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In an earlier paper [5] the authors compared the power of the BLUS test with the probability of a correct decision of the Durbin-Watson bounds test. A method to compute the distribution of the Von Neumann ratio under the null hypothesis and under the alternative hypothesis was given. In the present paper the latter method is used to tabulate the BLUS-test statistic and to compute the exact significance points of the Durbin-Watson test for several examples. Powers of both tests are computed and compared. It appears that, for the cases considered, the power of the exact Durbin-Watson test exceeds that of the BLUS procedure, while the latter is greater than the probability of a correct decision in the Durbin-Watson bounds test. [ABSTRACT FROM AUTHOR]

While distribution-free procedures are often appropriate when testing statistical hypotheses, they may become complicated or involve loss of power when the data are grouped. For rank tests the ties caused by grouping are generally broken either by using a randomization procedure or averaging the tied ranks. In this paper the power loss due to equi-spaced grouping (in terms of Pitman asymptotic relative efficiency) is investigated for some commonly used tests, for each method of tie-breaking. The tests considered are Wilcoxon's and Mood's tests for the two-sample problem, Mann's test for randomness, and Pitman's independence test. It is shown how the power loss depends on the width of the grouping intervals and the distribution of the data, and some numerical studies are given. The results seem to indicate that the power loss is small even for a sizable group interval, and that it may be preferable to break ties by randomization than by averaging ranks. [ABSTRACT FROM AUTHOR]

A number of examples which involve restricted alternatives are given; each of these, except one, deals with normal distributions. The examples demonstrate the following: (a) one way to construct a simple test when the alternative hypothesis is restricted, (b) a method by which the additional restrictions can be justified, and (c) a procedure that can be used to defend the original model. An interesting relationship between Bartholomew's chi[sup 2] and a test statistic, which is used in this paper, is pointed out. Finally, a certain distribution-free problem and a solution of it are proposed. [ABSTRACT FROM AUTHOR]

This paper presents theorems which can be used to obtain sufficient and minimal sufficient statistics for the two-way classification mixed model design. Using the general linear hypothesis model Y = X tau + Z beta + e the authors prove that the dimension of a minimal sufficient statistic is a function of the ranks of certain submatrices of Z'X. Minimal sufficient statistics are presented in tabular form for some two-way classification designs and some of the distributional properties are given. [ABSTRACT FROM AUTHOR]