1. Two Way ANOVAs Factorial Designs

2. Factors Same thing as Independent variables. Referred to as factors when there are more than one in a study. Factorial Design – a study in which there are more than two independent variables. In the design each level of each factor is represented at each level of each other factor.

3. Single MarriedDivorced Males Females Are there significant differences in Happiness among single, married and divorced respondents. This is the same as a One-way ANOVA.

4. Single MarriedDivorced Males Females Do the males and the females differ on their Happiness Scores.

5. Single MarriedDivorced Males Single MarriedDivorced Females Is the Pattern of differences in Happiness Ratings the same for males as for females?

6. Descriptive Statistics Dependent Variable: Happiness rating Marital Status SexMeanStd. Deviation N SingleMale4.20001.135310 Female6.60001.173810 Total5.40001.667020 MarriedMale7.70001.494410 Female5.60001.264910 Total6.65001.725220 DivorcedMale4.90001.286710 Female5.00002.211110 Total4.95001.761420 TotalMale5.60001.993130 Female5.73331.700630 Total5.66671.838160 SingleMarriedDivorcedMean Male 4.20 (1.14) Female Total

7. Two Way ANOVA Table SourceSum of Squares doMean SquareFSig. Marital Status31.033215.5177.137.002 Sex1.2671.2671.123.728 Marital Status * Sex50.633225.31711.645.001 Error117.400542.174 Total2127.00060 Main effect of Marital Status. Is it Significant? If yes – interpret Multiple Comparisons.

8. Multiple Comparisons Table (LSDs) Dependent* Variable: Happiness rating Mean Differenc e (I-J) Std. Error Sig. (I) Marriage Status (J) Marriage Status SingleMarried-1.250.466.010 Divorced.450.466.339 MarriedSingle1.250.466.010 Divorced1.700.466.001 DivorcedSingle-.450.466.339 Married-1.700.466.001

9. Two Way ANOVA Table SourceSum of Square s dfMean SquareFSig. Marital Status31.033215.5177.137.002 Sex1.2671.2671.123.728 Marital Status * Sex50.633225.31711.645.001 Error117.400542.174 Total2127.00060 Main effect of Sex. Is it Significant? If yes – look at means to see who is happier.

10. Two Way ANOVA Table SourceSum of Square s dfMean SquareFSig. Marital Status31.033215.5177.137.002 Sex1.2671.2671.123.728 Marital Status * Sex50.633225.31711.645.001 Error117.400542.174 Total2127.00060 Interaction Between Marital Status and Sex. Is it Significant? If yes – Do separate one-way ANOVAs, one for Males and One for Females.

11. Dependent Variable: Happiness rating One Way ANOVA - Males Source Sum of Squares dfMean SquareFSig. Marital Status68.600234.30019.873.001 Error46.600271.726 Total1056.00030 Multiple Comparisons Table (LSD) Dependent Variable: Happiness rating Mean Difference (I-J) Std. ErrorSig. (I) Marriage Status (J) Marriage Status SingleMarried-3.500.588.001 Divorced-.700.588.244 MarriedSingle3.500.588.001 Divorced2.800.588.001 DivorcedSingle.700.588.244 Married-2.800.588.001

12. Females. Tests of Between-Subjects Effects Dependent Variable: Happiness rating SourceSum of Squares dfMean Square FSig. Marital Status 12.51026.2552.297.121 Error70.800262.723 Total1045.00029 Multiple Comparisons Dependent Variable: Happiness rating LSD Mean Difference (I-J) Std. ErrorSig. (I) Marriage Status (J) Marriage Status SingleMarried1.0000.7380.187 Divorced1.6000.7582.045 MarriedSingle.7380.187 Divorced.6000.7582.436 DivorcedSingle-1.6000.7582.045 Married -.6000.7582.436

13. When you have a significant Interaction it means the effect of one factor Depends on the level of the second factor.