Module 6 Problem SetFactorial (2 3) MANOVAThis study investigates whether there are differences in the outcomes of three differenttreatments for anxiety. The treatment conditions that are compared are treatment withmedication, treatment with psychotherapy, and placebo (inactive pills). In addition, we want tosee if gender of the client moderates the effects of the treatment. Every participant had beendiagnosed with similar types and severity of anxiety disorders when they entered the study. Eachparticipant was randomly assigned only to one of the three treatment conditions. After 12-weeksof treatment (or placebo), all participants completed two questionnaires to measure worry andgeneral emotion. The higher the scores on these measures, the higher the anxiety level of theparticipant.Directions:The factorial MANOVA will combine what you have learned previously about1. Post hoc tests when you have more than two groups on an IV (one-way ANOVA),2. Main effects and interactions (factorial ANOVA), and3. Working with multivariate analyses of multiple DVs (one-way MANOVA).Using the SPSS data file for Module 6 (located in Topic Materials), answer the followingquestions:1. What are the independent variables in this study? What are the dependent variables?2. Why is a factorial MANOVA appropriate to use for this research design?3. Did you find any errors that the researcher made when setting up the SPSS data file (don’tforget to check the variable view)? If so, what did you find? How did you correct it?HINT:Yes, there are coding errors for Measures.4. Perform Initial Data Screening. What did you find regarding missing values, univariateoutliers, multivariate outliers, normality?HINT:Revisit instructions from last module’s readings on how to compute Mahalanobisdistance and then analyze for multivariate outliers.5. Perform a factorial MANOVA on the data. Before interpreting the multivariate results ofthe MANOVA, check outcomes that test other assumptions for this statistic: equality ofcovariance matrices (see Box’s Test) and sufficient correlation among the DVs (seeBartlett’s Test of Sphericity). Also check the results of the Levene’s Test of Equality ofError Variances to evaluate that assumption for the univariate ANOVAs that are run andshow in the Tests of Between-Subjects Effects output. What have you found aboutwhether the data meet these additional assumptions for the MANOVA and follow-upANOVAs? Explain.HINTS:Once in the Options box, remember to check box for "Residual SSCP matrix"to get results for the Bartlett’s test.Also, remember to ask for post hoc tests for Treatment because there are morethan two conditions. Profile plots also help with visualizing interactions.6. What are the outcomes of the multivariate tests (main effects and interaction)? Reporteither the Pillai’s Trace or Wilks’s Lambda for each result, as well as the associated Fvalue and its statistical significance. Use the following format for notation to report eachresult: Pillai’s Trace OR Wilks’ lambda = ____; F(df, df) = ____, p = ____.HINTS:Use Pillai’s trace if there are problems with heterogeneity of variancecovariance matrices for the DVs. Otherwise, Wilks’ lambda is fine.Eta squared cannot be calculated from the information provided in themultivariate tests results.7. Given the results of the multivariate tests, would you now move on to interpret the resultsof the Tests of Between-Subjects Tests? If yes, what are the results and what do theymean? (Report each of the results using the format of F(df, df) = _____, p = _____ , 2 =_____.)8. Because one IV has more than two conditions, you would need to do post hoc tests if theoverall F-value was statistically significant. If so, what results did you find?9. If you had a significant interaction effect, what follow-up tests do you need to perform tounderstand how gender moderates the effects of treatment? What are the results?10. Citing the results of your statistical analyses, what is the conclusion you can draw (andsupport) regarding research question that was posed in this research (see problemstatement)?HINT: Use the sample results write-up in the textbook to see what you shouldreport and how to say it. Just substitute the correct language and values for theanalyses you have done for this problem.
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