By default, Minitab displays a table of the four multivariate tests for each term in the model:

·    Wilks' test - the most commonly used test because it was the first derived and has a well-known F approximation

·    Lawley-Hotelling - also known as Hotelling's generalized T statistic

·    Pillai's - will give similar results to the Wilks' and Lawley-Hotelling's tests

·    Roy's - use only when the mean vectors are collinear; does not have a satisfactory F approximation

Though Wilks' test is the most widely used method, Pillai's is actually the best test to use in most situations.

Examine the p-values for the Wilks', Lawley-Hotelling, and Pillai's test statistic to judge whether significant evidence exists for model effects. If the p-value is larger than the a-level you have selected, the effect is not significant. Usually you reach the same conclusion using any of the tests. In cases when conclusions differ, base your decision on what test makes the most sense for your data.

For the door lock data, all p-values for the method by plants interaction plants are greater than 0.05, indicating that there is no interaction between method and plant.