Hypothesis testing plays a critical role in statistical inference, but its reliability can be significantly compromised when the underlying statistical model is misspecified. Model misspecification arises when the assumptions made about the data generation process do not align with the true nature of the data. This study investigates the comparative performance of five hypothesis testing approaches—Ordinary Least Squares (OLS), Bootstrap, Empirical Likelihood (EL), Gradient Statistic, and Robust Standard Errors (Robust SE)—under conditions of model misspecification across varying sample sizes (n = 20, 50, 100, 500, 1000). The evaluation was based on model selection criteria, specifically Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), to assess model fit and efficiency. Results reveal that the Gradient Statistic consistently produced the lowest AIC and BIC values across all sample sizes, demonstrating superior robustness and sensitivity to model misspecification. The Bootstrap method followed closely, with improved performance as sample size increased, due to its nonparametric and resampling-based nature. In contrast, OLS, EL, and Robust SE methods exhibited static performance across sample sizes, indicating limited adaptability under mis-specified models. The findings highlight the Gradient Statistic as the most effective approach for hypothesis testing in the presence of model uncertainty, followed by the Bootstrap technique. Based on these results, it is recommended that researchers prioritize the use of Gradient and Bootstrap methods when model assumptions are questionable, and rely less on traditional methods such as OLS, EL, and Robust SE under such conditions. The study underscores the importance of employing robust and adaptive statistical techniques to improve inference reliability, particularly in empirical research involving complex or uncertain model specifications.

Keywords: Hypothesis testing, Model misspecification, Gradient statistic, Bootstrap method, Empirical likelihood, Ordinary Least Squares (OLS), Robust Standard Error