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Errors and Incorrect Procedures When Utilizing χ2 Fitting Criteria

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Measurement Techniques Aims and scope

Abstract

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 χ2 k–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.

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REFERENCES

  1. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, Vol. 2: Inference and Relationship, 3rd. ed., Griffin, London (1973).

    Google Scholar 

  2. G. Kramer, Mathematical Methods of Statistics, Princeton University Press, Princeton, NJ (1946).

    Google Scholar 

  3. M. W. Birch, Ann. Math. Statist., 35, 817 (1964).

    Google Scholar 

  4. A. E. Sapkhan and B. G. Grinberg, Introduction to the Theory of Ordered Statistics [in Russian], Statistika, Moscow (1970).

    Google Scholar 

  5. B. Yu. Lemeshko, Abstracts of Papers Presented at the Third Intern. Scientific and Technical Conf. on Topical Problems of Electronic Instrumentation APÉP-96, Vol. 6, Part 1 [in Russian], Novosibirsk (1996), p. 37.

    Google Scholar 

  6. B. Yu. Lemeshko, Statistical Analysis of One-Dimensional Observations of Random Quantities: Software System [in Russian], State Technical University, Novosibirsk (1995).

    Google Scholar 

  7. B. Yu. Lemeshko and S. N. Postovalov, Proceedings of Intern. Scientific and Technical Conf. on Information Science and Problems of Telecommunications [in Russian], Novosibirsk (1998), p. 98.

  8. B. Yu. Lemeshko and S. N. Postovalov, Proceedings of Intern. Scientific and Technical Conf. on Information Science and Problems of Telecommunications [in Russian], Novosibirsk (1998), p. 80.

  9. S. N. R. Rao, Linear Statistical Interference and Its Applications, Wiley, New York (1973).

    Google Scholar 

  10. B. Yu. Lemeshko and S. N. Postovalov, Zavod. Laborat., 64, No. 5, 56 (1998).

    Google Scholar 

  11. V. I. Denisov, B. Yu. Lemeshko, and E. B. Tsoi, Optimal Grouping, Parameter Estimation, and Planning of Regression Experiments [in Russian], State Technical University, Novosibirsk (1993).

    Google Scholar 

  12. B. Yu. Lemeshko, Nadezh. Kontrol. Kachestv., No. 8, 3 (1997).

  13. B. Yu. Lemeshko, Zavod. Laborat., 64, No. 1, 56 (1998).

    Google Scholar 

  14. B. P. Levin, Theory of the Reliability of Electronic Systems (Mathematical Fundamentals) [in Russian], Sovetskoe Radio, Moscow (1978).

    Google Scholar 

  15. N. Sh. Kremer, Probability Theory and Mathematical Statistics [in Russian], Yuniti, Moscow (2000).

    Google Scholar 

  16. P. V. Novitskii and I. A. Zograf, Estimating the Errors of Results of Measurements [in Russian], Énergoatomizdat, Leningrad (1991).

    Google Scholar 

  17. M. S. Nikulin, Teor. Veroyat. Primen., XVIII, No. 3, 675 (1973).

    Google Scholar 

  18. M. S. Nikulin, Teor. Veroyat. Primen., XVIII, No. 3, 583 (1973).

    Google Scholar 

  19. M. Mirvaliev and M. S. Nikulin, Zavod. Laborat., 58, No. 3, 52 (1992).

    Google Scholar 

  20. N. Aguirre and M. Nikulin, Kybernetika, 30, No. 3, 214 (1994).

    Google Scholar 

  21. B. Yu. Lemeshko, S. N. Postovalov, and E. V. Chimitova, Zavod. Laborat. Diagnostika Materialov, 67, No. 3, 52 (2001).

    Google Scholar 

  22. V. I. Denisov and B. Yu. Lemeshko, Measurement Information Systems [in Russian], Novosibirsk (1979), p. 5.

  23. V. I. Denisov, B. Yu. Lemeshko, and S. N. Postovalov, Applied Statistics. Rules for Checking the Fitting of a Test Distribution to a Theoretical Distribution. Systematic Recommendations, Ch. 1, X2 Criteria [in Russian], State Technical University, Novosibirsk (1998).

    Google Scholar 

  24. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, Vol. 2: Inference and Relationship, 3rd. ed., Griffin, London (1973).

    Google Scholar 

  25. D. M. Chibisov and L. G. Gvantseladze, Third Soviet-Japanese Symp. on Probability Theory [in Russian], Fan, Tashkent (1975), p. 183.

    Google Scholar 

  26. A. A. Borovkov, Teor. Veroyat. Primen., XXII, No. 2, 375 (1977).

    Google Scholar 

  27. B. Yu. Lemeshko and E. V. Chimitova, Papers of Siberian Division of Academy of Sciences Higher School [in Russian], Novosibirsk (2000), No. 2, p. 53.

  28. L. N. Bol'shev and N. V. Smirnov, Mathematical Statistical Tables [in Russian], Nauka, Moscow (1983).

    Google Scholar 

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Authors
  1. B. Yu. Lemeshko
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  2. E. V. Chimitova
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Lemeshko, B.Y., Chimitova, E.V. Errors and Incorrect Procedures When Utilizing χ2 Fitting Criteria. Measurement Techniques 45, 572–581 (2002). https://doi.org/10.1023/A:1020118902949

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