Exploring when maternal interest is sufficient for high attainment in mathematics: A configurational analysis using longitudinal data

摘要

Qualitative Comparative Analysis (QCA) is a case-based method, developed by Ragin (1987, 2000), to analyse medium- and large-n datasets. It uses Boolean algebra to show which configurations of factors in a model are either necessary and/or sufficient for a specified outcome. In the social world, we rarely see perfect necessity and sufficiency but we can use QCA to assess the degree of necessity or sufficiency to find configurations which are quasi-necessary or quasi-sufficient. In this paper, I use crisp-set QCA on data from the 1970 Birth Cohort Study (BCS70) to investigate which configurations of sex, maternal interest, social class and, later, ability are quasi-sufficient for various levels of attainment in maths. Firstly, I explain how to conduct QCA, through the use of examples, before using a set-theoretic measure of consistency to explore the relationship between sex, social class, maternal interest and, what I term, above-average attainment in mathematics. To this model, I then introduce an additional factor of general ability (operationalised as several dichotomous factors, each indicating a certain level of ability) leading to instances of configurations having strong subset relations but containing very few cases. These rows, called remainders, cannot be included in a solution without theoretical justification (Ragin, 2008). For the final stage of the analysis, I create, for two different general ability levels, a 'most-complex solution' (which excludes all remainder rows) and a parsimonious solution (which includes any remainder row contributing to parsimony). These act as boundaries for the 'intermediate solution' which contains only those remainders which can, theoretically, be thought to obtain the outcome. I then discuss each intermediate solution and note that, in one case, it is the same as the relevant most-complex version.