Reference for citation: Vinnik P. М., Vinnik Т. V., Еskova Е. А. Optimal aggregation of clustered sample intervals for applying the χ2 test. Journal of Instrument Engineering. 2024. Vol. 67, N 9. P. 751–758 (in Russian). DOI: 10.17586/0021-3454-202467-9-751-758.

Abstract. The use of intervals of equal length or intervals of equal probability for using the χ2-type criterion is discussed. In this case, intervals of equal probability are predetermined by the distribution law being tested. When forming the initial sample based on real production data, it is often immediately grouped with predetermined and unchangeable grouping boundaries in production and may not satisfy the recommendations for applying χ2-type criteria. A method is proposed for constructing a set of optimal grouping intervals by combining some of the intervals available in the initial sample. An optimal set of such intervals is understood to be a set of intervals that has the least square deviation of weighted frequencies of hits from a discrete uniform distribution, which makes it possible not to change the set of intervals when changing the selected distribution law and to automatically solve the problem of choosing the optimal number of intervals. Some properties of such sets are listed, examples of situations arising during their construction are considered, and an example of forming such an optimal set is given.

Keywords: distribution law, empirical data, χ2 test, grouping intervals, grouped samples, grouping optimality

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