<![CDATA[The validity of statistical inference is a key pillar in data-driven decision making, but it is often threatened by the inappropriate selection of methods for non-ideal data. This study aims to evaluate the performance of single-sample hypothesis testing methods by comparing the frequentist paradigm (Student's t-test, Wilcoxon signed-rank test, sign test) and the Bayesian paradigm (Bayes factor). Through Monte Carlo simulations using R Studio with 1,000 iterations, this study investigates statistical power, Type I error rate, and the accuracy of effect size estimates (Cohen's d, Rank-Biserial Correlation, Cohen's g) under Normal, Heavy-tailed (t-Student), and Skewed (Log-normal) distribution conditions with sample variations . The results show that under the t-Student distribution ( ), the Wilcoxon test consistently outperforms the T-test in terms of power (0.514 vs. 0.416 at n ). Another crucial finding is the bias in Cohen's d estimation on Log-normal data, which tends to underestimate the actual impact of location when compared to Rank-Biserial Correlation. The Bayesian approach proved to be more conservative but provided better inference stability in large samples]]>
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