Lecture 14:Factorial ANOVA Practice

Laura McAvinue

School of Psychology

Trinity College Dublin

CBT Psychoanalytic Drug

Males 10 16 24

8 18 26

6 20 28

Females 22 6 20

20 4 22

18 8 24

Type of Therapy

Gen

der

Effectiveness of Therapy on Depression

Software / Kevin Thomas / Factorial ANOVA dataset

The variables in SPSS…

• How many variables are there?– 3

• What are they?– Gender, Therapy, Depress

• Which are the independent & dependent variables?– Independent = Gender, Therapy– Dependent = Depress

• How many levels does each independent variable have?– Gender = 2– Therapy = 3

The variables in SPSS…

• How many people took part in the study?– 18

• How many men and how many women?– 9 men & 9 women

• How many men got CBT?– 3

• How many women got psychoanalytic therapy?– 3

Have a look at the data…

CBT Psycho-analytic

Drug Total

Male

Female

Total

Mean Number of Depressive Symptoms for Men & Women receiving Three Kinds of Therapy

Have a look at the data

• To obtain the ‘totals’– Analyse, Descriptive Statistics, Explore– Dependent list = depress– Factor list = gender, therapy

• To obtain the cell means– Data, split file, organise output by groups– Groups based on gender– File is already sorted

– Analyse, Descriptive Statistics, Explore– Dependent list = depress– Factor list = therapy

Have a look at the data…

CBT Psycho-analytic

Drug Total

Male 8 18 26 17.33

Female 20 6 22 16

Total 14 12 24

Mean Number of Depressive Symptoms for Men & Women receiving Three Kinds of Therapy

Three kinds of Effects

• When we run the Factorial ANOVA, we will be interested in investigating if there are three kinds of effects that are causing the data to vary. What are these?

– Main effect due to Gender– Main effect due to Therapy– An Interaction between Therapy & Gender

Examine the Means Table…

CBT Psycho-analytic

Drug Total

Male 8 18 26 17.33

Female 20 6 22 16

Total 14 12 24

Which Means do we compare when investigating if there is a main effect of Gender?

Examine the Means Table…

CBT Psycho-analytic

Drug Total

Male 8 18 26 17.33

Female 20 6 22 16

Total 14 12 24

Which Means do we compare when investigating if there is a main effect of Therapy?

Examine the Means Table…

CBT Psycho-analytic

Drug Total

Male 8 18 26 17.33

Female 20 6 22 16

Total 14 12 24

Which Means do we compare when investigating if there is an Interaction between Gender & Therapy?

Run the ANOVA…

• Analyse>General Linear Model>Univariate– Dependent Variable: depression– Fixed Factors: these are our two IVs (gender & therapy)

• Plots – Horizontal axis: put one IV on this axis (typically, put IVs that have more

than two levels here)– Separate Lines: put the other IV in this window (typically, put IVs that

have only two levels here)– Don’t forget to click Add

• Options – Descriptive statistics and – homogeneity tests

• Continue • OK

Scroll through the output…

• Between-subjects factors– The independent variables in the analysis & the number of levels

in each

• Descriptive Statistics– Means, SDs & n for each level of the independent variables

• Levene’s test– Test for homogeneity of Variance

• Test of Between-Subjects Effects– Significance of Main Effects & Interactions

• Profile Plots– Plot of the means

Examine the Means Plot

• Does there appear to be a main effect of gender?

• Does there appear to be a main effect of Therapy?

• Does there appear to be an interaction?

Check the Assumptions

• Is Levene’s statistic significant?

• What can we conclude from this?

Levene's Test of Equality of Error Variancesa

Dependent Variable: depress

.000 5 12 1.000F df1 df2 Sig.

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

Design: Intercept+gender+therapy+gender * therapya.

Examine the Tests of Between-Subjects Effects

• Is there a main effect of Gender?– No!

• Report this…– There was no effect of Gender, F (1, 12) = 2, p = .183

Tests of Between-Subjects Effects

Dependent Variable: depress

952.000a 5 190.400 47.600 .000

5000.000 1 5000.000 1250.000 .000

8.000 1 8.000 2.000 .183

496.000 2 248.000 62.000 .000

448.000 2 224.000 56.000 .000

48.000 12 4.000

6000.000 18

1000.000 17

SourceCorrected Model

Intercept

gender

therapy

gender * therapy

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

R Squared = .952 (Adjusted R Squared = .932)a.

Examine the Tests of Between-Subjects Effects

• Is there a main effect of Therapy?– Yes!

• Report this…– There was a main effect of Therapy, F (2, 12) = 62, p <.001

Tests of Between-Subjects Effects

Dependent Variable: depress

952.000a 5 190.400 47.600 .000

5000.000 1 5000.000 1250.000 .000

8.000 1 8.000 2.000 .183

496.000 2 248.000 62.000 .000

448.000 2 224.000 56.000 .000

48.000 12 4.000

6000.000 18

1000.000 17

SourceCorrected Model

Intercept

gender

therapy

gender * therapy

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

R Squared = .952 (Adjusted R Squared = .932)a.

Examine the Tests of Between-Subjects Effects

• Is there a significant interaction between Gender & Therapy?– Yes!

• Report this…– There was a significant interaction between Gender & Therapy, F (2, 12) = 56,

p < .001

Tests of Between-Subjects Effects

Dependent Variable: depress

952.000a 5 190.400 47.600 .000

5000.000 1 5000.000 1250.000 .000

8.000 1 8.000 2.000 .183

496.000 2 248.000 62.000 .000

448.000 2 224.000 56.000 .000

48.000 12 4.000

6000.000 18

1000.000 17

SourceCorrected Model

Intercept

gender

therapy

gender * therapy

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

R Squared = .952 (Adjusted R Squared = .932)a.

Example 2, Eysenck’s Study

• Factorial ANOVA dataset– Variables: age, condition, recall

• Have a look at the dataset…

• What is the dependent variable?– Recall

• What are the independent variables?– Age & Condition

• What are the levels of Age?– Old & Young

Example 2, Eysenck’s Study

• What are the levels of Condition?– Counting, Adjective, Imagery

• Describe this ANOVA in two ways– Two Way Factorial ANOVA– 2x3 Factorial ANOVA

• How many people participated in this experiment?– 60

• How many old & how many young?– 30 old & 30 young

Example 2, 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.

What are the null and research hypotheses for this study?

Hypotheses

• Ho regarding Age:– There is no effect of age– Old and young participants have the same mean level of recall

across all conditions of processing

• Halt regarding Age:– There is a main effect of age– Old & young participants’ mean level of recall differs significantly

across all conditions of processing

Hypotheses

• Ho regarding Depth of Processing:– There is no effect of depth of processing– For both young and old participants, mean recall is the same

under each condition of processing

• Halt regarding Depth of Processing:– There is a main effect of depth of processing– For both young and old participants, at least one processing

condition mean is significantly different from the others

Hypotheses

• Ho regarding an Interaction between Age & Depth of Processing:– There is no interaction between age & depth of processing

• Halt regarding an Interaction between Age & Depth of Processing :– There is a significant interaction between age & depth of

processing– Age & depth of processing have a combined effect on recall

Run the ANOVA…

• Analyse>General Linear Model>Univariate

• Plots

• Options – Descriptive statistics

• Continue • OK

Have a look at the data…

Counting Adjective Imagery Total

Old

Young

Total

Mean Level of Recall for old & young participants learning material under three conditions

Have a look at the data…

Counting Adjective Imagery Total

Old 7 11 13.4 10.47

Young 6.5 14.8 17.6 12.97

Total 6.75 12.9 15.5

Mean Level of Recall for Old & Young Participants learning Material under Three Conditions

Does there appear to be a main effect of age?

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

Does there appear to be a main effect of learning strategy?

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

Does there appear to be an interaction between age & learning strategy?

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

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

In your own words, explain what is happening in these data?

There is a main effect of Age and Condition and a significant interaction between Age & Condition. It seems that overall, greater depth of processing leads to better recall. Also, older participants tend to show poorer recall than younger participants. However, this is only during conditions of deeper processing of material. In the counting condition, which involved a very shallow level of processing, older and younger participants performed equally well. This finding suggests that older participants do not benefit as much as the younger participants do from deeper processing of the material.