1. ANOVA with SPSS
Recap

2. Post hoc tests

3. Multifactorial Designs: Beginning Multivariate Analysis
Read G&W

4. Excel file – Multifactorial ANOVA introduction
More than one IV may influence a DV
Sex
Relationship Satisfaction
Family Type

5. Interaction effects There can be many different types of interactions
Interactions must be interpreted in the light of theory
They are symmetric mathematically
Main effects cannot be interpreted if there are interaction effects in the model
Main effects are “marginal” to the interaction effects

6. Satisfaction is influenced by family background in both groups but not by sex
Intact
Disrupted

7. Multifactorial ANOVA introduction
More than one IV may influence a DV
Sex
Relationship Satisfaction
Family Type

8. Satisfaction is influenced by family background and by sex
Intact
Disrupted

9. Multifactorial ANOVA introduction
More than one IV may influence a DV
Sex
Relationship Satisfaction
Family Type

10. Satisfaction is influenced by family background only in one group
Intact
Disrupted

11. Multifactorial ANOVA introduction
More than one IV may influence a DV
Sex
Relationship Satisfaction
Family Type

12. Satisfaction is influenced by family background but the effect differs by sex
Intact
Disrupted

13. SPSS output: Family type effects

14. SPSS output: Sex effects

15. SPSS output: Family type and sex effects at the same time

16. SPSS output: Family type and sex effects at the same time and interdependent

17. SPSS output: Family type and sex effects at the same time and interdependent

18. Conceptually – interaction effects

19. Understanding the F statistics: Equal sample sizes
Factor B
… m 1 2 k n
Factor A

20. Understanding the F statistics: Equal sample sizes
Variance of the attribute
in the subjects in each group
Factor B
… m 1 2 k n
Factor A

21. Understanding the F statistics: Equal sample sizes
Factor B
… m 1 2 k n
Factor A

22. Understanding the F statistics: Equal sample sizes
Factor B
… m 1 2 k n
Factor A

23. Understanding the F statistics: Equal sample sizes
Factor B
… m 1 2 k n
Factor A

24. Reviewing multifactor F statistics
Within group variance
Factor B
… m 1 2 k n
Between groups variance of Factor A
Factor A
Between groups variance of Factors A*B
Remember: This subtracts Factor A and Factor B marginal variances
Between groups variance of Factor B

25. Language of Multifactorial ANOVA
The present research has a m*n design.
Main (marginal) effects of Factor A were significant (not significant).
Main (marginal) effects of Factor B were significant (not significant).
Interaction effects of Factor A by Factor B were significant (not significant).

26. ANOVA Exercise

27. The problem
A training program was designed to enhance teamwork skills.
The designers of the program administered it to a group of 105 experimental and 105 control group subjects.
The subjects were from low-middle-high SES (70 each).
We have scores of post training skills.

28. What do we want to know? Hypotheses

29. What is the nature of the data?

30. Questions about interaction effects
Did the experimental training work for all SES groups?
Did the training have an SES bias?
(alternative formulation) Is it possible that the training was particularly beneficial or particularly ineffective for a given SES? (e.g., low skill – low SES group)

31. Effects of training

32. Effects of SES

33. Both factors together

34. Interaction effect????

35. Who does it work for?

36. Table of means