outline review of last week within-subject factorial
TRANSCRIPT
Within-subject factorial ANOVA
2008 Methodology A - Lecture 8
1. Review of Last Week
2. Today’s Learning Objectives
3. Effect Size for ANOVA
4. Within-subjects factorial ANOVA
5. Power
6. Review of Learning Objectives
7. Vocabulary
8. Sample Exam Questions
Outline Review of Last WeekFactorial Design
1. What is meant by ‘factors must be orthogonal’?
2. How many factors are in a 2x3 design?
3. How many groups are in a 2x2 design?
4. What would you call a design with 2 factors that had 3 levels each?
5. What is a main effect?6. What is an interaction?7. For a 2x2 design, be able to
recognise all of the possible graphical representations of a main effect or interaction.
Between-subject factorial ANOVA8. Which columns of data are
required to set up a between-subjects factorial ANOVA?
9. Which assumptions should you test when conducting a between-subjects factorial ANOVA?
10. If the assumption of homogeneity of variance is violated, what should you do?
11. Which numbers do you need to include when reporting the results of a between-subjects factorial ANOVA?
12. What is meant by “the main effect was qualified by an interaction”?
Today’s Learning ObjectivesWithin-subject factorial ANOVA
1. Which columns of data are required to set up a within-subjects factorial ANOVA?
2. Which assumptions should you test when conducting a within-subjects factorial ANOVA?
3. If the assumption of sphericity is violated, what should you do?
4. Which numbers do you need to include when reporting the results of a within-subjects factorial ANOVA?
Effect Size5. What is the most common
measure of effect size for ANOVA?6. What does a partial eta-squared
of .50 mean?
Power7. What does it mean if your
experiment has power of .20?8. If effect size increases, does power
increase or decrease?9. What can you do to increase the
power of an experiment?10. Which design is more powerful,
between-subjects or within-subject?
11. What do you need to know in order to calculate the power of a study?
12. What do you need to know in order to calculate the number of participants you will need for a study?
348
Effect Size
partial eta-squared (!p2)
Equal to the percent of variation in the dependent variable that is accounted for by the dependent variable(s)
Partial eta-squared (!p2)
Types of ANOVA
One IV More than one IV
OneOne-way between-subjects
Factorialbetween-subjects
Mixed-design(split-plot)
AllOne-way
within-subjectFactorial
within-subject
Number of Independent Variables
Conditio
ns p
er
Subje
ct
plus 1 or more continuous IVs = ANCOVA
1.Set up the data
2.Set up the ANOVA
3.Interpret the results
4.Write up the results
ANOVA Symmetry Preference
How attractive is this face?
Symmetricmale face
Asymmetricmale face
Symmetricfemale face
Asymmetricfemale face
No Effects
symmetric asymmetric
female facesmale faces7
6
5
4
3
2
1Mean a
ttra
ctiveness r
ating
No Effects
symmetric asymmetric
female facesmale faces
Main Effect of Face Sex
7
6
5
4
3
2
1Mean a
ttra
ctiveness r
ating
No Effects
symmetric asymmetric
female facesmale faces
Main Effect of Face SexMain Effect of Symmetry
7
6
5
4
3
2
1Mean a
ttra
ctiveness r
ating
Interaction between Face Sex and Symmetry
symmetric asymmetric
female facesmale faces7
6
5
4
3
2
1Mean a
ttra
ctiveness r
ating
Set Up the Data
Factor1aFactor2a
Factor1bFactor2a
Factor1aFactor2b
Factor1bFactor2b
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Subject 6
aa1 ba1 ab1 bb1
aa2 ba2 ab2 bb2
aa3 ba3 ab3 bb3
aa4 ba4 ab4 bb4
aa5 ba5 ab5 bb5
aa6 ba6 ab6 bb6
Set Up the Data
asymfemale
symfemale
asymmale
symmale
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Subject 6
2 5 1 3
3 6 2 4
4 4 3 5
3 7 2 3
4 5 2 4
2 6 3 4
Set Up the Data Set Up the ANOVA Set Up the ANOVA
Set Up the ANOVA Interpret the Results Homogeneity of Variance
Fmax = 1.1402 / 0.7462 = 2.34
Sphericity
317, 357
The book recommends routinely interpreting the G-G values, even when Mauchly’s test is non-significant (p. 317). However, I still want you to know when you need to check for sphericity and which values you should interpret depending on the significance of Mauchly’s test.
Write Up the Results Write Up the ResultsAnalysis revealed main effects of face sex, F(1, 20) = 17.6, p < .001, !p
2 = .47, and symmetry, F(1, 20) = 93.1, p < .001, !p
2 = .82.
Write Up the ResultsAnalysis revealed main effects of face sex, F(1, 20) = 17.6, p < .001, !p
2 = .47, and symmetry, F(1, 20) = 93.1, p < .001, !p
2 = .82.
Write Up the ResultsThese main effects were qualified by an interaction between face sex and symmetry, F(1, 20) = 12.6, p = .002, !p
2 = .39.
Simple Effects
343-7
361-4
Between-subjects
Within-subject
Simple EffectsSymmetric faces were judged as more attractive than asymmetric faces for both male faces, t(20) = 4.26, p < .001, d = 0.93, and female faces, t(20) = 7.71, p < .001, d = 1.68.
Simple EffectsSymmetric faces were judged as more attractive than asymmetric faces for both male faces, t(20) = 4.26, p < .001, d = 0.93, and female faces, t(20) = 7.71, p < .001, d = 1.68.
Simple EffectsFemale faces were judged as more attractive than male faces when faces were symmetric, t(20) = 5.59, p < .001, d = 1.22, but not when faces were asymmetric, t(20) = 0.28, p = .79, d = 0.06.
Simple EffectsFemale faces were judged as more attractive than male faces when faces were symmetric, t(20) = 5.59, p < .001, d = 1.22, but not when faces were asymmetric, t(20) = 0.28, p = .79, d = 0.06.
249-55
Power
Power is the chance that a study will find a significant effect, if there is one to find.
It varies from 0 (0%) to 1 (100%).
Factors Influencing Power
The effect size (actual or predicted)
The critical p-value
The number of participants
The type of statistical test
The study design
Whether the hypothesis is one-tailed
or two-tailed1
Calculating Power
The effect size
The critical p-value
The number of participants
Each statistical test requires a special power calculation. Although you will not need to know these for this class, see http://statpages.org/#Power for a list of online power calculators.
Calculating Number of Participants
The effect size
The critical p-value
The power level
critical p-valueeffect sizenon-parametricone-tailedparametricpartial eta squaredpowersimple effectstwo-tailed
Vocabulary
Sample exam questionsMale and female participants in an experiment were instructed to choose the more masculine face from 10 pairs of male faces and 10 pairs of female faces. Each participant saw all 20 face pairs. The experimenter’s hypothesis is that number of correct trials will be greater for male faces than for female faces.
What is/are the dependent variable(s)?
a) the sex of the facesb) the sex of the participantsc) the number of correct trialsd) both A and B
Sample exam questionsMale and female participants in an experiment were instructed to choose the more masculine face from 10 pairs of male faces and 10 pairs of female faces. Each participant saw all 20 face pairs. The experimenter’s hypothesis is that number of correct trials will be greater for male faces than for female faces.
What is/are the independent variable(s)?
a) the sex of the facesb) the sex of the participantsc) the number of correct trialsd) both A and B
Sample exam questions
What statistic would you use to test the hypothesis?
a) one-sample t-testb) independent samples t-testc) paired samples t-testd) between-subjects one-way ANOVA
Male and female participants in an experiment were instructed to choose the more masculine face from 10 pairs of male faces and 10 pairs of female faces. Each participant saw all 20 face pairs. The experimenter’s hypothesis is that number of correct trials will be greater for male faces than for female faces.