A Comparative Analysis of Bootstrap and Maximum Likelihood Estimation Methods for Assessing Reliability Index.

Abstract:

This study compares bootstrap and maximum likelihood estimation methods for assessing the reliability index using scores from the 2022 National Business and Technical Examination Board (NABTEB) Economics examination. Cronbach's Alpha reliability statistic was applied across various sample sizes (50, 100, 200, 500, 1000, and greater than 1000) to assess measurement reliability. Five confidence interval (CI) estimation methods were utilized: Wald, Profile Likelihood, Bootstrap Percentile, Bias-Corrected and Accelerated (BCa), and Studentized. Findings reveal that SE decreases as sample size increases, demonstrating greater precision with larger samples. The Wald confidence interval, though effective for large samples, proved unreliable for small ones due to its assumption of normality. The Profile Likelihood confidence interval, slightly wider than the Wald confidence interval, better accounted for non-normality. The Bootstrap Percentile confidence interval, a nonparametric approach, provided robust estimates when population distribution assumptions were violated. The BCa method improved accuracy by adjusting for bias and skewness, while the Studentized confidence interval offered conservative estimates, accounting for sample variability. Reliability estimates also increased with sample size. It was therefore recommended that for large samples, use Wald CI; for small samples or skewed data, opt for Profile Likelihood or Bootstrap CIs.