When your data table consists of a large number of rows (large n), the standard error used in testing can be very small. As a result, tests might be statistically significant, when in fact, the observed difference is too small to be of practical consequence. Tests of practical significance enable you to specify the size of the difference that you consider worth detecting. This difference is called the practical difference. Instead of testing that the difference is zero, you test whether the difference exceeds the practical difference. As a result, the tests are more meaningful, and fewer tests need to be scrutinized.

The Compare Means data table provides results for both tests of practical difference and tests of practical equivalence. Each row compares a response across two levels of a categorical factor. Results of the pairwise comparisons are color-coded to facilitate interpretation. See Practical Difference for a description of how the practical difference is specified. See Example of Tests of Practical Significance and Equivalence for an example.

The p-value for the usual Student's t-test for a pairwise comparison. This is the robust version of the t-test when the Robust option is selected. Tests that are significant at the 0.05 level are highlighted.

The p-value for a test of whether the absolute value of the mean difference in Y between Leveli and Levelj is less than or equal to the Practical Difference. A small p-value indicates that the absolute difference exceeds the Practical Difference. This indicates that Leveli and Levelj account for a difference that is of practical consequence.

Uses the Two One-Sided Tests (TOST) method to test for a practical difference between the means (Schuirmann, 1987). The Practical Difference specifies a threshold difference for which smaller differences are considered practically equivalent. One-sided t tests are constructed for two null hypotheses: the true difference exceeds the Practical Difference; the true difference is less than the negative of the Practical Difference. If both tests reject, this indicates that the absolute difference in the means falls within the Practical Difference. Therefore, the groups are considered practically equivalent.

The Practical Equivalence PValue is the largest p-value obtained on the one-sided t tests. A small Practical Equiv PValue indicates that the mean response for Leveli is equivalent, in a practical sense, to the mean for Levelj.