Once we have rejected *H*_{0} using ANOVA, we can determine which of the sample means are different using the Scheffé test. This test compares each pair of sample means from the ANOVA procedure. For the fertilizer example, we would compare *x*1 versus *x*_{2}, *x*_{1} versus *x*_{3} , and *x*_{2} versus *x*_{3} to see whether any differences exist.

After rejecting *H*_{0} using ANOVA, we can determine which of the sample means are different using the Scheffé test.

First, the following test statistic for the Scheffé test, F_{S}, is calculated for each of the pairs of sample means:

where:
*SSW* = the sum ...

= the sample means being compared

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