On simulation powers of new normality tests

Empirical study of powers in % of the Shapiro–Wilk test W and the new tests $T$ based on the characterization of probability distributions is presented using in simulations $100\,000$ replications and sample sizes $n=10,15,20,30,50,70$. Our tests compare favorably with the Shapiro–Wilk test and other recommended omnibus tests. The presented test statistics have a simple form and are free of restrictions required by many classical and recommended tests.