关于在方差分析中使用比率的影响

Dwane E. Anderson , Ralph Lydic
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引用次数: 37

摘要

在许多学科使用的实验设计中,原始数据被转换成比率,并对比率数据进行统计分析。虽然设计本身可能是适当的,但由比率转换引起的数学性质可能导致统计测试灵敏度的损失。由于有时必须使用这种设计,因此最好描述比率数据的统计分析是否适当的情况。为了提供这些信息,使用计算机模拟方法生成二元正态观测值X和Y,并使用以下方法进行分析:(1)忽略协变量的方差分析;(2)协方差分析;(3)比值Y/X的方差分析。通过累积每个模型的临界f值上的拒绝数(1−β),对三种模型进行比较。从超过一百万的分析结果讨论了广泛的特定治疗效果和自变量X和因变量Y之间已知的相关性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the effect of using ratios in the analysis of variance

In experimental designs used by a number of disciplines, raw data are transformed into ratios and statistical analyses are performed on the ratio data. Although the designs themselves may be appropriate, the mathematical properties induced by ratio transformations can produce a loss of sensitivity in statistical tests. Since there are times when such designs must be used, it would be desirable to characterize the circumstances under which the statistical analysis of ratio data is or is not appropriate. To provide such information, a computer simulation approach was used to generate bivariate normal observations X and Y which were analysed using: (1) an analysis of variance ignoring the covariate; (2) an analysis of covariance; (3) an analysis of variance on the ratio Y/X. Comparisons were made between the three models by accumulating the number of rejections (1−β) on critical F-values for each model. Results taken from over a million analyses are discussed for a wide range of specific treatment effects and known correlations between the independent variable X and the dependent variable Y.

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