The impact of uneven filling two-way contingency tables on the critical value of the test statistics

In: Wiadomości statystyczne / Glówny Urza̜d Statystyczny, Polskie Towarzystwo Statystyczne: czasopismo Głównego Urze̜du Statystycznego i Polskiego Towarzystwa = ˜Theœ Polish statistician, Band 61, Heft 4, S. 1-16

Abstract

The article concerns two-way (2×2) contingency tables. When the H0— hypothesis of independence of features is correct, very often — because of the small sample — the distribution of the test statistics differ from the chi-square. Quantile of the chi-square is therefore not a correct critical value. With the current performance of computers, designation of critical value by statistical modeling of Monte Carlo method is not a problem, but a problem is H0 modeling. The H0 modeling is generating such arrays, which feature value assigned rows are independent of the characteristics of the assigned columns. Suitable for such modeling are tables — uniform of the same probability of belonging to cells and uneven having equal probability in all rows of a given column or in all columns of a given row. Analysis of the results of statistical modeling revealed that even when H0 is right, the distribution of the test statistics significantly depends on the uneven array. The article shows that in order to maximize the power of the test should be set critical value, taking into account measures of inequality array. The final result of the study is offered the reader a ready tool for independent verification of the H0 hypothesis.