<![CDATA[A Conventional statistical inference often relies solely on the use of p-values, thereby overlooking the practical significance of results, particularly in categorical data analysis, where the reporting of effect sizes is frequently neglected. This study aims to evaluate the application of proportion hypothesis tests in five scenarios (one Population to k dependent and independent populations) by integrating manual calculations, effect size estimates, and post-hoc tests. The research method involved deconstructing the Z, McNemar, Chi-Square, and Cochran's Q test formulas, which were compared with effect metrics including Cohen's g, Cohen's h, Cramer's V, and Serlin's . The results of the analysis reveal an apparent discrepancy between statistical and practical significance. In the one-population test, statistically significant results (p < 0.05) turned out to have a negligible effect (Cohen's g = 0.12), whereas in the Cochran's Q test, the threshold p-value (p = 0.0497) was reinforced by a substantial effect size (Serlin's R² = 0.30). This study concludes that integrating omnibus tests with post-hoc procedures (such as Marascuilo and Pairwise McNemar) and reporting effect sizes is imperative to avoid misleading binary interpretations and enhance the validity of scientific conclusions. The main contribution of this paper is providing a consolidated, practical framework for researchers to transition into the "New Statistics" paradigm when dealing with diverse categorical data structures.]]>
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