Null hypothesis (H0): The samples follow a normal distribution.
Power comparison [?] :
Shapiro-Wilk: The best of the three methods, especially for samples of less than 30 elements.
D'Agostino-Pearson: It's less powerful than Shapiro-Wilk.
Kolmogorov-Smirnov: The less powerful.
Shapiro-Wilk: Shapiro, S. S. and Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591–611.
D'Agostino-Pearson: D’Agostino, R. B. and Pearson, E. S. (1973). Tests of departure from normality. Empirical results for the distribution of b2 and b1 . Biometrika, 60, 613–622.
Kolmogorov-Smirnov: Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione. Giorn dell’Inst. Ital. degli. Att., 4, 89–91.