This study investigates whether there are differences in the outcomes of three different treatments for anxiety. The treatment conditions that are compared are treatment with medication, treatment with psychotherapy, and placebo (inactive pills). In addition, we want to see if gender of the client moderates the effects of the treatment. Every participant had been diagnosed with similar types and severity of anxiety disorders when they entered the study. Each participant was randomly assigned only to one of the three treatment conditions. After 12-weeks of treatment (or placebo), all participants completed two questionnaires to measure worry and general emotion. The higher the scores on these measures, the higher the anxiety level of the participant.

5. Perform a factorial MANOVA on the data. Before interpreting the multivariate results of the MANOVA, check outcomes that test other assumptions for this statistic: equality of covariance matrices (see Box's Test) and sufficient correlation among the DVs (see Bartlett's Test of Sphericity). Also check the results of the Levene's Test of Equality of Error Variances to evaluate that assumption for the univariate ANOVAs that are run and show in the Tests of Between-Subjects Effects output. What have you found about whether the data meet these additional assumptions for the MANOVA and follow-up ANOVAs? Explain.
6. What are the outcomes of the multivariate tests (main effects and interaction)? Report either the Pillai's Trace or Wilks's Lambda for each result, as well as the associated F-value and its statistical significance. Use the following format for notation to report each result: Pillai's Trace OR Wilks' lambda = ____; F(df, df) = ____, p = ____.
7. Given the results of the multivariate tests, would you now move on to interpret the results of the Tests of Between-Subjects Tests? If yes, what are the results and what do they mean? (Report each of the results using the format of F(df, df) = _____, p = _____ , ?2 = _____.)