Piotr Sulewski
ARTICLE

(Polish) PDF

ABSTRACT

In the statistical literature there are many test measures to study the independence features in the two-way contingency tables. For statistical analysis, the family of six so-called “chi-squared statistic” was selected – including Pearson’s Χ2 statistics – and the proposal of the author in the form of modular statistics. In order to free themselves from the limitations of the applicability of the “chi-squared statisti c”, critical values for all analyzed statistics were determined by simulation methods of Monte Carlo. In order to compare the tests, the measure of untruthfulness of H0 was proposed and calculated the power of the tests which is the ability of two-way contingency tables to reject null hypothesis which says that between features X and Y there is no relation.

KEYWORDS

two-way contingency tables, independence test, critical values, Monte Carlo study

REFERENCES

Cochran W. G., (1954), Some Methods for Strengthening the Common Χ2 Tests, Biometrics, 10, 417–451.

Cressie N., Read T., (1984), Multinomial Goodness-of -Fit Tests, Journal of the Royal Statistical Society, Series B (Methodological), 46 (3), 440–464.

Freeman M. F., Tukey J. W., (1950), Transformations Related to the Angular and the Square root, Annals of Mathematical Statistics, 21, 607–611.

Kullback S., (1959), Information Theory and Statistics, Wiley, New York.

Neyman J., (1949), Contribution to the Theory of the Χ2 Test, Proceedings of the (First) Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, 239–273.

Pearson K., (1900), On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such that It Can be Reasonably Supposed to Have Arisen from Random Sampling, Philosophy Magazine Series, 5 (50), 157–172.

Shier R., (2004), The Chi-squared Test for Two-Way Tables, Mathematics Learning Support Centre.

Sokal R. R., Rohlf F. J., (2012), Biometry: The Principles and Practice of Statistics in Biological Research, Freeman, New York.

Sulewski P., (2013), Modyfikacja testu niezależności, Wiadomości Statystyczne, GUS, 10, 1–19.

Sulewski P., (2014), Statystyczne badanie współzależności cech typu dyskretne kategorie, Akademia Pomorska, Słupsk.

Sulewski P., Motyka R., (2015a), Independence Test. A Comparative Analysis of Its Six Variants, ZN AMW, Gdynia, LVI,1, 37–46.

Sulewski P., (2015b), Ocena zdolności tablic dwudzielczych do wykrywania związku między uporządkowanymi cechami typu jakościowego, Wiadomości Statystyczne, GUS, 5, 1–16.

Sulewski P., (2016), Moc testów niezależności w tablicy dwudzielczej 2 × 2, Wiadomości Statystyczne, GUS, 8.

Yates D., Moore D., McCabe G., (1999), The Practice of Statistics, 1st Ed., New York, W. H. Freeman.

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