Transcript Lecture 14: Factorial ANOVA Practice

Lecture 14:
Factorial ANOVA Practice
Laura McAvinue
School of Psychology
Trinity College Dublin
Effectiveness of Therapy on Depression
Type of Therapy
CBT
Gender
Males
Females
Psychoanalytic Drug
10
16
24
8
18
26
6
20
28
22
6
20
20
4
22
18
8
24
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…
Mean Number of Depressive Symptoms for Men &
Women receiving Three Kinds of Therapy
CBT
Male
Female
Total
Psycho- Drug
analytic
Total
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…
Mean Number of Depressive Symptoms for Men &
Women receiving Three Kinds of Therapy
CBT
Psycho- Drug
analytic
18
26
Male
8
Female
20
6
22
Total
14
12
24
Total
17.33
16
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…
Which Means do we compare when investigating if
there is a main effect of Gender?
CBT
Psycho- Drug
analytic
18
26
Male
8
Female
20
6
22
Total
14
12
24
Total
17.33
16
Examine the Means Table…
Which Means do we compare when investigating if
there is a main effect of Therapy?
CBT
Psycho- Drug
analytic
18
26
Male
8
Female
20
6
22
Total
14
12
24
Total
17.33
16
Examine the Means Table…
Which Means do we compare when investigating if
there is an Interaction between Gender & Therapy?
CBT
Psycho- Drug
analytic
18
26
Male
8
Female
20
6
22
Total
14
12
24
Total
17.33
16
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
Levene's Test of Equality of Error Variancesa
Dependent Variable: depress
F
df1
.000
df2
5
12
Sig .
1.000
Tests the null hypothesis that the error variance of the
dependent variable is equal across g roups.
a. Design: Intercept+gender+therapy+g ender * therapy
• Is Levene’s statistic significant?
• What can we conclude from this?
Examine the Tests of Between-Subjects
Effects
Tests of Between-Subjects Effects
Dependent Variable: depress
Source
Corrected Model
Intercept
gender
therapy
gender * therapy
Error
Total
Corrected Total
Type III Sum
of Squares
952.000a
5000.000
8.000
496.000
448.000
48.000
6000.000
1000.000
df
5
1
1
2
2
12
18
17
Mean Square
190.400
5000.000
8.000
248.000
224.000
4.000
F
47.600
1250.000
2.000
62.000
56.000
Sig .
.000
.000
.183
.000
.000
a. R Squared = .952 (Adjusted R Sq uared = .932)
• Is there a main effect of Gender?
– No!
• Report this…
– There was no effect of Gender, F (1, 12) = 2, p = .183
Examine the Tests of Between-Subjects
Effects
Tests of Between-Subjects Effects
Dependent Variable: depress
Source
Corrected Model
Intercept
gender
therapy
gender * therapy
Error
Total
Corrected Total
Type III Sum
of Squares
952.000a
5000.000
8.000
496.000
448.000
48.000
6000.000
1000.000
df
5
1
1
2
2
12
18
17
Mean Square
190.400
5000.000
8.000
248.000
224.000
4.000
F
47.600
1250.000
2.000
62.000
56.000
Sig .
.000
.000
.183
.000
.000
a. R Squared = .952 (Adjusted R Sq uared = .932)
• Is there a main effect of Therapy?
– Yes!
• Report this…
– There was a main effect of Therapy, F (2, 12) = 62, p <.001
Examine the Tests of Between-Subjects
Effects
Tests of Between-Subjects Effects
Dependent Variable: depress
Source
Corrected Model
Intercept
gender
therapy
gender * therapy
Error
Total
Corrected Total
Type III Sum
of Squares
952.000a
5000.000
8.000
496.000
448.000
48.000
6000.000
1000.000
df
5
1
1
2
2
12
18
17
Mean Square
190.400
5000.000
8.000
248.000
224.000
4.000
F
47.600
1250.000
2.000
62.000
56.000
Sig .
.000
.000
.183
.000
.000
a. R Squared = .952 (Adjusted R Sq uared = .932)
• 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
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…
Mean Level of Recall for old & young participants
learning material under three conditions
Counting Adjective Imagery Total
Old
Young
Total
Have a look at the data…
Mean Level of Recall for Old & Young Participants
learning Material under Three Conditions
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
Does there appear to be a main
effect of age?
Count
Adj
Image
Total
7
11
13.4
10.47
Young 6.5
14.8
17.6
12.97
Total
12.9
15.5
Old
6.75
Does there appear to be a main
effect of learning strategy?
Count
Adj
Image
Total
7
11
13.4
10.47
Young 6.5
14.8
17.6
12.97
Total
12.9
15.5
Old
6.75
Does there appear to be an interaction
between age & learning strategy?
Count
Adj
Image
Total
7
11
13.4
10.47
Young 6.5
14.8
17.6
12.97
Total
12.9
15.5
Old
6.75
What does the ANOVA tell us?
• Main effect of age
Tests of Between-Subjects Effects
– F (1, 54) = 11.08, p = .002
Dependent Variable: rcall
Source
Corrected Model
Intercept
age
conditio
age * conditio
Error
Total
Corrected Total
Type III Sum
of Squares
969.283a
8236.817
93.750
807.633
67.900
456.900
9663.000
1426.183
df
5
1
1
2
2
54
60
59
Mean Square
193.857
8236.817
93.750
403.817
33.950
8.461
a. R Squared = .680 (Adjusted R Sq uared = .650)
F
22.911
973.491
11.080
47.726
4.012
Sig .
.000
.000
.002
.000
.024
• 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.