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应用方差分析的两个假定是:(1)反应变量是正态分布,和(2)整个实验的实验误差方差相等。实际上,常需处理反应变量是0或1的分类数据。此时,常记录某现象的发生数,或发生的百分数。众所周知,每单位发生数,如,每件疵点数,每页错误数,每单位时间患者数,常服从Poisson分布,这样的反应变量不仅不是正态,且方差与均数相等。当以比例或百分率作反应变量时,数据为二项分布,方差也与均数有关系,不能遵守方差分析的基本假定。有研究表明,应用方差分析时缺乏正态性不是太严重
The two assumptions used for analysis of variance are: (1) the response variables are normally distributed, and (2) the experimental errors for the entire experiment are equal. In practice, it is often necessary to process classification data with a response variable of 0 or 1. At this point, often record the occurrence of a phenomenon, or the percentage of occurrence. It is well known that the number of occurrences per unit, such as the number of defects per page, the number of errors per page, and the number of patients per unit of time, are usually subject to the Poisson distribution. Such a response variable is not only normal, but also has a variance equal to the mean. When the ratio or percentage is used as the response variable, the data is a binomial distribution, and the variance is also related to the mean and cannot follow the basic assumptions of variance analysis. Studies have shown that lack of normality when applying ANOVA is not too serious