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Analyzing a Factorial ANOVA: Non-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:

  1. Analyzing a Factorial ANOVA: Non-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   Report main effects for each IV   Compute Cohen’s f for each IV   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 .117 30 .200(*) .972 30 .603 Women .156 30 .060 .924 30 .033 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 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 .523 1 .523 15.856 .000 .227 method 1.174 2 .587 17.809 .000 .397 gender * method .193 2 .096 2.921 .062 .098 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. Determine interaction effect Balkin, R. S. (2008) 7

  8. Report main effects for each IV 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 .523 1 .523 15.856 .000 .227 method 1.174 2 .587 17.809 .000 .397 gender * method .193 2 .096 2.921 .062 .098 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) 8

  9. Compute Cohen’s f/d for each IV Descriptive Statistics Dependent Variable: Change in GPA Gender Note -Taking methods Mean Std. Deviation N Men Method 1 .3350 .22858 10 Method 2 .6400 .17764 10 Control .1650 .14916 10 Total .3800 .26993 30 Women Method 1 .1700 .18288 10 Method 2 .3050 .19214 10 Control .1050 .14615 10 Total .1933 .18880 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/d for each IV Descriptive Statistics Dependent Variable: Change in GPA Gender Note -Taking methods Mean Std. Deviation N Men Method 1 .3350 .22858 10 Method 2 .6400 .17764 10 Control .1650 .14916 10 Total .3800 .26993 30 Women Method 1 .1700 .18288 10 Method 2 .3050 .19214 10 Control .1050 .14615 10 Total .1933 .18880 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 Note -Taking methods Multiple Comparisons Dependent Variable: Change in GPA Tukey HSD 95% Confidence Interval Mean Diffe rence king methods (J) Note -Taking methods (I-J) Std. Error Sig. Lower Bound Upper Bound Method 2 -.2200(*) .05741 .001 -.3584 -.0816 Control .1175 .05741 .111 -.0209 .2559 Method 1 .2200(*) .05741 .001 .0816 .3584 Control .3375(*) .05741 .000 .1991 .4759 Method 1 -.1175 .05741 .111 -.2559 .0209 Method 2 -.3375(*) .05741 .000 -.4759 -.1991 Based on observed means. * The mean difference is significant at the .05 level. Balkin, R. S. (2008) 11

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