Methodological Comparison of Frequentist and Bayesian Two-Sample Tests on Regional Socioeconomic Disparities in Indonesia

Abstrak

The socioeconomic gap between Western Indonesia and Eastern Indonesia is a persistent challenge in the national development agenda. This study has two main objectives: (1) to empirically compare poverty levels and income inequality (Gini ratio) between the western region (Sumatra, Java, Bali) and the eastern/other regions of Indonesia using hypothetical data from 38 provinces in 2025; and (2) to conduct a systematic comparative analysis of five independent two-sample statistical tests (frequentist and Bayesian tests) to evaluate their consistency and applicability. The results confirm statistically and substantively significant disparities, particularly in rural poverty and inequality, with eastern regions exhibiting much higher levels. The comparative analysis shows a high degree of convergence among the existing statistical tests; most methods produce the same substantive conclusions, reinforcing the validity of the findings. However, methods robust to assumption violations, such as the Brunner-Munzel Test, proved to provide more reliable results theoretically. Through Bayes Factor calculations, the Bayesian approach offers a more nuanced measure of evidence strength than p-value-based binary decisions, allowing for the quantification of evidence for both alternative and null hypotheses.