Normality testing is a statistical technique that assesses whether a given dataset conforms to a normal distribution, which is a fundamental aspect of evaluating its goodness of fit. It is a crucial hypothesis testing tool and involves the use of various methods such as the Kolmogorov-Smirnov test, Shapiro-Wilk test, and skewness-kurtosis test.

 Many statistical analysis methods require the assumption of normal distribution. If the data fails to meet this assumption, then alternative methods must be used, such as the t-test, correlation analysis, or variance analysis. In correlation analysis, the choice between the Pearson correlation coefficient and the Spearman correlation coefficient depends on whether the data meets the assumption of normality. The former is used when the variables follow a normal distribution, while the latter is used when they do not.

  This statistical analysis approach yields outcomes for both the Kolmogorov-Smirnov and the Shapiro-Wilk tests. The Kolmogorov-Smirnov test should be used for sample sizes that are equal to or greater than 50, while the Shapiro-Wilk test should be used for sample sizes that are less than 50.

References：

• Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: a guide for non-statisticians. International journal of endocrinology and metabolism, 10(2), 486–489.
• 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.
• Yap, B. W., & Sim, C. H. (2011). Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation, 81(12), 2141-2155.