Asian Journal of Probability and Statistics

The decade - old academic achievement discrepancies at the basic school level that are widely emphasized are still being worked on heavily in current research. In this study, we present a novel Neutrosophic-Principal Component Analysis and Two-way Neutrosophic ANOVA to analysing the causes of Performance Gap among private and public school students in the Basic Education Certificate Examination. One-hundred and eighty-nine respondents from the Ada East and West Districts of Ghana were involved in the study. We present a modified Neutrosophic regression equivalence of the classical least squares to solve problems of indeterminacy. The results showed that of the total 87% variability, three main components—student characteristics, instructor characteristics, and administrative-logistic features—accounted for 36%, 31%, and 20%, respectively. The remaining 13% of the variability, which was attributed to random effects by the Neutrosophic PCA technique, was tested using a two-way Neutrosophic ANOVA where the results identified that interaction between the identified factors was a contributing factor that needed to be explained. Our results reveal that Neutrosophic-PCA is a potential method to lessen human response errors, which are frequently tainted with ambiguous, conflicting, imprecise, indeterminate or uncertainty. When there is just a slight difference between the two options, the forced selection caused by the traditional Likert method will be eliminated by our new approach. When studying respondents' opinions, we recommend researchers to employ Neutrosophic- PCA in order to minimize any bias that may result from the responses' lack of precision.