- Familiarity with how to use set-theoretic multi-method research (SMMR) for the identification of cases for follow-up case studies after QCA.

- Ability to implement theory evaluation and SMMR in R.