Stats: Scheffe' and Tukey Tests
When the decision from the OneWay Analysis of Variance is to reject the null hypothesis, it
means that at least one of the means isn't the same as the other means. What we need is a way to
figure out where the differences lie, not just that there is a difference.
This is where the Scheffe' and Tukey tests come into play. They will help us analyze pairs of
means to see if there is a difference  much like the difference of two means covered earlier.
Hypotheses
Both tests are set up to test if pairs of means are different. The formulas refer to mean i and mean
j. The values of i and j vary, and the total number of tests will be equal to a combination of k
objects, 2 at a time C(k,2), where k is the number of samples.
Scheffé Test
The Scheffe' test is customarily used with unequal sample sizes, although it
could be used with equal sample sizes.
The critical value for the Scheffe' test is the degrees of freedom for the between variance times
the critical value for the oneway ANOVA. This simplifies to be:
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 Spring '08
 AKBAS
 Statistics, Variance, critical value, Scheffe

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