Within-subjects
One-way ANOVA
2009 Methodology A - Lecture 5
Outline
Review of Last Week
1. Review of Last Week
1.
2. Today’s Learning Objectives
2.
3. Experimental design
3.
a. Within-subjects variables
4.
b. Order of conditions
5.
4. Within-subjects one-way ANOVA
5. Planned Comparisons
Between-subjects One-way ANOVA
6. What two columns of data are
required to set up a betweensubjects one-way ANOVA?
6. Review of Learning Objectives
7. Vocabulary
1.
2.
3.
4.
5.
6.
Within-subjects One-way ANOVA
7. Which columns of data are
required to set up a withinsubjects one-way ANOVA?
8. Which assumptions should you
test when conducting a withinsubjects one-way ANOVA?
9. If the assumption of sphericity is
violated, what should you do?
10. Which numbers do you need to
include when reporting the
results of a within-subjects oneway ANOVA?
Planned Comparisons
11. How are planned comparisons
different from post-hoc
analyses?
12. What is a trend analysis?
Within-subjects Factors
Within-Subjects
Experimental
Design
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
Within-subjects Factors
Within-subjects Design
Advantages
Neutral
Neutral
Neutral
Happy
Neutral
Happy
Individual differences
Post-hoc Analyses
9. Why are post-hoc anaylses
run?
10. How do you calculate the
critical p-value for Bonferroni
correction?
11. When is Bonferroni correction
likely to be too conservative?
1 2 3 4 5 6 7 8 9
! Controls for individual
differences
! Requires fewer participants
! More powerful
! Ensures equal number of
participants in each
condition
Happy
7. Which assumptions should you
test when conducting a
between-subjects one-way
ANOVA?
8. Which numbers do you need to
include when reporting the
results of a between-subjects
one-way ANOVA?
Within-subjects
Today’s Learning Objectives
Experimental Design
What types of variables suggest
a within-subjects design?
What are the advantages of a
within-subjects design?
What are the disadvantages of a
within-subjects design?
How do you minimise the
disadvantages of a withinsubjects design?
What are the different ways you
can assign participants to
conditions?
How many different orders would
you need to fully counterbalance
5 conditions?
Experimental Design
What types of variables require
a between-subjects design?
What are the advantages of a
between-subjects design?
What are the disadvantages of
a between-subjects design?
How do you minimise the
disadvantages of a betweensubjects design?
What are the different ways you
can assign participants to
conditions?
Individual differences
Happy
Disadvantages
! Not possible for some
variables (e.g. sex)
! Order effects
! Carryover effects
! Practice effects
! Participant fatigue
! Large numbers of
conditions are difficult to
counterbalance
Minimising the disadvantages
1. Counterbalancing condition order
2. Randomisation of condition order
3. Analyse for order effects
4. Long breaks between conditions
Counterbalancing
A
Orders:
A-B
B-A
Counterbalancing
B
Counterbalancing
Randomisation
If you have more than 3
conditions and order
effects are unlikely, you
can randomise the order of
the conditions.
4 ! 3 ! 2 ! 1 = 4! = 24
A
B
C
Orders:
A-B-C
A-C-B
B-A-C
B-C-A
C-A-B
C-B-A
ANOVA
1.Set up the data
2.Set up the ANOVA
3.Interpret the results
To fully counterbalance N conditions,
you need N! different orders. This is
difficult for more than 3 conditions.
Avoid within-subjects designs if you have
many conditions that are likely to cause
order effects. Between-subjects designs
are more appropriate in this case.
4.Write up the results
Set Up the Data
Symmetry Preference
Set Up the Data
Level 1
Level 2
Level 3
Level 1
Level 2
Level 3
Subject 1
x1
y1
z1
Subject 1
x1
y1
z1
Subject 2
x2
y2
z2
Subject 2
x2
y2
z2
Subject 3
x3
y3
z3
Subject 3
x3
y3
z3
Subject 4
x4
y4
z4
Subject 4
x4
y4
z4
Subject 5
x5
y5
z5
Subject 5
x5
y5
z5
Subject 6
x6
y6
z6
Subject 6
x6
y6
z6
Asymmetric
Original
Symmetric
How attractive is this face?
Set Up the Data
Set Up the Data
Set Up the ANOVA
Set Up the ANOVA
Set Up the ANOVA
Set Up the ANOVA
Interpret the Results
Interpret the Results
Write Up the Results
asymmetric
original
symmetric
Subject 1
3
4
4
Subject 2
2
3
4
Subject 3
4
5
7
Subject 4
3
3
3
Subject 5
2
2
3
Subject 6
2
1
2
Analysis revealed a main
effect of symmetry,
F(1.50, 30.0) = 43.6, p < .001.
Planned Comparisons
Polynomial Contrasts
1.00
A significant linear trend,
F(1, 20) = 59.5, p < .001,
indicated that attractiveness
ratings increased as
symmetry increased.
0.75
0.50
0.25
0
asymmetric
original
symmetric
Vocabulary
carryover effects
counterbalance
Greenhouse-Geisser
Mauchly’s test
order effects
planned comparisons
power
practice effects
sphericity
trend
within-subjects