Errors and Incorrect Procedures When Utilizing χ2 Fitting Criteria

It is shown that the practice of using χ2 criteria is accompanied by errors of two types. Firstly, those associated with the checking of complex hypotheses and with the use of a χ2k–m–1 distribution as the limiting law when estimating the m parameters of the law from point samples. Errors of this type result in an increase in the probability of errors of the first kind. Secondly, those associated with incorrect procedures involving the choice of the number of intervals and the grouping method. It is asserted that the choice of the number of intervals and of the method of dividing the domain of definition into intervals should be made on the basis of the maximum criterion power for the close alternatives.