Suchergebnisse

Readers of some domestic statistical textbooks and Internet publications related to F test are advised to accomplish the following test scheme: After having sample variances calculated use quotient of greater to smaller of them as the test statistics. Then take 1 quantile of the F distribution as the critical value. This paper identifies this advice to be wrong and gives reason for it: test statistics in question definitely does not follow the F distribution. So, derivation of the proper test statistics named WF as well as the method of calculating WF' s cumulative distribution function is given. Analytical considerations are confirmed by two Monte Carlo experiments. These show that following the advice one makes first type error two times greater than wanted.

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.