It's shown that the practice of χ{sup}2-criterion usage is accompanied by two types of mistakes: firstly concerned with composite hypothesis testing in the case when m distribution parameters are estimated from point samples and the (χ{sub}(k-m-1){sup}2 distribution law is used as the limit distribution, such errors result in the increase of alpha-error probability; secondly concerned with wrong procedures of a grouping method and the choice of a number of intervals. It is asserted that the number of intervals choice and of the method for dividing the domain to the intervals should be chosen from the position of maximal criterion power for the close alternative hypotheses.
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