Two Way ANOVAs Factorial Designs.

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Presentation transcript:

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 two or more independent variables. In the design each level of each factor is represented at each level of each other factor.

Main Effect of Marital Status Single Married Divorced Males Females Total Are there significant differences in Happiness among single, married and divorced respondents. This is the same as a One-way ANOVA. Main Effect of Marital Status

Total Males Females Main Effect of Sex Single Married Divorced Do the males and the females differ on their Happiness Scores? Main Effect of Sex

Interaction between Marital Status and Sex Single Married Divorced Males Is the Pattern of differences in Happiness Ratings the same for males as for females? Single Married Divorced Females

4.20 (1.14) Descriptive Statistics Dependent Variable: Happiness rating Marital Status Sex Mean Std. Deviation N Single Male 4.2000 1.1353 10 Female 6.6000 1.1738 Total 5.4000 1.6670 20 Married 7.7000 1.4944 5.6000 1.2649 6.6500 1.7252 Divorced 4.9000 1.2867 5.0000 2.2111 4.9500 1.7614 1.9931 30 5.7333 1.7006 5.6667 1.8381 60 Single Married Divorced Mean Male 4.20 (1.14) Female Total

Two Way ANOVA Table Main effect of Marital Status. Is it Significant? Source Sum of Squares do Mean Square F Sig. Marital Status 31.033 2 15.517 7.137 .002 Sex 1.267 1 .267 1.123 .728 Marital Status * Sex 50.633 25.317 11.645 .001 Error 117.400 54 2.174 Total 2127.000 60 Main effect of Marital Status. Is it Significant? If yes – interpret Multiple Comparisons.

Multiple Comparisons Table (LSDs) Dependent* Variable: Happiness rating Mean Difference (I-J) Std. Error Sig. (I) Marriage Status (J) Marriage Status Single Married -1.250 .466 .010 Divorced .450 .339 1.250 1.700 .001 -.450 -1.700

Two Way ANOVA Table Main effect of Sex. Is it Significant? Source Sum of Squares df Mean Square F Sig. Marital Status 31.033 2 15.517 7.137 .002 Sex 1.267 1 .267 1.123 .728 Marital Status * Sex 50.633 25.317 11.645 .001 Error 117.400 54 2.174 Total 2127.000 60 Main effect of Sex. Is it Significant? If yes – look at means to see who is happier.

Two Way ANOVA Table Source Sum of Squares df Mean Square F Sig. Marital Status 31.033 2 15.517 7.137 .002 Sex 1.267 1 .267 1.123 .728 Marital Status * Sex 50.633 25.317 11.645 .001 Error 117.400 54 2.174 Total 2127.000 60 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 df Mean Square F Sig. Marital Status 68.600 2 34.300 19.873 .001 Error 46.600 27 1.726 Total 1056.000 30 Multiple Comparisons Table (LSD) Dependent Variable: Happiness rating Mean Difference (I-J) Std. Error Sig. (I) Marriage Status (J) Marriage Status Single Married -3.500 .588 .001 Divorced -.700 .244 3.500 2.800 .700 -2.800

Females. Tests of Between-Subjects Effects Dependent Variable: Happiness rating Source Sum of Squares df Mean Square F Sig. Marital Status 12.510 2 6.255 2.297 .121 Error 70.800 26 2.723 Total 1045.000 29 Multiple Comparisons Dependent Variable: Happiness rating LSD Mean Difference (I-J) Std. Error Sig. (I) Marriage Status (J) Marriage Status Single Married 1.0000 .7380 .187 Divorced 1.6000 .7582 .045 -1.0000 .6000 .436 -1.6000 -.6000

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