Tests for normality of the probabilistic distribution when data are rounded

Tests for normality are less sensitive to the data rounding than, for example, tests for exponentiality but among normality tests, the sensitivity is very different. In this paper, the authors find out which tests are more and which ones are less sensitive. The authors show that tests based on sample moments are much more robust with respect to the data rounding than tests based on order statistics (in contrast to the robustness with respect to outliers where order statistics are more robust than sample moments). This, however, only applies to the probability of Type I error. The probability of Type II error is very insensitive to the data rounding for all normality tests.