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Two k-sample versions of an Anderson-Darling rank statistic are proposed for testing the homogeneity of samples. Their asymptotic null distributions are derived for the continuous as well as the discrete case. In the continuous case the asymptotic distributions coincide with the (k - 1)-fold convolution of the asymptotic distribution for the Anderson-Darling one-sample statistic. The quality of this large sample approximation is investigated for small samples through Monte Carlo simulation. This is done for both versions of the statistic under various degrees of data rounding and sample size imbalances. Tables for carrying out these tests are provided, and their usage in combining independent one- or k-sample Anderson-Darling tests is pointed out. The test statistics are essentially based on a doubly weighted sum of integrated squared differences between the empirical distribution functions of the individual samples and that of the pooled sample. One weighting adjusts for the possibly different sample sizes, and the other is inside the integration placing more weight on tail differences of the compared distributions. The two versions differ mainly in the definition of the empirical distribution function. These tests are consistent against all alternatives. The use of these tests is two-fold: (a) in a one-way analysis of variance to establish differences in the sampled populations without making any restrictive parametric assumptions or (b) to justify the pooling of separate samples for increased sample size and power in further analyses. Exact finite sample mean and variance formulas for one of the two statistics are derived in the continuous case. It appears that the asymptotic standardized percentiles serve well as approximate critical points of the appropriately standardized statistics for individual sample sizes as low as 5. The application of the tests... [ABSTRACT FROM AUTHOR]

Large-sample covariance matrices for the analysis of variance (ANOVA), minimum norm quadratic unbiased estimator (MINQUE), restricted maximum likelihood (REML), and maximum likelihood (ML) estimates of variance components are presented for the unbalanced one-way model when the underlying distributions are not necessarily normal. The limiting variances depend on the design sequence, on the actual values of the variance components, and on the kurtosis parameters of the underlying distributions. (The skewness parameters and other moments do not affect the limiting distributions.) Because all estimates are consistent and asymptotically normal, it is reasonable to compare the estimates using their asymptotic variances. Thus the efficiency of one estimate relative to another is defined as the ratio of their asymptotic variances, and these efficiencies are evaluated numerically and analytically for a variety of nonnormal situations. Various authors, including Hocking and Kutner (1975), Corbeil and Searle (1976), and Swallow and Monahan (1984), have compared the variances and/or mean squared errors of variance component estimates in a variety of finite-sample models assuming normally distributed effects. The purpose of this article is to extend this line of research to incorporate nonnormal distributions and large samples. Some special cases of MINQUE considered in this article are called MINQUE(0), MINOUE(1), MINOUE(Infinity), and MIVQUE (minimum variance quadratic unbiased estimator); these are defined by setting the a priori variance ratio to 0, 1, infinity (in a sense to be explained), and to the actual variance ratio, respectively. Because the actual variance ratio is usually unknown, the MIVQUE estimates cannot be computed for unbalanced designs. (In balanced designs MIVQUE and ANOVA correspond.) It turns out, however, that ML... [ABSTRACT FROM AUTHOR]