Scheffé

Scheffé refers to a range of statistical methods developed by Henry Scheffé, primarily used for post-hoc analysis following an Analysis of Variance (ANOVA). These methods are designed to identify which specific group means are significantly different from each other after an ANOVA has indicated an overall significant difference among the means.

The most well-known Scheffé method is the Scheffé's test. This is a conservative test, meaning it is less likely to find a significant difference than some other post-hoc tests, but when it does, it is more reliable. It achieves this conservatism by comparing all possible contrasts (linear combinations of group means) between the groups, not just pairwise comparisons. The critical value for the Scheffé test is based on the F-distribution, making it closely related to the ANOVA procedure itself.

Scheffé's method is particularly useful when the number of groups is large or when the researcher is interested in testing complex contrasts beyond simple pairwise differences. It controls the family-wise error rate, ensuring that the probability of making at least one Type I error across all comparisons is kept at the desired significance level (e.g., alpha = 0.05). While it offers robust control over Type I errors, its conservatism can lead to lower statistical power, meaning it might fail to detect real differences that other tests could identify. The application of Scheffé's test requires that the assumptions of ANOVA, such as normality of residuals and homogeneity of variances, are met.