Results of the new test and other considered here tests for normality for two real-world datasets at significance levels of <i>c</i> = 0.01 and <i>c</i> = 0.05.

Tests taken into consideration: the new test proposed in this paper, Jarque-Bera (JB) test [5], D’Agostino-Pearson (DP) test [4], Shapiro-Wilk (SW) test [3], test based on the empirical characteristic function (CF) [22], Kolmogorov-Smirnov (KS) test [2], Kuiper test [6], Watson test [7], Cramer-von Mises (CvM) test [8], Anderson-Darling (AD) test [9] and χ2 goodness-of-fit test [1]. “0” means that the normality is not rejected, “1”—it is rejected. In parentheses values of the test statistic for the new test are presented.