Beyond the T-Distribution: Robust confidence interval estimation in small-sample inference using bootstrap and Bayesian techniques

Accurate confidence interval (CI) estimation is fundamental to statistical inference, yet traditional methods particularly the classical t-distribution-based intervals are often unreliable in small-sample contexts and under non-normal conditions. This study investigates the performance of alternative CI estimation approaches, including bootstrap methods (percentile and bias-corrected and accelerated [BCa]) and Bayesian credible intervals, with the aim of identifying robust methods suitable for small samples. A simulation-based framework was employed, generating synthetic data from three distinct distributions: normal, exponential (skewed), and t-distribution with 3 degrees of freedom (heavy-tailed). For each distribution, sample sizes of n=10,15,20 and 30 were examined, with 10,000 replications per condition. Each CI method was evaluated based on coverage probability, average interval width, bias, and root mean squared error (RMSE). The results reveal that classical t-intervals perform adequately only under normality and larger sample sizes but exhibit significant under-coverage and inflated bias under skewed or heavy-tailed distributions. Bootstrap percentile intervals, while simple to implement, fail to correct for bias and skewness. In contrast, the BCa bootstrap method consistently achieved closer-to-nominal coverage and improved accuracy across all conditions. Bayesian credible intervals demonstrated the most robust performance overall, providing reliable coverage, minimal bias, and the lowest RMSE across all distributions and sample sizes. The study concludes that researchers working with small samples should reconsider their reliance on classical CI methods. Bootstrap BCa and Bayesian credible intervals are recommended as more robust alternatives for reliable inference. These findings have important implications for statistical methodology, applied research practice, and the reform of statistical training and reporting standards. Keywords: Confidence Intervals, Small Samples, Bootstrap, Bca, Bayesian Inference, Simulation, Coverage Probability, Interval Estimation.