An exact F-test for a term is one in which the expected value of the numerator mean squares differs from the expected value of the denominator mean squares only by the variance component or the fixed factor of interest.
Sometimes, however, such a mean square cannot be calculated. In this case, Minitab uses a mean square that results in an approximate F-test and displays an "x" beside the p-value to identify that the F-test is not exact.
For example, suppose you performed an ANOVA with the fixed factor Supplement and the random factor Lake, and the got following output for the expected mean squares (EMS):
||Expected Mean Square for Each Term|
||(4) + 1.7500(3) + Q
||(4) + 1.7143(3) + 5.1429(2)
||(4) + 1.7500(3)
The F-statistic for Supplement is the mean square for Supplement divided by the mean square for the Supplement*Lake interaction. If the effect for Supplement is very small, the expected value of the numerator equals the expected value of the denominator. This is an example of an exact F-test.
Notice, however, that for a very small Lake effect, there are no mean squares such that the expected value of the numerator equals the expected value of the denominator. Therefore, Minitab uses an approximate F-test. In this example, the mean square for Lake is divided by the mean square for the Supplement*Lake interaction. This results in an expected value of the numerator being approximately equal to that of the denominator if the Lake effect is very small.