Refining Constructivist Assessment. How to Measure the Main Traditional Indexes in Binary Grids through Formal Concept Analysis

Abstract

This paper aims to expand knowledge on the application of formal concept analysis, a mathematical theory, to the elaboration of a repertory grid, which is a method designed for exploring the structure and content of a respondent’s system of constructs. After a critical reexamination of the ways in which the commonly used statistical procedures for the analysis of repertory grids can affect data analysis, we revisit an alternative methodology that is more consistent with both personal construct theory and measurement properties of the variables collected by means of repertory grids. We use a classic example of repertory grid technique and describe it according to both traditional analysis and the alternative methodology. This comparison is aimed at displaying how formal concept analysis applied to repertory grids can provide all the main measures and cognitive indexes that are included in traditional repertory grid analysis. We then provide further evidence to highlight how this proposal can be used to collect more consistent and detailed information from repertory grids, thus preserving the nature of the respondents’ data.

Acknowledgements

This work was carried out within the scope of the project “Use-inspired basic research”, for which the Department of General Psychology of the University of Padova has been recognized as “Dipartimento di Eccellenza”; by the Italian Ministry of University and Research.

Notes

1 Of course, this is an arbitrary choice and other authors proposed alternative solutions to this issue. For instance, Caputi and Hennessy (2008) split each construct into two attributes and did not assign any of them to the neutral element. While this choice allows for neutral treatment of the central value, it introduces in the matrix non-independent attributes. Since this may be critical from a formal point of view, we decided to apply the proposed solution. In any case, the application of FCA to RGs will be optimal if the grid is conceived from the beginning as dichotomous, or, for instance, if an even number of levels is selected for the task.

2 Notice that in the dichotomous case the symmetric distance is equivalent to the Manhattan distance.