Scheffe's test is compatible with the analysis of variance test, where this test never states a significant contrast if the F test is not significant. Scheffe's test developed by Henry Scheffe (1959) is used for comparisons that do not need to be orthogonal. This test controls the MEER for each contrast including pairwise comparisons. The test procedure allows for different types of comparisons so it is less sensitive in finding significant differences than other comparison procedures.
The analysis of variance method is useful and a reliable tool for comparing treatment means. In comparing t treatments, the null hypothesis states that all treatment means are not different (H0: 1 = 2 = ... = t). If the F test is real, then the HA is accepted, which states that not all treatment averages are the same or one treatment average is different from the others. Furthermore, a comparison is made to determine which treatment is different by parsing the Number of Treatment Squares for additional F-tests to answer several questions that have been planned. Contrasting or orthogonal methods to separate the averages require a certain level of knowledge that is a priori, either based on certain scientific considerations or based on the results of previous research.
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