Effect of the Roundoff on the Properties of Criteria for Testing Statistical Hypotheses

The results of numerical studies of the effect of roundoff errors on the distribution of test statistics of statistical hypotheses are presented. The effect of the roundoff on the distribution of statistics of different goodness-of-fit and homogeneity tests is investigated. It is shown that, when the roundoff errors in the analyzed samples are comparable with the standard deviation of the measurement errors, the distribution of test statistics may vary significantly. Under such conditions the application of a test in the systems of data processing using the classical results may lead to false conclusions. The recommendations for resolving this issue are proposed.