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In statistics, Scheffé's method, named after the American statistician Henry Scheffé, is a method for adjusting significance levels in a linear regression analysis to account for multiple comparisons. It is particularly useful in analysis of variance (a special case of regression analysis), and in constructing simultaneous confidence bands for regressions involving basis functions. Scheffé's method is a single-step multiple comparison procedure which applies to the set of estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by the Tukey–Kramer method. ==The method== Let ''μ''1, ..., ''μ''''r'' be the means of some variable in ''r'' disjoint populations. An arbitrary contrast is defined by : where : If ''μ''1, ..., ''μ''''r'' are all equal to each other, then all contrasts among them are 0. Otherwise, some contrasts differ from 0. Technically there are infinitely many contrasts. The simultaneous confidence coefficient is exactly 1 − α, whether the factor level sample sizes are equal or unequal. (Usually only a finite number of comparisons are of interest. In this case, Scheffé's method is typically quite conservative, and the experimental error rate will generally be much smaller than α.) We estimate ''C'' by : for which the estimated variance is : where * ''n''''i'' is the size of the sample taken from the ''i''th population (the one whose mean is ''μ''''i''), and * is the estimated variance of the errors. It can be shown that the probability is 1 − α that all confidence limits of the type : are simultaneously correct, where as usual N is the size of the whole population. 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「Scheffé's method」の詳細全文を読む スポンサード リンク
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