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Mauchly's sphericity test : ウィキペディア英語版
Mauchly's sphericity test
Mauchly's sphericity test is a statistical test used to validate a repeated measures analysis of variance (ANOVA).
==What is sphericity?==
Sphericity is an important assumption of a repeated-measures ANOVA. It refers to the condition where the variances of the differences between all possible pairs of groups (i.e., levels of the independent variable) are equal. The violation of sphericity occurs when it is not the case that the variances of the differences between all combinations of the groups are equal. If sphericity is violated, then the variance calculations may be distorted, which would result in an F-ratio that would be inflated. Sphericity can be evaluated when there are three or more levels of a repeated measure factor and, with each additional repeated measures factor, the risk for violating sphericity increases. If sphericity is violated, a decision must be made as to whether a univariate or multivariate analysis is selected. If a univariate method is selected, the repeated-measures ANOVA must be appropriately corrected depending on the degree to which sphericity has been violated.

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