Analysis of variance

Japanese: 分散分析 - ぶんさんぶんせき（英語表記）analysis of variance

Analysis of variance is a method for decomposing the overall variation in measurements into variation due to various factors, and this decomposition is carried out in the form of sums of squares. The measurements are decomposed into a grand mean, a variation portion, and error, and the variation is calculated using unbiased variance, with the variance ratio between the variation portion and the error portion being calculated and tested using an F distribution table. This method is appropriate for problems that involve comparing the effects of several qualitatively different treatments. A t -test is used to compare two mean values, but Fisher's F -test is used when comparing mean values of many samples [Griffiths: 1967, Koch & Link: 1971].

Source: Asakura Publishing Dictionary of Petrology Information

Japanese:

分散分析は測定値全体の変動を様々な要因に基づく変動に分解する方法で，この分解は平方和の形で進められる．測定値は総平均と変動部分と誤差に分解され，変動は不偏分散を用い，変動部分と誤差部分の二つの分散比を計算し，F分布表を用いて検定する．何種類かの質的に異なる処理の効果を比較する問題に適切な方法である．二つの平均値の比較にはt検定を用いるが，多くの標本の平均値を比較する場合にはフィッシャーによるF検定が用いられる［Griffiths : 1967, Koch & Link : 1971］．

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