论文信息 - Approximations of the critical region of the fbietkan statistic

Approximations of the critical region of the fbietkan statistic

The Friedman (1937) test for the randomized complete block design is used to test the hypothesis of no treatment effect among k treatments with b blocks. Difficulty in determination of the size of the critical region for this hypothesis is com¬pounded by the facts that (1) the most recent extension of exact tables for the distribution of the test statistic by Odeh (1977) go up only to the case with k6 and b6, and (2) the usual chi-square approximation is grossly inaccurate for most commonly used combinations of (k,b). The purpose of this paper 2 is to compare two new approximations with the usual x2 and F large sample approximations. This work represents an extension to the two-way layout of work done earlier by the authors for the one-way Kruskal-Wallis test statistic.

R. Iman | J. Davenport

[1] M. Friedman. The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance , 1937 .

[2] F. E. Satterthwaite. Synthesis of variance , 1941 .

[3] Satterthwaite Fe. An approximate distribution of estimates of variance components. , 1946 .

[4] D. Owen,et al. Handbook of Statistical Tables. , 1962 .

[5] W. J. Conover,et al. Practical Nonparametric Statistics , 1972 .

[6] Douglas A. Wolfe,et al. Nonparametric Statistical Methods , 1973 .

[7] Ronald L. Iman,et al. Use of a t-statistic as an approximation to the exact distribution of the wildcoxon signed ranks test statistic , 1974 .

[8] Ronald L. Iman,et al. New approximations to the exact distribution of the kruskal-wallis test statistic , 1976 .

[9] Ronald L. Iman. An approximation to the exact distribution of the wilcoxon-mann-whitney rank sum test statistic , 1976 .

[10] R. E. Odeh. Extended tables of the distribution of friedman’ s s-statistic in the two-way layout , 1977 .

[11] D. R. Jensen. On approximating the distributions ofFriedman's 75-175-175-1and related statistics , 1977 .

[12] R. Iman,et al. Approximations of the critical region for spearman’s rho with and without ties present , 1978 .