1. PSY 2005 Week 10 – Simple Effects

2. Factorial Analysis of Variance Simple Effects

3. Aims Interpretation of interactions To explain, using example data, how an analysis of simple effects allows an interpretation of potential main effects when an interaction is present.

4. Learning Outcomes Interpret graphical representations of interactions Define simple effects. Explain the steps in an analysis of simple effects. Interpret the results of a simple effects analysis. At the end of this lecture you will be able to :

5. Definitions 2-way ANOVA – 2 independent variables (IVs) Main Effect – The effects of one independent variable (factor) summed (averaged) over all levels of the other independent variable. Interaction – When the effect of one factor is not constant across all levels of the other factors.

6. Example Effect of music and alcohol on driving performance IV 1: Music – On vs. Off IV 2: Alcohol – None vs 2 units DV: Mean no. of errors made

7. offon IV1: Music DV: mean no of errors Possible Outcomes No main effects No interaction 2units no alcohol IV2: Alcohol

8. Main effect for factor1 No main effect for factor 2 No interaction offon IV1: Music DV: mean no of errors 2units no alcohol IV2: Alcohol Possible Outcomes

9. No main effect for factor1 Main effect for factor 2 No interaction offon IV1: Music DV: mean no of errors 2units no alcohol IV2: Alcohol Possible Outcomes

10. Main effect for factor1 Main effect for factor 2 No interaction offon IV1: Music DV: mean no of errors 2units no alcohol IV2: Alcohol Possible Outcomes

11. No main effects Interaction offon IV1: Music DV: mean no of errors 2units no alcohol IV2: Alcohol Possible Outcomes

12. Main effect for factor1 Main effect for factor 2 Interaction offon IV1: Music DV: mean no of errors 2units no alcohol IV2: Alcohol Possible Outcomes

13. Example Data ABC Drug 2424 5757 2424 1111 3131 3333 4 2 243 depression Schizo- phrenia Factor 1 Factor 2

14. Drug A Type of Drug Schizophrenics Depressives Mean improvement score Drug CDrug B Interaction Graph

15. Interpreting Interactions In order to interpret any potential main effects, an analysis of Simple Effects should be conducted. A Simple Effect is the effect of one independent variable at a particular level of the other independent variable. For our example there are two simple effects for type of drug and three simple effects for type of problem. In order for a main effect to be interpretable, the simple effects for that variable must be the same for all levels of the other independent variable.

16. Simple Effects for Type of Drug There are two simple effects for type of drug: 1. the effect of drug for schizophrenics 2. the effect of drug for depressives 1. the effect of drug for schizophrenics Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the three drugs for schizophrenics only.

17. 2. the effect of drug for depressives Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the three drugs for depressives only. If the effect of drug is the same for schizophrenics and depressives then there is an interpretable main effect for drug. Is there? The question we are addressing here is: Is the effect for drug consistent (the same) for schizophrenics and depressives?

18. Simple Effects for Type of Problem There are three simple effects for type of problem: 1. the effect of type of problem for Drug A 2. the effect of type of problem for Drug B 3. the effect of type of problem for Drug C 1. the effect of type of problem for Drug A Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the participants for Drug A only.

19. 2. the effect of type of problem for Drug B Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the participants for Drug B only. 3. the effect of type of problem for Drug C Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the participants for Drug C only.

20. If differences between schizophrenics and depressives are in the same direction for all three types of drug then there is an interpretable main effect for type of problem. Is there? The question we are addressing here is: Is the effect for type of problem consistent (the same) for all three types of drug?