Formal Concept Analysis in Statistical Hypothesis Testing

Abstract

In the present research, we examined the solution of a “Hypothesis Testing for Paired Samples t-test” problem that can be ideally subdivided into four parts: (1) hypothesis generation and formal expression, (2) calculation of the t value, (3) identification of the correct critical t value for the acceptance-refusal of H ₀, and (4) the assumption of the correct decision from the comparison between the calculated t and the critical t value. Different response patterns for the problem were obtained. The derived structure represents a partial order. The relation between response patterns and the single elements of the main exercise can be well represented within the framework of the Formal Concept Analysis. From the analysis of the response patterns of a sample of 114 students in a psychometrics course, we derived a Formal Context where the six parts of the “Hypothesis Testing for Paired Samples t-test” exercise were the formal attributes and the response patterns were the formal objects. In our sample only 25 out of the 2⁶ possible response patterns were encountered. A Logistic Model has been applied to develop a measure of the adequacy of each solution’s pattern actually observed. The obtained results are discussed.