Article 7321

Title of the article

New statistical high power test, obtained by differentiating random data of a small sample 

Authors

Aleksandr I. Ivanov, Doctor of engineering sciences, associate professor, scientific adviser, Penza Scientific Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: ivan@pniei.penza.ru
Aleksandr Yu. Malygin, Doctor of engineering sciences, professor, head of the Intersectoral testing laboratory of biometric devices and technologies, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: mal890@yandex.ru
Svetlana A. Polkovnikova, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: 1996svetlanaserikova@gmail.com 

Index UDK

519.24 

DOI

10.21685/2072-3059-2021-3-7

Abstract

Background. The research considers the problem of statistical analysis of small samples by synthesizing new statistical criteria. Materials and methods. It is proposed to perform the operation of differentiation of random data of a small sample before calculations. Results. The probability of errors of the first and second kind of classical hi-squared criterion with a small sample of 16 experiments is 0.33, which is unacceptable for practice. The new statistical criterion under the same conditions reduces the probability of errors to 0.075, which is already quite acceptable for a number of neural network biometrics applications. Conclusions. It is generally believed that the operation of differentiating random sample data should lead to a significant loss of stability of calculations. This article shows a situation that is an exception to the general rule. The synthesized statistical criterion has a significantly lower probability of errors compared to the classical chi-squared criterion when solving the problem of neural network separation of normal data and data with a uniform distribution. 

Key words

statistical analysis of small samples, testing of the normality hypothesis, xisquare criteria, differentiation of random data of small samples, artificial neurons 

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References

1. Kobzar' A.I. Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov = Applied mathematical statistics. for engineers and scientists. Moscow: Fizmatlit, 2006:816. (In Russ.)
2. R 50.1.037–2002. Rekomendatsii po standartizatsii. Prikladnaya statistika. Pravila proverki soglasiya opytnogo raspredeleniya s teoreticheskim: v 2 ch. Chast' I. Kriterii tipa χ2. Gosstandart Rossii = Recommendations for standardization. Applied statistics. Rules for checking the agreement of the experimental distribution with the theoretical: in 2 chapters. Chapter 1. χ2 criteria. State Standart of the Russian Federation. Moscow, 2001:140. (In Russ.)
3. Ivanov A.I. Iskusstvennye matematicheskie molekuly: povyshenie tochnosti statisticheskikh otsenok na malykh vyborkakh (programmy na yazyke MathCAD): preprint = Artificial mathematical molecules: improving the accuracy of statistical estimates on
small samples (MathCAD programs): preprint. Penza: Izd-vo PGU, 2020:36. (In Russ.)
4. Ivanov A.I., Bannykh A.G., Bezyaev A.V Artificial molecules assembled from artificial neurons that reproduce the work of classical statistical criteria. Vestnik Permskogo universiteta. Seriya: Matematika. Mekhanika. Informatika = Bulletin of Perm University. Series: Mathematics. Mechanics. Informatics. 2020;(1):26–32. (In Russ.)
5. Ivanov A.I., Bannykh A.G., Kupriyanov E.N. [et al.]. A collection of artificial neurons equivalent to statistical criteria for their combined use in testing the hypothesis of normality of small samples of biometric data. Bezopasnost' informatsionnykh tekhnologiy: sb. nauch. st. po materialam I Vseros. nauch.-tekhn. konf. = Information technology security: proceedings of the 1st All-Russian scientific and engineering conference. Penza, 2019:156–164. (In Russ.)
6. Bezyaev A.V. Biometriko-neyrosetevaya autentifikatsiya: obnaruzhenie i ispravlenie oshibok v dlinnykh kodakh bez nakladnykh raskhodov na izbytochnost': preprint = Biometrical neural network authentication: detecting and correcting errors in long codes without the overhead of redundancy: preprint. Penza: Izd-vo PGU, 2020:40. (In Russ.)
7. Lukin V.S. Comparison of the power of ordinary and logarithmic forms of statistical tests of the harmonic mean when used to test the hypothesis of normal distribution of small sample data. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University proceedings. Volga region. Engineering sciences. 2020;(4):19–26. (In Russ.)
8. Ivanov A.I., Perfilov K.A, Lukin V.S. Neural network generalization of a family of statistical criteria for geometric mean and harmonic mean for precision analysis of small samples of biometric data. Informatsionno-upravlyayushchie telekommunikatsionnye sistemy, sredstva porazheniya i ikh tekhnicheskoe obespechenie: sb. nauch. st. Vseross. nauch.-tekhn. konf. = Information and control telecommunication systems, weapons and their technical support: proceedings of the All-Russian scientific and engineering conference. Penza: NPP «Rubin», 2019:50–63. (In Russ.)
9. Ivanov A.I., Perfilov K.A., Malygina E.A. Evaluation of the quality of small samples of biometric data using the differential version of the statistical criterion of the geometric mean. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta = Bulletin of Siberian State Aerospace University. 2016;(4):864–871. (In Russ.)

 

Дата создания: 09.12.2021 08:48
Дата обновления: 09.12.2021 09:41