PSY 2005

Week 10 – Simple Effects

Factorial Analysis of Variance

Simple Effects

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.

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 :

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.

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

off on

IV1: Music

DV

: m

ean

no

of e

rror

s

Possible Outcomes

• No main effects• No interaction

2units

no alcohol

IV2: Alcohol

• Main effect for factor1• No main effect for factor 2• No interaction

off on

IV1: Music

DV

: m

ean

no

of e

rror

s

2units

no alcohol

IV2: Alcohol

Possible Outcomes

• No main effect for factor1• Main effect for factor 2• No interaction

off on

IV1: Music

DV

: m

ean

no

of e

rror

s

2units

no alcohol

IV2: Alcohol

Possible Outcomes

• Main effect for factor1• Main effect for factor 2• No interaction

off on

IV1: Music

DV

: m

ean

no

of e

rror

s

2units

no alcohol

IV2: Alcohol

Possible Outcomes

• No main effects• Interaction

off on

IV1: Music

DV

: m

ean

no

of e

rror

s

2units

no alcohol

IV2: Alcohol

Possible Outcomes

• Main effect for factor1• Main effect for factor 2• Interaction

off on

IV1: Music

DV

: m

ean

no

of e

rror

s

2units

no alcohol

IV2: Alcohol

Possible Outcomes

Example Data

A B C

Drug

24

57

24

11

31

33

3x 6x 3x

1x 2x 3x

x

4

2

x 2 4 3 3x

depression

Schizo-phrenia

Factor 1

Factor 2

Drug A

Type of Drug

Schizophrenics

DepressivesMean improvement score

Drug CDrug B

Interaction Graph

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.

Simple Effects for Type of Drug

• There are two simple effects for type of drug:

1. the effect of drug for schizophrenics2. 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.

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?

Simple Effects for Type of Problem

• There are three simple effects for type of problem:

1. the effect of type of problem for Drug A2. the effect of type of problem for Drug B3. 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.

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.

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?