The context for this paper is the ongoing debate concerning the relative merits, for the analysis of quantitative data, of, on the one hand, variable-analytic correlational methods, and, on the other, the case-based set theoretic methods developed by Charles Ragin. While correlational approaches, based in linear algebra, typically use regression to establish the net effects of several “independent” variables on an outcome, the set theoretic approach analyses, more holistically, the conjunctions of factors sufficient and/or necessary for an outcome to occur. Here, in order to bring out key differences between the approaches, we focus our attention on the basic building blocks of the two approaches: respectively, the concept of linear correlation and the concept of a sufficient and/or necessary condition. We initially use invented data (for ability, educational achievement, and social class) to simulate what is at stake in this methodological debate and we then employ data taken from the British National Child Development Study to explore the structuring of the relationship between respondents‟ early measured ability and later educational achievement across various configurations of parental and grandparental class origin and sex. The substantive idea informing the analysis, derived from Boudon‟s work, is that, for respondents from higher class origins, ability will tend to be sufficient but not necessary for later educational achievement while, for lower class respondents, ability will tend to be necessary but not sufficient. We compare correlational analyses, controlling for class and gender, with fuzzy set analyses to show that set theoretic indices can better capture these varying relationships than correlational measures. In conclusion, we briefly consider how our demonstration of some of the advantages of the set theoretic approach for modelling empirical relationships might be related to the debate concerning the relation between observed regularities and causal mechanisms
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