On the robustness of the T 0 2 test in multivariate analysis of variance when variance-covariance matrices are not equal
协方差矩阵不等时多元方差分析检验的稳健性AI 解读 ↓
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协方差矩阵不等时多元方差分析检验的稳健性
- 研究问题
- 多元方差分析中协方差矩阵相等的假设被违反时，样本量是否平衡会怎样影响所研究检验的显著性水平与功效？
- 方法与思路
- 作者初步考察协方差矩阵差异的影响，区分两组及多组样本、等量及不等量设计，并讨论很大样本下的检验表现。
- 材料陈述的贡献
- 摘要称很大且平衡或部分近似平衡的样本对适度协方差差异较稳健，不平衡设计下则可能明显影响检验水平与功效。
- 阅读关注点
- 应查阅原文确认检验统计量记号，并核对很大样本、适度差异和近似平衡的定义，以及其余假设在分析中是否保持。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；检验符号上下标不清，需查原 PDF；摘要未给定量阈值，不能重构公式或推断刊本变化。
原文摘要
Current interest in multivariate analysis in biometrics and other areas of applied statistics must inevitably lead to a scrutiny of the robustness of the procedure used. One widely used test is the T02 test in multivariate analysis of variance (MANOVA). Among the assumptions underlying MANOVA are: (1) muitivariate normal distributions, (2) equality of variance covariance matrices, and (3) serially uncorrelated observations. The purpose of the present paper is to explore, in a preliminary fashion, the consequence to this test of violation of the assumption of equality of variance-covariance matrices. It is shown that in the case of two samples of equal size, the test is well behaved when there are variations of variance covariance matrices if the samples are very large; further that in the case of two samples of nearly equal size or k samples of equal size, the test is not affected seriously by moderate inequality of variance-covariance matrices as long as samples are very large. However, if some or all of k samples are of unequal size, quite a large effect occurs on the level of signi ficance and the power of the test from even moderate variations. It is to be noted that among numerous works in univariate analysis on the effect of heteroscedasticity of variances (see, e.g. David & Johnson, 1951; Gronow, 1951; Horsnell, 1953; Box, 1954; Scheffé, 1959, pp. 334–58), the present investigation is related to and has extended the work by Scheffé and Box as far as the effect on the level of significance of the test is concerned.