  In this paper, we treat the problem of testing for normality as a binary
classification problem and construct a feedforward neural network that can
successfully detect normal distributions by inspecting small samples from them.
The numerical experiments conducted on small samples with no more than 100
elements indicated that the neural network which we trained was more accurate
and far more powerful than the most frequently used and most powerful standard
tests of normality: Shapiro-Wilk, Anderson-Darling, Lilliefors and
Jarque-Berra, as well as the kernel tests of goodness-of-fit. The neural
network had the AUROC score of almost 1, which corresponds to the perfect
binary classifier. Additionally, the network's accuracy was higher than 96% on
a set of larger samples with 250-1000 elements. Since the normality of data is
an assumption of numerous techniques for analysis and inference, the neural
network constructed in this study has a very high potential for use in everyday
practice of statistics, data analysis and machine learning in both science and
industry.
