Analysis of Nonparametric and Parametric Criteria for Statistical Hypotheses Testing. Chapter II. Agreement Criteria of Romanovsky, Student and Fisher

Keywords: statistical hypotheses, ‎level of statistical significance, degrees of freedom, critical point, distribution laws, empirical frequency, theoretical frequency, mathematical expectation (average), variance, ‎mean square deviation, gross mistakes, parametric criteria, Romanovsky criterion, Student criterion, Fisher criterion.


Any assumptions or waiting for that or another distribution of random values are statistical hypotheses. The objective knowledge about hypotheses can obtain always using the spatial statistical tests that are named agreement criteria. It’s known about 100 different agreement criteria.

Nonparametric tests don’t include in calculations the parameters of the probability distribution and operates with frequency only. They don’t assume that the experimental data have a specific distribution. Nonparametric criteria are widely used in analysis of the empirical data, in the checking of the hope models, the simple and complex statistical hypotheses and take a prominent place in science and practice.

Parametric tests contain the distribution parameters. They are used for the samples with the normal distribution. Parametric tests permit: 1) to check the statistical hypotheses about the normal distribution characteristics of the population obtained on the base of sample processing; 2) to except the gross errors; 3) to evaluate the difference of the mathematical average values ; 4) and to distinguish the dispersions. That is why these tests are very extensively used in mathematical statistics too.

The paper continues ideas of the author’s works [1; 2] devoted to advanced based tools of the mathematical statistics. The aim of the work is to generalize the well known theoretical and experimental results about the statistical tests of the hypotheses testing. Parametric criteria (Romanovsky, Student, Fisher) are discussed carefully from the uniform point of view. The peculiarities of its using for statistical hypothesis testing are highlighted. The typical tasks are suggested and solved. All this takes an opportunity to cover the main point (essence) of the problem as a whole and evaluate its actuality directly.


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Romanovsky, V. I. (1947). Primenenie matematicheskoi statistiki v opytnom dele [Application of mathematical statistics in the practice of experience]. Моskow-Leningrad: Gostechizdat (in Russian).

Marusina, M. Ya., Tichanovskii, A. B., Tkalich, V. L., Ushakov, O. Yu., & Cherniyev, A. A. Metrologiia. sertifikatsiia i standartizatsiia. Razdel 6.14 Grubye pogreshnosti i kriterii ich otsenki [Metrology, certification and standardization. Part 6.14. Blunders and criteria of their assessment]. Retrieved from (in Russian).

Student’s t-test. Retrieved from (in English).

Student’s t-test: Comparison of two means. Retrieved from (in English).

F-test. Retrieved from (in English).

Polyakova, O.V . (2011). Metody i sposoby povysheniia tochnosti izmerenii [The methods and ways of of the measurement accuracy increase]. Retrieved from (in Russian).

Rudi, D. Yu., Popova, M. V., Petrov, S. I. Grubye pogreshnosti i criterii ich iskluchenia [Blunders and criteria of their exclusion]. Retrieved from (in Russian).

Popukailo, V. S. (2015). Issledovanie kriteriev grubych oshibok primenitelno k vyborkam malogo obyoma [The criterion study of blunders put into practice of a small volume]. Radioelectronni i kompiuterni systemy – Radio electronic and computer systems, 3 (73), 39–44 (in Russian).

Kriterii soglasiia Pirsona, Kolmogorova, Romanovskogo [Pearson, Kolmogorov and Romanovsky coordination criteria]. www. Retrieved from https://www. (in Russian).

Popukailo, V. S. (2016). Obnaruzhenie anomalnych izmerenii pri obrabotke dannych malogo obyoma [Detection of the abnormal measurements in the small volume data processing]. Tekhnologiya i Konstruirovanie v Elektronnoi Apparature – Technology and design in electronic equipment, № 4–5, 42–46 (in Russian).

Kriterii soglasiia Romanovskogo [Romanovsky coordination criterion]. Retrieved from (in Russian).

Zaliazhnych, V. V. Kriterii Romanovskogo. Tablichnye znacheniia [Romanovsky criterion. The table mining]. Retrieved from (in Russian).

Zaliazhnych, V. V. Kriterii Romanovskogo. Laboratornaia rabota № 8. [Romanovskyi criterion. Laboratory work № 8]. Retrieved from (in Russian).

Van der Varden, B. L. (1960). Matematicheskaia statistika [Mathematical Statistics]. Moskow: Izdatelstvo Inostrnnoi Literatury (in Russian).

Matematicheskaia statistika dlya psikhologov. t-kriterii Studenta dlya odnoi vyborki [Mathematical Statistics for Psychologists. Student test for one sample]. Retrieved from (in Russian).

Metody statisticheskoy proverki gipotez o razlichii dannykh eksperimentalnykh grupp. Kriterii t-Studenta dlya odnoy vyborki [Methods for statistical testing of hypotheses about the difference between experimental data. Student test for one sample]. Retrieved from (in Russian).

Matematicheskaia statistika dlya psikhologov. Primer rasscheta t-kriteriia Studenta dlya odnoi vyborki [Mathematical Statistics for Psychologists. The calculation example of the Student test for one sample]. Retrieved from https:/ (in Ukraine).

‎58. T-kriterii. Portal znanii StatSoft [T-test. The StatSof knowledge portal]. Retrieved from (in Russian).

Matematicheskie metody psikhologicheskogo issledovaniia. Parametricheskie metody [Mathematical methods in the psychology. Parametrical methods]. Retrieved from (in Russian).

Nizhegorodtseva, N. V., Mishina, T. V. (Comp.). Metodicheskiye rekomendatsii po napisaniyu i oformleniyu kursovoy i vypusknoy kvalifikatsionnoy raboty po psikhologii i konfliktologii. Razdel 8.5.1. T-kriterii Studenta [Guidelines for writing and design coursework and final qualifying work on psychology and conflictology. Part 8.5.1. Student T-test]. Retrieved from (in Russian).

‎61. Zavisimye i nezavisimye vyborki [Dependent and independent samples]. Retrieved from (in Russian).

Kartashov, M. V. (2008). Imovirnist, protsesy, statystyka [Probability, processes, statistics]. Kyiv: VPTs “Kyivskyi Universytet” (in Ukrainian).

Delei, V. I. Osnovy matematicheskoi statistiki. Tema 2.12. Kriterii Fishera. [Fundamentals of Mathematical Statistics. Chapter 2.12. Fisher test]. Retrieved fromіjj_-Fіs.html (in Ukrainian).

Algoritmika. statistika i teoriya veroyatnostey. Kriterii Fishera [Algorithmics, statistics and probability theory. F-test]. Retrieved from (in Russian).

Kriterii Fishera [Fisher test]. Retrieved from (in Russian).

Marmoza, A. T. (2013). Teoriia statystyky. Rozdil 7.5 Perevirka statystychnych gipotez shcodo rozpodiliv [Theory of Statistics. Part 7.5 The testing of statistical hypothesis about distributions]. Retrieved from (in Ukrainian).

Laboratorne zannyattya № 9. Tema: f-kriterii Fishera (f-distribution). Otsinka riznytsi mizh koefitsiientamy variatsii [Laboratory work № 9. Subject: f-test. Estimation of the difference between coefficients of variation]. Retrieved from (in Russian).

Fundamentals of Statistics. Two-Sample F-Test. Retrieved from (in English).

Kriterii Fishera i kriterii Studenta v ekonometrike [Fisher Criterion and Student test in Econometrics]. Retrieved from (in Russian).

Kriterii soglasia Pirsona [Pearson coordination criterion]. Retrieved from (in Russian).

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How to Cite
Motsnyi, F. V. (2019). Analysis of Nonparametric and Parametric Criteria for Statistical Hypotheses Testing. Chapter II. Agreement Criteria of Romanovsky, Student and Fisher . Statistics of Ukraine, 84(1), 13-23.