DISTRIBUTION OF STATISTICS IN HYPOTHESES TESTING
[For the English abstract and full text of the article please see the attached PDF-File (English version follows Russian version)]. ABSTRACT The article considers the influence of the form of laws of distribution of single observations on quantile of statistics used for statistical hypotheses testing and having chi-square distribution of or Fisher distribution with the normal distribution of individual observations. Through mathematical modeling on the example of four options it is shown that difference of the distribution law as compared to normal law results in a significant change in the value of quantiles. This is equivalent to an unjustified change in the level of significance in the choice of a decision rule. Keywords: mathematical statistics, distribution law, quantiles, statistical hypothesis, statistical modeling. REFERENCES 1. Kramer, G. Mathematical Methods of Statistics [Matematicheskie metody statistiki]. Moscow, Mir publ., 1975, 648 p. 2. GOST R ISO 17123-1-2011 GSI. Optics and opti­cal instruments. Methods of field trials of geodetic and topographical instruments. Part 1: Theory [State standard GOST R ISO 17123-1-2011 GSI. Optika i opticheskie pri­bory. Metodiki polevyh ispytanij geodezicheskih i topogra­ficheskih priborov. Chast’ 1. Teorija]. 3. GOST 50779.21-2004. Rules for determination and methods of calculating the statistical characteristics of sample data. Part 1. Normal distribution [State standard GOST 50779.21-2004. Pravila opredelenija i metody rasch­jota statisticheskih harakteristik po vyborochnym dannym. Chast’ 1. Normal’noe raspredelenie]. 4. Rubichev, N.A., Ryabtsev, G.G. Standard errors of applying statistical methods for processing of measurement information and workarounds [Tipovye oshibki primen­enija statisticheskih metodov obrabotki izmeritel’noj infor­macii i sposoby ih ustranenija]. Metrologija, 2012, Iss. 6, pp. 3-16. 5. Rubichev, N.A., Seydakhmetov N.B. Confidence limits of measurement results. World of Transport and Transportation, 2014, Vol.12, Iss.5, pp. 38-51.