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Rizal Kurniawan
Universitas Negeri Padang
Religion Arts Humanities Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Environmental Science Health Professions Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics Medicine & Pharmacology Physics Public Health Social Sciences Other

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Bayesian vs. Frequentist Estimation Under Small-Sample and Non-Normal Conditions: A Full-Factorial Monte Carlo Evaluation Aflah Zakinov Irta; Rizal Kurniawan
UNP Journal of Statistics and Data Science Vol. 4 No. 3 (2026): UNP Journal of Statistics and Data Science
Publisher : Departemen Statistika Universitas Negeri Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/ujsds/vol4-iss3/507

Abstract

The replication crisis in social and behavioral sciences has systematically exposed the fundamental limitations of Null Hypothesis Significance Testing (NHST). In these disciplines, small samples and non-normal data distributions are the operational norm, frequently leading to underpowered studies and fragile empirical findings. Addressing this methodological gap, we conducted a comprehensive Monte Carlo simulation (144,000 iterations) to evaluate alternative inferential frameworks under realistic research constraints. We systematically compared frequentist approaches (Welch’s t-test and Wilcoxon-Mann-Whitney) with Bayesian estimation across varied sample sizes (n = 20 to 200), effect sizes, data distributions, and prior specifications. Estimation accuracy was rigorously assessed using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and coverage rates, incorporating an explicit null condition to precisely capture Type I error dynamics. Simulation results demonstrate that under small-sample conditions typical of social and health research, Bayesian estimation utilizing an empirically derived informative prior substantially outperforms traditional frequentist models. For instance, at n = 20, the Bayesian approach reduced MAE by approximately 65% (0.124 versus 0.358) while meaningfully increasing statistical power. Critically, prior sensitivity analyses reveal that the choice of prior dictates inferential performance far more than the basic Bayesian-frequentist dichotomy. This advantage introduces a fundamental trade-off: while informative priors optimize power and minimize error in limited samples, they incrementally inflate Type I error rates. These empirically grounded findings provide behavioral researchers with actionable, condition-specific guidance for navigating inferential decisions under the realistic constraints of their discipline.
Co-Authors Ade, Frihapma Semita Aflah Zakinov Irta Afnan, Salsa Fadhilah Agitia Kurniati Asrila Aisyah Mawar Jingga Situngkir Aisyah Putri, Aisyah Akbar, Amin Aldi, Aldi Pratama Altashya Nurul Budiani Andhita Nurul Khasanah Anika, Suci Oktavia Anjelika, Tiara Aulia Arifa Putri Aulia, Rahmadianti Citra Anriani Dani, Tri Ahmad Dedi Supendra Dedi Supendra Dedi Supendra Dira Meri Andika Elrisva Magistarina Eryandra, Alvin Fadhlullah Oktaraihan Fahrel Aprizaldo Farah Aulia, Farah Farhan Rivaleno Felinaweny, Riffa Fikri Ramadhan Efendi Firunika Intan Cahyani Guspa, Anindra Haq, Syaiful Hasanah, Afifah Nur Holly Aura Army Bias Huda Nabillah, Nurul Husna, Wildatul Indri Juliyanti Indriyani Santoso Irfan Oktavianus M. Farhan Putra Maisoni M. Yasep Setiawan Mardianto Mardianto Mardianto Muhammad Farhan Ibrahimovich Nelia Afriyeni Niken Wulandari Olivia Marlius Ananta Puspaneli Putri Anisa Rahayu Hardianti Utami Rahayu Hardianti Utami Raihan Almadani Auly Reno Fernandes Reza Fahmi Rinaldi Rinaldi Rizkiqa Tria Fanesha Rozi Sastra Purna Sabar Aulia Rahman Sari, Ayuthia Mayang Sartana Sujaya, Mutiara Suryani, Cahya Syadza Noverta Vizia Zelfi Syadza Tya Syahrani Utama, Rizky Indra Utami, Rahayu Hardianti Verlanda Yuca Widia Suci Rahmadani Wirani, Zahra Wita Nur Hafidzah Witri Syafrida Femelia Yafi Rafif Irfi Yonatri Cahya Ningtias Yuca, Verlanda