不等重复系统分组试验设计分析

Analysis of nested design with unbalanced subclass numbers

对普通最小二乘法和加权最小二乘法在不等重复单因素系统分组试验中的分析效果进行了比较研究。前者以组平均数为基础进行方差分析,后者以原单个数据为基础并采用KENWARDROGER法确定自由度进行分析。通过分析和模拟研究,结果表明,在数据不平衡性较小时,两种方法分析的结果相近,且一类统计错误率控制性较好;在数据不平衡性较大时,加权最小二乘法的一类统计错误率偏差比普通最小二乘法的小。因此,建议在遇到不等重复系统分组试验资料时,宜采用加权最小二乘法进行分析。

In this paper,the effects of OLS method and WLS method in analysis of one-way nested design with unequal subclass numbers are examined.The first method is to subject the cell means to an analysis of variance,the second method uses the individual observations and KENWARDROGER approximation for calculation of degree of freedom.The analysis and simulation results showed that the results of the two methods were similar and the type one errors were well controlled when the data were lightly unbalanced;when the data were severely unbalanced,the WLS method was robuster than the OLS method.It is suggested that,in cases of unbalanced data,the WLS method is to be used.