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In statistics and uncertainty analysis, the Welch–Satterthwaite equation is used to calculate an approximation to the effective degrees of freedom of a linear combination of independent sample variances, also known as the pooled degrees of freedom,〔()〕〔()〕 corresponding to the pooled variance. For sample variances , each respectively having degrees of freedom, often one computes the linear combination : where is a real positive number, typically . In general, the probability distribution of cannot be expressed analytically. However, its distribution can be approximated by another chi-squared distribution, whose effective degrees of freedom are given by the Welch–Satterthwaite equation : There is ''no'' assumption that the underlying population variances are equal. This is known as the Behrens–Fisher problem. The result can be used to perform approximate statistical inference tests. The simplest application of this equation is in performing Welch's t test. ==See also== * Pooled variance 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Welch–Satterthwaite equation」の詳細全文を読む スポンサード リンク
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