The Role of Data Assumptions in Selecting Between Parametric and Nonparametric Tests

Aims: This study aimed to examine the role of data assumptions particularly normality in determining the appropriate use of parametric and nonparametric statistical tests. Specifically, it compared the robustness, effect size, and performance of the Independent t-test and Mann–Whitney U test, as well as the Paired t-test and Wilcoxon Signed-Rank test, using simulated Likert-scale data under normal and non-normal distributions. Study Design: A quantitative, comparative design was employed to analyze the effects of normality violations on the outcomes and effect sizes of selected parametric and nonparametric tests. Place and Duration of Study: The study was conducted through simulated datasets developed for instructional and comparative statistical analysis purposes in October 2025. Methodology: Simulated Likert-scale data (n = 100) were generated using SPSS under both normal and non-normal distributions. Descriptive statistics and the Shapiro–Wilk test assessed normality. Independent and Paired t-tests were applied to normal data, while Mann–Whitney U and Wilcoxon Signed-Rank tests were used for non-normal data. Effect sizes were computed using Cohen’s d and rank-biserial correlation. Results: Under normal conditions, the Independent t-test produced a larger effect size (d = –3.75) than the Mann–Whitney U test (r = 0.997). In non-normal data, both tests were significant (p = 0.001), but the Mann–Whitney U test remained more stable (r = 0.921). For paired data, the Paired t-test (d = –0.217, p = 0.032) and Wilcoxon test (r = –0.291, p = 0.012) yielded consistent outcomes, though the Wilcoxon test showed greater robustness under non-normality. Conclusion: The study concludes that statistical test selection must be guided by data assumptions. While parametric tests are efficient for normally distributed data, nonparametric methods demonstrate superior robustness when normality is violated. Using inappropriate tests can lead to inflated Type I errors or misleading interpretations. Therefore, researchers are strongly encouraged to assess distributional assumptions prior to analysis and apply proper statistical treatments to ensure validity, reliability, and accuracy in data interpretation.