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三条及以上回归直线所有对比的精确置信界AI 解读

It is desired to compare κ ≥ 3 treatments. Under the assumption of iid normal errors, it is well known that the Scheffé method produces exact simultaneous confidence bounds for all contrasts of the treatment means. Furthermore, it is known that the Scheffé method is conservative when one desires confidence bounds for a specific subset of contrasts of means. Exact methods, such as those due to Tukey and Dunnett, yield tighter bounds than the Scheffé method for specific…

三条及以上回归直线所有对比的精确置信界AI 解读

It is desired to compare κ ≥ 3 treatments. Under the assumption of iid normal errors, it is well known that the Scheffé method produces exact simultaneous confidence bounds for all contrasts of the treatment means. Furthermore, it is known that the Scheffé method is conservative when one desires confidence bounds for a specific subset of contrasts of means. Exact methods, such as those due to Tukey and Dunnett, yield tighter bounds than the Scheffé method for specific…

与对照组比较实验中同时推断的样本量分配AI 解读

A common experiment is to compare p ≥ 2 test treatments with a control in a one-way layout. The object of the experiment can be to establish which test treatments are statistically significantly different from or better than the control or to give simultaneous confidence bounds on the amount of improvement that each of the test treatments offers over the control. Frequently, further experimentation is done with the promising treatments. We consider the problem of optimal…

Steel 多处理对照多元符号检验的推广AI 解读

Steel (1959) introduced a nonparametric multivariate sign test to allow one to compare p ≥ 2 test treatments simultaneously with a control or standard treatment in a randomized-block setting. Steel proposed using blocks of size p + 1 composed of one observation from each treatment. Intuitively, it seems that the control should be observed more often that a test treatment, because the control is involved in all treatment-control comparisons and an individual test treatment is…

概率与随机变量AI 解读

Probability Conditional probability and independence Random variables Continuous distributions Distribution function Functions of random variables Bivariate distributions Expectation of a random variable Variance of a random variable Moment generating functions Moments of bivariate distributions Probability generating functions Sums of random variables Unbiased estimators Sampling finite populations Generating random variables.

用于处理与对照比较的渐近最优平衡处理不完全区组设计子类AI 解读

Incomplete block designs for estimation of treatment-control differences are studied. A class of designs for this purpose, called balanced treatment incomplete block designs, has recently been proposed and studied by several authors. Here, a relatively small subclass of these designs is shown to contain the asymptotically optimal design under the criterion of minimizing the length of simultaneous confidence intervals for treatment-control differences. These results can be…

用于处理与对照比较的渐近最优平衡处理不完全区组设计子类AI 解读

Incomplete block designs for estimation of treatment-control differences are studied. A class of designs for this purpose, called balanced treatment incomplete block designs, has recently been proposed and studied by several authors. Here, a relatively small subclass of these designs is shown to contain the asymptotically optimal design under the criterion of minimizing the length of simultaneous confidence intervals for treatment-control differences. These results can be…

三个正态总体均值两两比较的精确同时置信区间AI 解读

The problem of simultaneously estimating the pairwise differences of means of three independent normal populations with equal variances is considered. A computational method involving a bivariate t density is used to form confidence intervals with simultaneous coverage probability equal to 1 — a. For equal sample sizes, the method is the Tukey studentized range procedure. With unequal sample sizes, the method is superior to the various generalized Tukey methods. A table of…

第一类删失下指数分布参数的检验AI 解读

Consider a life-testing experiment subject to Type I censoring, where m items are put on test at the outset and are not replaced on failure. Assume an exponential failure distribution F(t) = 1 – exp (– t/θ). A test of H 0: θ ≥ ξ versus H 1: θ < ξ based on the maximum likelihood estimator of θ is proposed. It is shown that early termination of the test resulting in either acceptance or rejection of H 0 is possible. Critical points are presented. The test is shown to compare…

用 U 统计量检验正态性：双尾较重或较轻的备择AI 解读

U–statistics are used to construct statistics for testing normality against alternatives that have both tails heavy or both tails light. One resulting test statistic is equivalent to D'Agostino's D, and insights on the nature of D are given through the U–statistic approach. A Monte Carlo power study is reported, which includes D, another statistic derived from the U–statistic approach, a statistic suggested by Hogg for use in adaptive inference, the sample kurtosis, and the…

利用 U 统计量针对非对称备择检验正态性AI 解读

We propose a class of tests for normality and investigate a subclass of these tests for testing against nonsymmetric alternatives. Attention is devoted to a convenient linear combination of the order statistics divided by the sample standard deviation and to a second statistic. The null distribution of the first statistic is for most purposes satisfactorily approximated by a normal distribution if the sample size is 20 or greater, and the same is true of the second statistic…