Two Way ANOVAs Factorial Designs

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.

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.

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

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

Descriptive Statistics Dependent Variable: Happiness rating Marital Status SexMeanStd. Deviation N SingleMale Female Total MarriedMale Female Total DivorcedMale Female Total TotalMale Female Total SingleMarriedDivorcedMean Male 4.20 (1.14) Female Total

Two Way ANOVA Table SourceSum of Squares doMean SquareFSig. Marital Status Sex Marital Status * Sex Error Total Main effect of Marital Status. Is it Significant? If yes – interpret Multiple Comparisons.

Multiple Comparisons Table (LSDs) Dependent* Variable: Happiness rating Mean Differenc e (I-J) Std. Error Sig. (I) Marriage Status (J) Marriage Status SingleMarried Divorced MarriedSingle Divorced DivorcedSingle Married

Two Way ANOVA Table SourceSum of Square s dfMean SquareFSig. Marital Status Sex Marital Status * Sex Error Total Main effect of Sex. Is it Significant? If yes – look at means to see who is happier.

Two Way ANOVA Table SourceSum of Square s dfMean SquareFSig. Marital Status Sex Marital Status * Sex Error Total Interaction Between Marital Status and Sex. Is it Significant? If yes – Do separate one-way ANOVAs, one for Males and One for Females.

Dependent Variable: Happiness rating One Way ANOVA - Males Source Sum of Squares dfMean SquareFSig. Marital Status Error Total Multiple Comparisons Table (LSD) Dependent Variable: Happiness rating Mean Difference (I-J) Std. ErrorSig. (I) Marriage Status (J) Marriage Status SingleMarried Divorced MarriedSingle Divorced DivorcedSingle Married

Females. Tests of Between-Subjects Effects Dependent Variable: Happiness rating SourceSum of Squares dfMean Square FSig. Marital Status Error Total Multiple Comparisons Dependent Variable: Happiness rating LSD Mean Difference (I-J) Std. ErrorSig. (I) Marriage Status (J) Marriage Status SingleMarried Divorced MarriedSingle Divorced DivorcedSingle Married

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