ANOVA with SPSS Recap

Post hoc tests

Multifactorial Designs: Beginning Multivariate Analysis Read G&W 428-435

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

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

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

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

Satisfaction is influenced by family background and by sex Intact Disrupted

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

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

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

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

SPSS output: Family type effects

SPSS output: Sex effects

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

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

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

Conceptually – interaction effects

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

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

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

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

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

Reviewing multifactor F statistics Within group variance Factor B 1 2 … 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

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).

ANOVA Exercise

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.

What do we want to know? Hypotheses

What is the nature of the data?

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)

Effects of training

Effects of SES

Both factors together

Interaction effect????

Who does it work for?

Table of means