Difficulty, Discrimination and Pseudo - Guessing Indices of West African Examinations Council Core Mathematics Multiple Choice Items: Theoretical and Practical Implications of Using Item Response Theory

Abstract

Viewing from the psychometric models of modern assessment, it is imperative to note that assessment has been undergoing major constructive modifications. One of the main modifications is the transition from the use of classical test theory (CTT) to modern test models (IRT) as well as methods used in test construction. This is to say that the pendulum swing in test construction techniques is from CTT to IRT. Clearly, the properties of IRT create several benefits in the area of test design and item banking over CTT. This paper estimated the IRT psychometric proprieties (difficulty-1PL, discrimination-2PL and guessing indices-3PL) of West African Examinations Council (WAEC) 2020 core mathematics objectives test examination in Ghana within the remit of IRT. The study revealed that averagely, the 2020 core mathematics objectives test examination were within the difficulty level (1PL) of the examines. In terms of discrimination level (2PL), the psychometric properties indicated that most of the items discriminated among the examinees. However, on the Pseudo-guessing parameter (3PL), it was found that most items were subjected to pseudo-guessing. Theoretically and practically, the way items are constructed could have influenced outcome. Therefore, we strongly advocate and recommend that item writers for examination body like West African Examinations Council (WAEC) should rigorously be trained to be more conscious of theoretical and practical implications of the guessing parameter. This will help in avoiding test items that are prone to pseudo-guessing.

Psychometric Analysis at Item Level of the Waec May/June Mathematics Multiple Choice Questions Using the Classical Test Theory

“…According to Okoye (2015), items with discrimination indices less than 0.3 should be discarded, replaced or revised, if they will be used in future examinations. This study is in agreement with the findings of Cobbinah and Ntumi (2022) who submitted that the 2020 core mathematics objective test items of the West African Examinations Council discriminated among the examinees.…”

“…In 2021, seven items (14%) out of the fifty items were easy, thirty-eight items (76%) out of the fifty items were moderately difficult while five items (10%) out of the fifty items were too difficult. These findings are in agreement with Cobbinah and Ntumi (2022) who revealed that averagely, the 2020 core mathematics objective test items of the West African Examinations Council in Ghana were within the difficulty level. This study is related to the related to the current study in the areas of subject (mathematics) and theoretical framework but differ in the area of study and sample size.…”

“…A considerable number of studies on psychometric item analysis on mathematics tests have been conducted. For instance, Cobbinah and Ntumi (2022) carried out a study on the difficulty, discrimination and pseudo-guessing indices of the West African Examinations Council core mathematics objective test items in Ghana within the remit of IRT. The study revealed that averagely, the 2020 core mathematics objective test items were within the difficulty level.…”