Using the inverse Pearson’s chi-square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample data
Background. The study considers the issue of analyzing small samples by synthesizing new statistical tests generated by combining the classical statistical chi-square Pearson test and other well-known statistical tests. Methods. It is proposed to perform the inversion of the chi-square test by sh...
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| Format: | Article |
| Language: | English |
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Penza State University Publishing House
2023-10-01
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| Series: | Известия высших учебных заведений. Поволжский регион:Технические науки |
| Subjects: |
| _version_ | 1797667831888740352 |
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| author | A.I. Ivanov A.P. Ivanov E.N. Kupriyanov |
| author_facet | A.I. Ivanov A.P. Ivanov E.N. Kupriyanov |
| author_sort | A.I. Ivanov |
| collection | DOAJ |
| description | Background. The study considers the issue of analyzing small samples by synthesizing
new statistical tests generated by combining the classical statistical chi-square
Pearson test and other well-known statistical tests. Methods. It is proposed to perform the
inversion of the chi-square test by shifting it, scaling and dividing one by its final result. It
is proposed to obtain new statistical criteria by multiplying the inverse Pearson’s chi-square
test by the results of convolutions of small samples according to such classical criteria as
the Smirnov-Cramer-von Mises test and the Anderson-Darling test. Results and conclusions.
For the product of the inverse chi-square test and the Smirnov-Kramer-von Mises
test, it is possible to reduce the probabilities of errors of the first and second kind by more
than 1.45 times. By analogy with the chi-square test, inverse statistical tests can be obtained
for any currently known statistical tests for testing the hypothesis of normality of small
samples, which opens up the possibility of obtaining many new statistical tests by their
multiplicative combination in pairs, triplets and other groups. |
| first_indexed | 2024-03-11T20:20:16Z |
| format | Article |
| id | doaj.art-46e0f62d00bb431ebed2104368524077 |
| institution | Directory Open Access Journal |
| issn | 2072-3059 |
| language | English |
| last_indexed | 2024-03-11T20:20:16Z |
| publishDate | 2023-10-01 |
| publisher | Penza State University Publishing House |
| record_format | Article |
| series | Известия высших учебных заведений. Поволжский регион:Технические науки |
| spelling | doaj.art-46e0f62d00bb431ebed21043685240772023-10-03T07:15:45ZengPenza State University Publishing HouseИзвестия высших учебных заведений. Поволжский регион:Технические науки2072-30592023-10-01210.21685/2072-3059-2023-2-2Using the inverse Pearson’s chi-square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample dataA.I. Ivanov0A.P. Ivanov1E.N. Kupriyanov2Penza Scientific Research Electrotechnical InstitutePenza State UniversityPenza State UniversityBackground. The study considers the issue of analyzing small samples by synthesizing new statistical tests generated by combining the classical statistical chi-square Pearson test and other well-known statistical tests. Methods. It is proposed to perform the inversion of the chi-square test by shifting it, scaling and dividing one by its final result. It is proposed to obtain new statistical criteria by multiplying the inverse Pearson’s chi-square test by the results of convolutions of small samples according to such classical criteria as the Smirnov-Cramer-von Mises test and the Anderson-Darling test. Results and conclusions. For the product of the inverse chi-square test and the Smirnov-Kramer-von Mises test, it is possible to reduce the probabilities of errors of the first and second kind by more than 1.45 times. By analogy with the chi-square test, inverse statistical tests can be obtained for any currently known statistical tests for testing the hypothesis of normality of small samples, which opens up the possibility of obtaining many new statistical tests by their multiplicative combination in pairs, triplets and other groups.statistical analysis of small samplestesting of the hypothesis of normalitypearson’s chi-square testsmirnov-kramer-von mises testanderson-darling test |
| spellingShingle | A.I. Ivanov A.P. Ivanov E.N. Kupriyanov Using the inverse Pearson’s chi-square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample data Известия высших учебных заведений. Поволжский регион:Технические науки statistical analysis of small samples testing of the hypothesis of normality pearson’s chi-square test smirnov-kramer-von mises test anderson-darling test |
| title | Using the inverse Pearson’s chi-square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample data |
| title_full | Using the inverse Pearson’s chi-square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample data |
| title_fullStr | Using the inverse Pearson’s chi-square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample data |
| title_full_unstemmed | Using the inverse Pearson’s chi-square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample data |
| title_short | Using the inverse Pearson’s chi-square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample data |
| title_sort | using the inverse pearson s chi square test in the multiplicative synthesis of new statistical tests from already known tests to test the hypothesis of normal distribution of small sample data |
| topic | statistical analysis of small samples testing of the hypothesis of normality pearson’s chi-square test smirnov-kramer-von mises test anderson-darling test |
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