POWER INCREASE OF THE CHI-SQUARE TEST AT A TENFOLD INCREASE
IN THE NUMBER OF DEGREES FREEDOM IN STATISTICAL CALCULATIONS ON SMALL TEST SAMPLES  

Ivanov Aleksandr Ivanovich, doctor of technical sciences, associate professor, head of laboratory of biometric and neural-network technologies, Penza Research Electrotechnical Institute (440000, 9 Sovetskaya street, Penza, Russia), ivan@pniei.penza.ru
Akhmetov Berik Bakhytzhanovich, candidate of technical sciences, professor, vice president of International Kazakh-Turkish University named after A. Yasavi (29 B. Sattarhanov street, Turkestan, Kazakhstan), berik.akhmetov@ayu.edu.kz
Serikova Yuliya Igorevna, master degree student, Penza State University (440026, 40 Krasnaya street, Penza, Russia), julia-ska@yandex.ru

519.24; 57.017

10.21685/2307-4205-2016-4-17

Background. Statistical processing of real data of chemistry, economics, biometrics, medicine is usually necessary to use the limited test samples. The aim of this work is to increase the power of the chi-square test due to an artificial increase in the number of degrees of freedom in statistical calculations.
Materials and methods. It is proposed to increase by 10 times the number of histogram intervals, which leads to the emergence of a large number of empty slots. Empty slots are filled with a linear smoothing filter with a rectangular window averaging without phase distortion. The width of the smoothing filter window is selected to be 9 counts.
Results and conclusions. It is shown that an artificial increase in the number of degrees of freedom at Pearson leads to the growth of its power. Estimations criterion for increasing the power of 5, 6, ...., 30 in a test sample examples. Power criteria is assessed as negative logarithm of the equally probable errors of the first and second kind in the normal and uniform distribution of the test data. A decrease in the probability of error of up to 20 times on a sample of 30 examples by implementing proposed in statistical processing algorithm.

Key words

chi-squared test, a small sample, the artificial increase in the number of degrees of freedom