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Ranked-set samples have been shown to lead to improved methods of estimation in parametric settings under specific distributional forms when actual measurement of the sample observations is difficult but ranking them is relatively easy. The earliest work with ranked-set data concentrated on estimating a population mean or variance. More recently, a ranked-set sample estimator of a cumulative distribution function was developed and used to obtain a simultaneous confidence interval for the function. In this article, we take the next logical step and use this ranked-set empirical distribution function to construct distribution-free competitors to the standard Mann-Whitney-Wilcoxon estimation and testing procedures. The appropriate null distribution tables for the associated test are presented for the case of perfect ranking. Asymptotic relative efficiency comparisons between the simple random sample Mann-Whitney-Wilcoxon procedures and their ranked-set analogues are discussed, and the results of a small-sample Monte Carlo simulation study of the same arc presented. [ABSTRACT FROM AUTHOR]

The BC[sub a] bootstrap procedure (Efron 1987) for constructing parametric and nonparametric confidence intervals is considered. Like the bootstrap, this procedure can be applied to complicated problems in a wide range of situations. For models indexed by a scalar parameter theta with efficient estimator theta, the BC[sub a] procedure relies on the existence of a transformation g(.) such that g(O) is approximately normally distributed with standard deviation 1 + ag(theta), although explicit knowledge of g(.) is not required. In this article, we show how to construct this transformation by generalizing the one given by Efron (1987, sec. 10) for translation families. This construction consists of the composition of a variance-stabilizing transformation and a skewness-reducing transformation. It produces a new interval, the BC[sup 0, sub a] interval, that is asymptotically equivalent to the BC[sub a] interval and can be computed without bootstrap sampling. We also derive from this construction an accurate approximation to the bootstrap distribution of theta that also does not require bootstrap sampling. Both the new interval and the approximation require only n + 2 evaluations of the statistic. Like the BC[sub a] procedure, the BC[sup 0, sub a] interval can be extended to multiparameter and nonparametric problems. As an example, we compute the BC[sup 0, sub a] interval for Cox's partial likelihood estimator, a complicated statistic that is obtained by iterative solution of a score equation. [ABSTRACT FROM AUTHOR]

For samples of equal size, the p values of Bartlett's, Cochran's, and Hartley's tests for the equality of several variances, obtained under the normality assumption, are shown to underestimate the true p values when the parent distribution is a normal or a chi[sup 2] scale mixture or when there is within-sample dependence. The proof uses elements of majorization theory. When the sample sizes are not equal, a partial extension is obtained for the two-sample case. [ABSTRACT FROM AUTHOR]

Smith (1936) suggested a method that can be used for setting confidence limits on linear combinations of variances. This method was studied and expanded by Satterthwaite (1941, 1946) and has become known as Satterthwaite's procedure. The procedure has been widely used for the past 40 years. In this article a new procedure is proposed for this problem that is better than Satterthwaite's procedure and very easy to compute from existing tables. [ABSTRACT FROM AUTHOR]

Permutation tests are applied to the maximal t statistic in two- sample, completely randomized designs, and in two-sample, matched- pair designs, where the response is a vector and the experimenter is interested in one specific direction in each component. Recommendations for subsampling are also included for cases when the number of permutations required to complete the test is prohibitive. These procedures are then applied to data from two medical trials. [ABSTRACT FROM AUTHOR]

This article deals with the behavior of some tests of significance in sampling from a mixture of two normal populations. Three particular cases are considered: (i) one-sample t-test; (ii) analysis-of-variance test for the equality of two or more means and (iii) analysis-of-variance test for the regression coefficient being zero. The assessment is based on the actual value alpha (level of significance) when the nominal is .05. [ABSTRACT FROM AUTHOR]

Consider sampling in two stages for testing a simple hypothesis about a population whose elements may be classified into a finite number of classes. The joint asymptotic distribution of the two Pearson chi[sup 2] statistics based on the first and combined samples is derived and used to construct a two-stage test. The advantage of this test relative to the conventional one-stage test is discussed in terms of its asymptotic power. Tables of critical values for 1 percent and 5 percent level tests for 1-10 degrees of freedom ore given as well as modifications for cases involving unknown parameters. [ABSTRACT FROM AUTHOR]

Results are given of an empirical sampling study of the sensitivities of nine statistical procedures for evaluating the normality of a complete sample. The nine statistics are W (Shapiro and Wilk, 1965), square root of b[sub I] (standard third moment), b[sub 2] (standard fourth moment), KS (Kolmogorov-Smirnov), CM (Cramer-Ven Mises), WCM (weighted CM), D (modified KS), CS (chi-squared) and u (Studentized range). Forty-five alternative distributions in twelve families and five sample sizes were studied. Results are included on the comparison of the statistical procedures in relation to groupings of the alternative distributions, on means and variances of the statistics under the various alternatives, on dependence of sensitivities on sample size, on approach to normality as measured by the W statistic within some classes of distribution, and on the effect of misspecification of parameters on the performance of the simple hypothesis test statistics. The general findings include: (I) The W statistic provides a generally superior omnibus measure of non-normality; (ii) the distance tests (KS, CM, WCM, D) are typically very insensitive; (iii) the u statistic is excellent against symmetric, especially short-tailed, distributions but has virtually no sensitivity to asymmetry; (iv) a combination of both square root of b[sub 1] and b[sub 2] usually provides a sensitive judgment but even their combined performance is usually dominated by W; (v) with sensitive procedures, good indication of extreme non-normality (e.g., the exponential distribution) can be... [ABSTRACT FROM AUTHOR]

Confidence intervals for the population mean of a normal distribution can be determined from the distribution of the variate H = Square root of n(x - mu)/d, analogue to Student's t-distribution but based on the mean absolute deviation d instead of the standard deviation. The H-distribution is derived: the frequency function is symmetric about zero, with central ordinate (1/pi) Square root of (1-n[sup -1]); asymptotically it is normal, N(0, Square root of (pi/2)). An approximate formula for the calculation of the percent values is developed and numerical factors tabulated by which the mean absolute deviation of a normal sample of size n is to be multiplied in order to obtain 95 percent and 50 percent confidence limits of the mean, for n = 2(1)15(5)30, 40, 60,120. It is shown that the increase in length against confidence intervals from the standard deviation and Student's t is negligible. The usefulness of confidence intervals from the mean absolute deviation for estimating the precision of measurements in Physics is discussed. [ABSTRACT FROM AUTHOR]

Estimators for finite population parameters and their variances in two-stage sampling have been developed by using the linear least-squares prediction approach in a recent article by Royall (1976). This article considers a special case of the superpopulation model assumed by Royall and uses a new technique involving linear combinations of the sample observations to estimate the variances of these estimators. An exact confidence interval for the finite population total is calculated for the case in which all clusters have an equal number of elements and an equal number of elements are sampled from each selected cluster. [ABSTRACT FROM AUTHOR]