Multivariate Tests of Within-Subjects Effects
The multivariate tests table displays four tests of signifcance for each model effect. In analogy to univariate tests, the "ratio" of the hypothesis SSCP matrix to the error matrix is used to evaluate the effect of interest. More specifically, the eigenvalues of the test matrix defined by the matrix product of the appropriate hypothesis SSCP matrix and the inverse of the error SSCP matrix are used to compute the statistics in the multivariate tests table.
- Pillai's trace is a positive-valued statistic. Increasing values of the statistic indicate effects that contribute more to the model.
- Wilks' Lambda is a positive-valued statistic that ranges from 0 to 1. Decreasing values of the statistic indicate effects that contribute more to the model.
- Hotelling's trace is the sum of the eigenvalues of the test matrix. It is a positive-valued statistic for which increasing values indicate effects that contribute more to the model. Hotelling's trace is always larger than Pillai's trace, but when the eigenvalues of the test matrix are small, these two statistics will be nearly equal. This indicates that the effect probably does not contribute much to the model.
- Roy's largest root is the largest eigenvalue of the test matrix. Thus, it is a positive-valued statistic for which increasing values indicate effects that contribute more to the model. Roy's largest root is always less than or equal to Hotelling's trace. When these two statistics are equal, the effect is predominantly associated with just one of the dependent variables, there is a strong correlation between the dependent variables, or the effect does not contribute much to the model.
There is evidence that Pillai's trace is more robust than the other statistics to violations of model assumptions 1.
Each multivariate statistic is transformed into a test statistic with an approximate or exact F distribution. The hypothesis (numerator) and error (denominator) degrees of freedom for that F distribution are shown.
The significance values for all effects are greater than 0.10, indicating they do not contribute to the model, with they exception of the test for Roy's larget root for WEEK*PROMO*MARKETID. However, the footnote for this F statistic notes that this particular test provides a lower bound for the significance value, so you can conclude that the reported value of 0.025 is an overly optimistic estimate.