Expected mean squares
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If you do not specify any factors to be random, Minitab will assume that they are fixed. In this case, the denominator for F-statistics will be the MSE. However, for models which include random terms, the MSE is not always the correct error term. You can examine the expected means squares to determine the error term that was used in the F-test.

When you select Display expected mean squares and variance components in the Results subdialog box, Minitab will print a table of expected mean squares, estimated variance components, and the error term (the denominator mean squares) used in each F-test. The expected mean squares are the expected values of these terms with the specified model. If there is no exact F-test for a term, Minitab solves for the appropriate error term in order to construct an approximate F-test. This test is called a synthesized test.

The estimates of variance components are the usual unbiased analysis of variance estimates. They are obtained by setting each calculated mean square equal to its expected mean square, which gives a system of linear equations in the unknown variance components that is then solved. Unfortunately, this method can result in negative estimates, which should be set to zero. Minitab, however, prints the negative estimates because they sometimes indicate that the model being fit is inappropriate for the data. Variance components are not estimated for fixed terms.