In statistics, Scheffé's method, named after 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.
It works on similar principles as the Working–Hotelling procedure for estimating mean responses in regression, which applies to the set of all possible factor levels.
, whether the factor level sample sizes are equal or unequal.
In this case, Scheffé's method is typically quite conservative, and the family-wise error rate (experimental error rate) will generally be much smaller than
that all confidence limits of the type are simultaneously correct, where as usual
Norman R. Draper and Harry Smith, in their 'Applied Regression Analysis' (see references), indicate that
is a result of failing to allow for the additional effect of the constant term in many regressions.
[3] Frequently, subscript letters are used to indicate which values are significantly different using the Scheffé method.
For example, when mean values of variables that have been analyzed using an ANOVA are presented in a table, they are assigned a different letter subscript based on a Scheffé contrast.
[citation needed] If only a fixed number of pairwise comparisons are to be made, the Tukey–Kramer method will result in a more precise confidence interval.
In the general case when many or all contrasts might be of interest, the Scheffé method is more appropriate and will give narrower confidence intervals in the case of a large number of comparisons.
This article incorporates public domain material from the National Institute of Standards and Technology