Lecture 16:Factorial ANOVA Interactions

Practice

Laura McAvinue

School of Psychology

Trinity College Dublin

Recall Eysenck’s Study

Eysenck was interested in the effects of Age & Depth of Processing on Recall. He obtained a sample of 60 old & young participants and randomly assigned them to three groups. All three groups were given a list of words to study. The first group was asked to count the number of letters in each word, the second group was asked to think of an adjective that could be used with the word and a third group was asked to form an image associated with the word.

The Data

Count Adj Image Total

Old 7 11 13.4 10.47

Young 6.5 14.8 17.6 12.97

Total 6.75 12.9 15.5

• This factorial ANOVA will allow us to investigate three kinds of effects. What are these?

– Main effect due to Age– Main effect due to Learning Condition– Interaction between Age & Learning Condition

Factorial ANOVA

• Dependent variable = Recall

• Independent variables = Age & Learning Condition

• Ask for descriptive statistics

• Ask for homogeneity of variance test

• Ask for profile plot of the means

Run the Factorial ANOVA

Check the Assumptions

• Is Levene’s statistic significant?– Yes!

• What can we conclude from this?– We cannot assume equality of variance

among the groups– Results of ANOVA may not be valid

Levene's Test of Equality of Error Variancesa

Dependent Variable: rcall

3.167 5 54 .014F df1 df2 Sig.

Tests the null hypothesis that the error variance of thedependent variable is equal across groups.

Design: Intercept+age+conditio+age * conditioa.

• Is there a main effect of age? – Report this

• Is there a main effect of Condition? – Report this

• Is there an interaction between Age & Condition? – Report this

Examine the Output

What does the ANOVA tell us?

Tests of Between-Subjects Effects

Dependent Variable: rcall

969.283a 5 193.857 22.911 .000

8236.817 1 8236.817 973.491 .000

93.750 1 93.750 11.080 .002

807.633 2 403.817 47.726 .000

67.900 2 33.950 4.012 .024

456.900 54 8.461

9663.000 60

1426.183 59

SourceCorrected Model

Intercept

age

conditio

age * conditio

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

R Squared = .680 (Adjusted R Squared = .650)a.

• Main effect of age– F (1, 54) = 11.08, p = .002

• Main effect of Condition – F (2, 54) = 47.726, p

< .001

• Interaction between Age & Condition – F (2, 54) = 4.012, p = .024

• What is a main effect?– The effect of one independent variable averaged across the levels

of the other independent variable

– The effect of one independent variable ignoring the other variable

• What is a simple effect?– The effect of one variable at one level of another variable

• Should we do an analysis of simple effects here?– Yes!

• Why?– Because there is a significant interaction between Age & Condition

– In order to tease apart the interaction

Simple Effects

What are the Simple Effects we can analyse?

• The effects of Age at each level of Learning Condition

– The effect of age under counting condition– The effect of age under adjective condition– The effect of age under imagery condition

• The effects of Learning Condition at each level of Age

– The effect of learning condition for young participants– The effect of learning condition for old participants

• Split File

• Organise output according to Learning Condition

• One Way ANOVA with Recall as the dependent variable & Age as the independent variable

• Split File

• Organise output according to Age

• One Way ANOVA with Recall as the dependent variable and Learning Condition as the Independent variable

Simple Effects of Age at each Level of

Learning Condition

Simple Effects of Learning Condition at

each Level of Age

Simple Effects ANOVA Table

Source of Variation

SS Df MS F

Age

Age at Counting

Age at Adjective

Age at Imagery

Learning Cond.

Learning at Old

Learning at Young

Error

Simple Effects ANOVA Table

Source of Variation

SS Df MS F

Age

Age at Counting 1.25 1 1.25 .148

Age at Adjective 72.2 1 72.2 8.53

Age at Imagery 88.2 1 88.2 10.424

Learning Cond.

Learning at Old 209.067 2 104.533 12.35

Learning at Young 666.467 2 333.233 39.38

Error 456.9 54 8.461

Find the Critical F Values for each Simple Effect

• Use the F Distribution Table…

• Critical value for simple effects of age = .05, 4.02 = .01, 7.12

• Critical value for simple effects of Condition = .05, 3.17 = .01, 5.01

Simple Effects ANOVA Table

Source of Variation

SS Df MS F Crit F

p<.05

Crit F

p<.01

Signif?

Age

Counting 1.25 1 1.25 .148 4.02 7.12 No!

Adjective 72.2 1 72.2 8.53 4.02 7.12 Yes

Imagery 88.2 1 88.2 10.424 4.02 7.12 Yes

Learning Cond.

Old 209.067 2 104.533 12.35 3.17 5.01 Yes

Young 666.467 2 333.233 39.38 3.17 5.01 Yes

Error 456.9 54 8.461

Interpretation

• Explain the effects of Age & Learning Strategy on Recall, drawing on the results of the ANOVA to back up your explanation.

• Are there any further analyses that you think might be required?– posthoc

• Examine the dataset…

• What is the dependent variable?– ‘tpstress’, perceived stress

• What are the independent variables?– ‘sex’ & ‘age’

• What are the levels of each variable?– Sex = male / female– Age = 18-29 / 30-44 / 45+

• What do you think this study is investigating?– The effects of sex & age on perceived stress

Example 2: ANOVA Interactions Dataset

• Ask for descriptives, homogeneity test & a means plot

Run the Two Way Factorial ANOVA

Have a look at the means plot

• Main effect of sex?

• Main effect of age?

• Interaction?

Have a look at the results of the ANOVA

• Main effect of sex?

• Main effect of age?

• Interaction?

Tests of Between-Subjects Effects

Dependent Variable: total perceived stress

494.549a 5 98.910 2.958 .012

298051.152 1 298051.152 8914.003 .000

274.236 1 274.236 8.202 .004

178.315 2 89.158 2.666 .071

58.365 2 29.183 .873 .419

14277.294 427 33.436

324089.000 433

14771.843 432

SourceCorrected Model

Intercept

sex

agegp3

sex * agegp3

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

R Squared = .033 (Adjusted R Squared = .022)a.

• Are any other analyses required?

• Explain the results of the study in your own words.

Interpretation