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

3. 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

4. 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

5. 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

6. 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

7. 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 54
2.174
Total 60
Main effect of Marital Status. Is it Significant?
If yes – interpret Multiple Comparisons.

8. 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

9. 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 54
2.174
Total 60
Main effect of Sex. Is it Significant?
If yes – look at means to see who is happier.

10. 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 54
2.174
Total 60
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 df
Mean Square F
Sig.
Marital Status
68.600 2
34.300
19.873
.001
Error
46.600 27
1.726
Total 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

12. 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 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
.6000
.436
-.6000

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