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Statistical Analysis of Treatment and Gender Effects on Emotion and Worry: A Two-Way Factorial MANOVA

Statistical evaluation of gender differences in emotional responses to treatment.

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    Statistical Analysis of Treatment and Gender Effects on Emotion and Worry: A Two - Way Factorial MANOVA 1. What are the independent variables in this study? What are the dependent variables? Independent variables: TREATMENT, GENDER Dependent variables: EMOTION , WORRY 2. Why is a factorial MANOVA appropriate to use for this research design? There are two reasons why MANOVA is better for this research design: (1) MANOVA is a more powerful statistical technique because it is better able to detect differences when such difference do exist, when compared to a series of ANOVAS. (2) MANOVA provides a way to control inflated type I error. 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. Treatment and Gender variables should be nominal, not ordinal. The Emotion and Worry variables are not labeled. 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. MISING VALUES: There are no missing values. Univariate Statistics N Mean Std. Deviation Missing No. of Extremes a Count Percent Low High Treatme nt 100 2.00 .829 0 .0 0 0 Gender 100 .50 .503 0 .0 0 0

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    Emotion 100 27.64 13.977 0 .0 0 0 Worry 100 34.88 8.985 0 .0 1 0 a. Number of cases outside the range (Q1 - 1.5*IQR, Q3 + 1.5*IQR). OUTLIERS . From the box plot, there is one outlier for WORRY. Observation No. 96, value = 8. Residuals Statistics a Minimum Maximum Mean Std. Deviation N Predicted Value - .44 1.19 .50 .432 100 Std. Predicted Value - 2.168 1.591 .000 1.000 100 Standard Error of Predicted Value .028 .092 .051 .011 100

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    Adjusted Predicted Value - .46 1.20 .50 .433 100 Residual - .673 .504 .000 .257 100 Std. Residual - 2.582 1.934 .000 .985 100 Stud. Residual - 2.619 1.975 - .001 1.005 100 Deleted Residual - .692 .526 .000 .268 100 Stud. Deleted Residual - 2.703 2.006 - .002 1.016 100 Mahal. Distance .116 11.387 2.970 1.859 100 Cook's Distance .000 .132 .011 .018 100 Centered Leverage Value .001 .115 .030 .019 100 a. Dependent Variable: Gender

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    outlier Tests of Normality Kolmogorov - Smirnov a Shapiro - Wilk Statistic df Sig. Statistic df Sig. Emotion .095 100 .028 .969 100 .017 Worry .085 100 .069 .986 100 .366 a. Lilliefors Significance Correction EMOTION is not normal, p = 0.028 < 0.05 WORRY is normal, p = 0.069 > 0.05 Outlier Statistics a Case Number Statistic Mahal. Distance 1 96 11.387 2 39 8.173 3 71 7.761 4 7 7.586 5 57 7.431 6 3 6.373 7 1 6.049 8 22 5.564 9 95 5.400 10 68 5.382 a. Dependent Variable: Gender

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    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. Equality of covariance matrices (Box's Test) Box's Test of Equality of Covariance Matrices a Box's M 12.642 F .983 df1 12 df2 7143.492 Sig. .463 Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups. a. Design: Intercept + Treatment + Gender + Treatment * Gender Sufficient correlation among the DVs (Bartlett's Test of Sphericity) Bartlett's Test of Sphericity a Likelihood Ratio .000 Approx. Chi - Square 51.982 df 2 Sig. .000

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