Tests for the homogeneity of a set of variances against ordered alternatives
针对有序备择的一组方差齐性检验AI 解读 ↓
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针对有序备择的一组方差齐性检验
- 研究问题
- 当多个正态总体的方差可能按指定次序变化时，如何检验方差齐性，并比较利用次序限制的检验功效？
- 方法与思路
- 作者基于次序限制下的方差估计修改 Bartlett、Fmax 和 Cochran 统计量，研究零分布并用模拟比较功效。
- 材料陈述的贡献
- 摘要称推导了修改统计量的零分布并计算部分临界值；在所报告的蒙特卡洛比较中，修改的 Bartlett 统计量表现最佳。
- 阅读关注点
- 应核对有序备择的具体形式、各组样本量条件、临界值近似方法，以及模拟中的备择配置与功效比较范围。
- 阅读边界
- 依据版本未注明的 OpenAlex 索引摘要；最佳表现限于摘要所述模拟，完整条件和结果未提供，不能外推为普遍优势。
原文摘要
SuIMMAPRY Several statistics are investigated for testing the homogeneity of a set of variances of normal populations against ordered alternatives. The null distributions of these statistics are studied. Comparisons of powers of the tests are also made by Monte Carlo experiments. The test based on the modified Bartlett's statistic M* is found to perform best. For testing the homogeneity of variances of several normal distributions test statistics such as M by Bartlett (1937), Fmax by Hartley (1950) and G by Cochran (1941) have been proposed. These test statistics are appropriate when the alternative hypothesis is merely that the variances are not all equal. In this paper we consider the problem of testing against ordered alternatives. In ? 2 the modified M, the modified Fmax and the modified G statistics based on estimates of variances under order restrictions are introduced. We derive their null distributions. The approximate critical points of the modified M are computed for 3 to 12 populations by using the method due to Hartley (1939) for approximating the null distribution of M statistic. The critical points of the modified Fmax are computed for 3 to 6 populations. In ? 3 some comparisons of the powers of tests are made by computer simulation, including the conventional test statistics mentioned above, one proposed by Vincent (1961) and a modification of it.