An If-Item-Deleted Sensitive Analysis of Cronbach’s Alpha Technique using Simulated Anneling Algorithm

Abstract

This work proposes a nonlinear model and also a solution method to improve the overall Cronbach’s alpha coefficient technique, by grouping items of an instrument (questionnaire) that should be considered to deletion. The classical method called if-item-deleted Alpha also improves the overall reliability, however it considerers the deletion of only one item per time. Due to the combinatorial nature of the proposed model, a simulated annealing algorithm was implemented in order to achieve optimal or near optimal solutions. We presented an example for a simulated questionnaire with 15 items and 22 respondents. The obtained solution indicates the deletion of 8 items for maximum alpha or 2 items to exclude the most problematic items.