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一、方差分析的基本原理 在比较两个样本平均数差异的显著性时,可应用t测验,已如前述。但如果样本数在三个以上也采用t测验,就要将样本两两分别比较,这样就显得麻烦。而且,由于整个试验的误差要分成许多组来分别估计,因而影响了分析的准确性。因此就要考虑合并进行分析,借以达到精确、简便的目的。这种合并的分析法,就是方差分析,也叫做变量分析。 本来衡量变异量的大小可用标准差来表示,但因计算标准差时要进行开方,为了简便起见,就直接用标准差的平方值来表示。在统计学上,样本标准差的平方叫做均方,总体标准差的平方叫做方差。 现结合单因素试验的方差分析实例,来说明方差分析的基本原理。
First, the basic principle of analysis of variance in the comparison of the significance of the difference between the mean of two samples, the t test can be applied, as described above. However, if the number of samples in more than three also use t test, it is necessary to compare the sample two or two, so it is too much trouble. Moreover, the accuracy of the analysis is affected by the fact that the error of the whole experiment is divided into many groups to be estimated separately. Therefore, we must consider the merger analysis, in order to achieve the precise and easy purpose. This combined analysis is an analysis of variance, also known as variable analysis. Originally measured by the size of the amount of variance can be used to represent the standard deviation, but to calculate the standard deviation of the time to open the square, for simplicity, the square of the standard deviation directly. In statistics, the square of the standard deviation of samples is called the mean square, and the square of the total standard deviation is called the variance. Now combined with single factor test analysis of variance to illustrate the principle of variance analysis.