# Statistics

**Factorial (2 **× **3) MANOVA**

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.

**Directions:**

The factorial MANOVA will combine what you have learned previously about

1. Post hoc tests when you have more than two groups on an IV (one-way ANOVA),

2. Main effects and interactions (factorial ANOVA), and

3. Working with multivariate analyses of multiple DVs (one-way MANOVA).

Using the SPSS data file for Module 6 (located in Topic Materials), answer the following questions:

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’t forget 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, univariate outliers, multivariate outliers, normality?

HINT:

Revisit instructions from last module’s readings on how to compute Mahalanobis distance and then analyze for multivariate outliers.

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.

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 more than two conditions. Profile plots also help with visualizing interactions.

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* = ____.

HINTS:

· Use Pillai’s trace if there are problems with heterogeneity of variance-covariance matrices for the DVs. Otherwise, Wilks’ lambda is fine.

· Eta squared cannot be calculated from the information provided in the multivariate tests results.

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* = _____ , h^{2 }= _____.)

8. Because one IV has more than two conditions, you would need to do post hoc tests if the overall 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 to understand 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 (and support) regarding research question that was posed in this research (see problem statement)?

HINT: Use the sample results write-up in the textbook to see what you should report and how to say it. Just substitute the correct language and values for the analyses you have done for this problem.

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