Comparison between the syllogistic and correlational methods in calculating item discrimination in light of variations in sample size and test length

Abstract

This study presents a theoretical comparison between two common methods for calculating item discrimination within classical measurement theory: the extreme groups method and the correlational method (item-to-group correlation). The research problem lies in the potential for discrepancies in discrimination estimates depending on the method used, and in the sensitivity of these estimates to variations in sample size and test length. This sensitivity can impact decisions regarding item retention or exclusion, as well as test quality. The study aims to develop a conceptual framework that clarifies the fundamental differences between the two methods, analyzes the impact of sample size and test length on the stability, accuracy, and potential biases of the estimation, and ultimately provides theoretical guidelines for selecting the most appropriate indicator within the measurement context. The study employs a theoretical and analytical approach based on an analysis of psychometric literature and a discussion of the assumptions governing discrimination indicators in light of sample and test characteristics. The study addresses the following key areas: the concept of item discrimination and its relationship to difficulty, reliability, and validity; a description of the two methods and their characteristics; and a comparison of the impact of n and test length on each method. The expected conclusions are that the traditional method is more direct in its explanation but less stable at small samples due to sample reduction and neglect of the mean, while the correlational method - especially the corrected one - tends to have greater consistency with internal consistency, with a notable influence of test length, sample homogeneity and dimension structure.