Normality Test Reconciliation. When one test is significant and the other is not, what is the appropriate and why are they different? This apparent contradiction can be
explained by the differential sensitivities and strengths of these two tests.
The Shapiro-Wilk test is generally considered more powerful and appropriate for sample sizes less than 50. Research has consistently demonstrated that the Shapiro-Wilk test has superior statistical power to detect deviations from normality compared to the Kolmogorov-Smirnov test, particularly in smaller samples (Razali & Wah, 2011). The Kolmogorov-Smirnov test is known to have less sensitivity to deviations in the tails of the distribution and may fail to detect departures from normality that other tests identify.
References for Normality Discussion
Razali, N. M., & Wah, Y. B. (2011). Power comparisons of Shapiro-Wilk, Kolmogorov-
Smirnov, Lilliefors and Anderson-Darling tests. Journal of Statistical Modeling and
Analytics, 2(1), 21-33.
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