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Analyzing a Factorial ANOVA: Significant interaction Rick Balkin, Ph.D., LPC-S, NCC Department of Counseling Texas A&M University-Commerce Rick_balkin@tamu-commerce.edu Balkin, R. S. (2008) 1 Analyzing a Factorial ANOVA: Non-significant

  1. Analyzing a Factorial ANOVA: Significant interaction Rick Balkin, Ph.D., LPC-S, NCC Department of Counseling Texas A&M University-Commerce Rick_balkin@tamu-commerce.edu Balkin, R. S. (2008) 1

  2. Analyzing a Factorial ANOVA: Non-significant interaction 1.Analyze model assumptions 2.Determine interaction effect Non-significant interaction Significant interaction 3. Plot the interaction 4. Analyze simple effects 3. Report main effects for each IV 5. Compute Cohen’s f for each simple 4. Compute Cohen’s f for each IV effect 5. Perform post hoc and Cohen’s d if necessary. 6. Perform post hoc and Cohen’s d if necessary. Balkin, R. S. (2008) 2

  3. Analyzing a Factorial ANOVA: Non-significant interaction  Analyze model assumptions   Determine interaction effect   Plot the interaction   Analyze simple effects   Compute Cohen’s f for each simple effect  Perform post hoc and Cohen’s d if necessary. Balkin, R. S. (2008) 3

  4. Analyze model assumptions Kolmogorov -Smirnov(a) Shapiro-Wilk Gender Statistic df Sig. Statistic df Sig. Change in GPA Men .137 30 .155 .968 30 .487 Women .158 30 .053 .921 30 .029 Kolmogorov -Smirnov(a) Shapiro -Wilk Note -Taking methods Statistic df Sig. Statistic df Sig. Change in GPA Method 1 .126 20 .200(*) .916 20 .081 Method 2 .154 20 .200(*) .971 20 .766 Control .144 20 .200(*) .952 20 .392 Balkin, R. S. (2008) 4

  5. Analyze model assumptions Levene's Test of Equality of Error Variances(a) Dependent Variable: Change in GPA F df1 df2 Sig. .575 5 54 .719 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a Design: Intercept+gender+method +gender * method Balkin, R. S. (2008) 5

  6. Determine the interaction effect Tests of Between -Subjects Effects Dependent Variable: Change in GPA Type III Sum Partial Eta Source of Squares df Mean Square F Sig. Squared Corrected Model 1.889(a) 5 .378 11.463 .000 .515 Intercept 4.931 1 4.931 149.582 .000 .735 gender .020 1 .020 .612 .438 .011 method 1.174 2 .587 17.809 .000 .397 gender * method .695 2 .348 10.543 .000 .281 Error 1.780 54 .033 Total 8.600 60 Corrected Total 3.669 59 a R Squared = .515 (Adjusted R Squared = .470) Balkin, R. S. (2008) 6

  7. Plot the interaction Balkin, R. S. (2008) 7

  8. Analyze simple effects UNIANOVA gpaimpr BY gender method /emmeans=table(gender*method) comp(method). Univariate Tests Dependent Variable: Change in GPA Sum of Gender Squares df Mean Square F Sig. Men Contrast .165 2 .082 2.498 .092 Error 1.780 54 .033 Women Contrast 1.705 2 .852 25.855 .000 Error 1.780 54 .033 Each F tests the simple effects of Note -Taking methods within each level combination of the other effects shown. The based on the linearly independent pairwise comparisons amo ng the estimated marginal means. Balkin, R. S. (2008) 8

  9. Compute Cohen’s f for each simple effect Descriptive Statistics Dependent Variable: Change in GPA Gender Note -Taking methods Mean Std. Deviation N Men Method 1 .3350 .22858 10 Method 2 .3050 .19214 10 Control .1650 .14916 10 Total .2683 .20064 30 Women Method 1 .1700 .18288 10 Method 2 .6400 .17764 10 Control .1050 .14615 10 Total .3050 .29254 30 Total Method 1 .2525 .21853 20 Method 2 .4725 .24893 20 Control .1350 .14699 20 Total .2867 .24938 60 Balkin, R. S. (2008) 9

  10. Compute Cohen’s f for each simple effect Descriptive Statistics Dependent Variable: Change in GPA Gender Note -Taking methods Mean Std. Deviation N Men Method 1 .3350 .22858 10 Method 2 .3050 .19214 10 Control .1650 .14916 10 Total .2683 .20064 30 Women Method 1 .1700 .18288 10 Method 2 .6400 .17764 10 Control .1050 .14615 10 Total .3050 .29254 30 Total Method 1 .2525 .21853 20 Method 2 .4725 .24893 20 Control .1350 .14699 20 Total .2867 .24938 60 Balkin, R. S. (2008) 10

  11. Perform post hoc and Cohen’s d if necessary (I) Note- (J) Note- Mean Taking Taking Difference Gender methods methods (I-J) Std. Error Sig.(a) Men Method 1 Method 2 0.03 0.081 0.71 Control .170(*) 0.081 0.04 Method 2 Method 1 -0.03 0.081 0.71 Control 0.14 0.081 0.09 Control Method 1 -.170(*) 0.081 0.04 Method 2 -0.14 0.081 0.09 Women Method 1 Method 2 -.470(*) 0.081 0.00 Control 0.065 0.081 0.43 Method 2 Method 1 .470(*) 0.081 0.00 Control .535(*) 0.081 0.00 Control Method 1 -0.065 0.081 0.43 Method 2 -.535(*) 0.081 0.00 Balkin, R. S. (2008) 11

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