Two Way ANOVAs
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Two Way ANOVAs Factorial Designs
description
Two Way ANOVAs. Factorial Designs. Factors. Same thing as Independent variables. Referred to as factors when there are more than one in a study. - PowerPoint PPT Presentation
Transcript of Two Way ANOVAs
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.
Single
Married Divorced
Males
Females
Are there significantdifferences in Happiness amongsingle, married anddivorced respondents. This is the same as a One-way ANOVA.
Single
Married Divorced
Males
Females
Do the males and the females differ on their Happiness Scores.
Single
Married Divorced
Males
Single
Married Divorced
Females
Is the Pattern of differences in Happiness Ratings the same for males as for females?
Descriptive StatisticsDependent Variable:
Happiness rating Marital Status
Sex Mean Std. Deviation
N
Single Male 4.2000 1.1353 10
Female 6.6000 1.1738 10
Total 5.4000 1.6670 20
Married Male 7.7000 1.4944 10
Female 5.6000 1.2649 10
Total 6.6500 1.7252 20
Divorced Male 4.9000 1.2867 10
Female 5.0000 2.2111 10
Total 4.9500 1.7614 20
Total Male 5.6000 1.9931 30
Female 5.7333 1.7006 30
Total 5.6667 1.8381 60
Single Married Divorced Mean
Male 4.20
(1.14)
Female
Total
Two Way ANOVA TableSource Sum of
Squaresdo 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 2 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 Differenc
e (I-J)
Std. Error
Sig.
(I) Marriage Status
(J) Marriage Status
Single Married -1.250 .466 .010
Divorced .450 .466 .339
Married Single 1.250 .466 .010
Divorced 1.700 .466 .001
Divorced Single -.450 .466 .339
Married -1.700 .466 .001
Two Way ANOVA TableSource 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 2 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 TableSource 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 2 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
SourceSum 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 .588 .244
Married Single 3.500 .588 .001
Divorced 2.800 .588 .001
Divorced Single .700 .588 .244
Married -2.800 .588 .001
Females. Tests of Between-Subjects EffectsDependent 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 ComparisonsDependent 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
Married Single -1.0000 .7380 .187
Divorced .6000 .7582 .436
Divorced Single -1.6000 .7582 .045
Married -.6000 .7582 .436
When you have a significant Interaction it means the effect of one factor Depends on the level of the second factor.
