What Is Scheffe's Test
A Scheffe Test is a statistical test that is post-hoc test used in statistical analysis. It was named after American statistician Henry Scheffe. The Scheffe Test is used to make unplanned comparisons, rather than pre-planned comparisons, among group means in an analysis of variance (ANOVA) experiment.
An unplanned comparison is a comparison made within a data set after an ANOVA test has been run, so the parameters of the comparison are not built into the ANOVA experiment. Scheffe's test can be used in situations where the results of an ANOVA experiment have yielded a significant F-statistic. This indicates that there is a meaningful difference in the means of the groups being compared.
Understanding Scheffe's Test
While Scheffe's test has the advantage of giving the experimenter the flexibility to test any comparisons that appear interesting, the drawback of this flexibility is that the test has very low statistical power.
While pre-planned comparisons can be made using tests such as t-tests or F-tests, these tests are not suitable for post hoc or unplanned comparisons. For such comparisons, multiple comparison tests such as Scheffe's test, the Tukey-Kramer method, or the Bonferroni test are appropriate.