Nonparametric goodness-of-fit tests for normality testing under rounding-off measurements

Abstract

When analyzing measurement series in various applications, the verification of whether measurement errors belong to the normal law is considered as a mandatory procedure. For this purpose, various special tests for testing hypotheses about normality can be used; non-parametric tests of goodness or chi-square tests can be used. When using nonparametric goodness-of-fit tests to test normality, it must be taken into account that a complex hypothesis is being tested. When testing a complex hypothesis, the distributions of the statistics of the goodness-of-fit tests differ significantly from the classical ones that occur when testing simple hypotheses. It is known that the presence of rounding errors can significantly change the distribution of test statistics. In such situations, ignoring the fact of influence can lead to incorrect conclusions about the results of the normality test. In metrology, when carrying out high-precision measurements, as a rule, scientists do not even allow thoughts about the possible influence of D rounding errors on the results of statistical analysis. This allows the possibility of incorrect conclusions since there is no influence not only at small D, but at values of D much less than the standard deviation s of the measurement error distribution law and sample sizes n not exceeding some maximum values. For sample sizes larger than these maximum values, the real distributions of the test statistics deviate from the asymptotic ones towards larger statistics values. In this work, based on real and well-known data, using statistical modeling methods, we demonstrate the dependence of the distributions of statistics of nonparametric goodness-of-fit tests when testing normality on the ratio of D and s for specific n. The possibility of correct application of the tests under the influence of rounding errors on the conclusions is shown and implemented.