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Following the results of Bhat and Nagnur [2], the locally asymptotically most stringent test of the hypothesis of no preference in paired comparison experiments is derived for the models of Rao and Kupper [9] and Davidson [3]. It is shown that the asymptotic relative efficiency of these tests when compared to the test based on the likelihood ratio statistic is unity. [ABSTRACT FROM AUTHOR]

Cochran's Q-test, proposed to test the equality of three proportions for correlated observations, may have a larger asymptotic significance level than the nominal one, unless the admissible family of distributions is restricted to ensure that under the hypothesis the correlations between the observations are also equal. For a large class of such restricted families, optimal C[sup 2](alpha) tests of the hypothesis are obtained, and the family for which the Q-test is an optimal C[sub 2](alpha) test is identified. The use of Q for testing a related hypothesis, suggested by Madansky, is also discussed: it is shown that the Q-test is not consistent against all alternatives to Madansky's hypothesis, while the classical chi[sup 2]-test provides an optimal C[sub 4](alpha) test for it. [ABSTRACT FROM AUTHOR]

Two methods, one based upon grouping, are proposed for fitting o regression line to bivariate data when the means of the observations have known order along the line. The two procedures are compared with respect to their limiting distributions and asymptotic efficiency. Criteria are given for choosing one of these procedures to fit the line. [ABSTRACT FROM AUTHOR]

A measure of variation for categorical data is discussed. We develop an analysis of variance for a one-way table, where the response variable is categorical. The data can be viewed alternatively as falling in a two-dimensional contingency table with one margin fixed. Components of variation are derived, and their properties are investigated under a common multinomial model. Using these components~ we propose a measure of the variation in the response variable explained by the grouping variable. A test statistic is constructed on the basis of these properties, and its asymptotic behavior under the null hypothesis of independence is studied. Empirical sampling results confirming the asymptotic behavior and investigating power are included. [ABSTRACT FROM AUTHOR]

Cronholm and Revusky [4] have proposed a rank test based on independent subexperiments for the comparison of a treatment effect with a control when the treatment is destructive but the control produces at most a transient effect. This article provides a thorough study of its performance under two sampling situations. With the aid of a computer, the exact small sample power of the test is evaluated for some important alternatives. A modification of the test is proposed for the situation where numerical measurements are available rather than merely the ranks within each stage. The modification is found to substantially improve the power. Both tests are shown to be unbiased. Finally, the Pitman asymptotic efficiencies are obtained and comparisons are made with the appropriate Wilcoxon tests. [ABSTRACT FROM AUTHOR]

A simple derivation of asymptotic efficiency for the two sample Kolmogorov-Smirnov statistic is given and evaluated for normal location and normal scale alternatives. Using equal samples to simplify the derivation, the limiting efficiency is obtained by letting the type I error go to zero while the type II error goes to beta, 0 < beta < 1. For unimodal symmetric location alternatives, the efficiency is the same as that obtained for the Mood and Brown median test. Limits of relative efficiencies for alternatives which approach the null hypothesis are 2/pi for normal location alternatives and (pi e)[sup -1] for normal scale alternatives. [ABSTRACT FROM AUTHOR]

This paper deals with the asymptotic relative efficiency (A.R.E.) and the asymptotic power of certain tests. These tests are distribution-free goodness-of-fit tests based on the empirical distribution function. They are the one and two sided Kolmogorov-Smirnov tests and a new one based on the absolute values of the order statistics. The method of obtaining the A.R.E. is due to Quade [5] and is outlined in Section 1. In this paper we are concerned with the case of scalar alternatives. The asymptotic power for the Kolmogorov-Smirnov tests is obtained in Section 2. Section 3 deals with a new test which allows a more facile use of a one-sided statistic while utilizing the same information normally included in a two-sided statistic. In Section 4, three examples are considered to illustrate the superiority of this new test. [ABSTRACT FROM AUTHOR]

The article focuses on comments given by the author on topics related to 2 X 2 contingency tables. As statistician William J. Conover points out in his article, the evidence he presents against Yates' "correction" is not very convincing. Therefore, the controversy seems likely to continue. The dilemma seems to arise from the contrast between the evidence accrued from two lines of inquiry. The first is directed to the question of whether the correction tends to make the sampling distribution of the test statistic in the null case more consistent with the theoretical model for the distribution so as to secure a more nearly correct level for the test. The second line of inquiry focuses on the question of whether the p-values from the corrected statistic tend to agree better with the corresponding "exact" p-values. Generally speaking, evidence from the first line of inquiry is against Yates' correction, whereas the correction tends to improve the agreement between the asymptotic and exact p-values. This incongruence is particularly confusing when the two approaches to the evaluation are regarded as interchangeable.

The asymptotic efficiency of a simple group rank test is examined in the case of testing that the location parameter of a symmetric distribution is zero against the alternative it is positive. Asymptotic optimality is shown subject to a condition on the density function. Efficiencies in relation to the sample mean and the sign test are found in several cases. [ABSTRACT FROM AUTHOR]