Factorial ANOVA. - University of Illinois at Urbana-Champaign

92 Pages·2007·0.78 MB·English

Factorial Designs
Edpsy 580
Carolyn J. Anderson
Department of Educational Psychology
I L L I N O I S
UNIVERSITY OF ILLINOIS AT URBRANA-CHAMPAIGN
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Outline
n Motivation and Advantages
Motivation/Advantages
n Interactions: The only new concept.
Interaction
2–FactorANOVA
n 2–Factor ANOVA.
AsaGLM
Estimation n Factorial ANOVA as a GLM.
StatisticalInference
n Estimation
Examples
UnbalancedDesigns
n Statistical Inference
Higher-wayDesigns
n Examples
n Unbalanced designs
n Statistical Model and 3 or more factors. . . .
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Example 2-Way ANOVA
Example of multiple factor design: Wiley & Voss (1999)
Motivation/Advantages
lExample2-WayANOVA
Constructing arguments from multiple sources: Tasks that
lSomeData:ReadingScores
lAdvantagesofFactorial
promote understanding and not just memory for texts. Journal of
ANOVA
lMoreefficient
2 Educational Psychology, 91, 301–311.
lReduceσ(cid:15)
lExperimentalControl
lGeneralityofResults n Response/dependent variable = understanding as
lGeneralityofResults
lGeneralityofResults measured by 10 item inference verification test (IVT),
Interaction Y = IVT .
i i
2–FactorANOVA
AsaGLM
nn Factors:
Estimation
StatisticalInference
u Format (text or web)
Examples
UnbalancedDesigns u Instructions participants received: write a Narrative (N),
Higher-wayDesigns
Summary (S), Explanation (E), Argument (A).
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Some Data: Reading Scores
From Keppel:
Motivation/Advantages
lExample2-WayANOVA
n Purpose: studying things that effect reading scores.
lSomeData:ReadingScores
lAdvantagesofFactorial
ANOVA
lMoreefficient n Dependent variable: reading scores.
2
lReduceσ(cid:15)
lExperimentalControl
lGeneralityofResults
n Independent variables:
lGeneralityofResults
lGeneralityofResults
u Line length: Length of the line of text (3", 5", 7").
Interaction
2–FactorANOVA
u Contrast: The contrast between paper and print. There
AsaGLM
are three levels (low, medium, high).
Estimation
StatisticalInference
Examples
UnbalancedDesigns
Higher-wayDesigns
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Advantages of Factorial ANOVA
n Economy
n Experimental control
n Generality of results
Motivation/Advantages
lExample2-WayANOVA
lSomeData:ReadingScores Economy:
lAdvantagesofFactorial
ANOVA
lMoreefficient n Want to study the effect of two different factors on some
2
lReduceσ(cid:15)
behavior or performance measure.
lExperimentalControl
lGeneralityofResults
lGeneralityofResults n Could to two 1-factor ANOVA’s.
lGeneralityofResults
Interaction u Suppose want n = 30 per level of a factor.
2–FactorANOVA u 1-factor ANOVA for line length:
AsaGLM
3" 5" 7"
Estimation
n = 30 n = 30 n = 30 N = 90
1 2 3
StatisticalInference
u 1-factor ANOVA for Print/Paper contrast:
Examples
Low Med. High
UnbalancedDesigns
Higher-wayDesigns n = 30 n = 30 n = 30 N = 90
1 2 3
u Two separate experiments: need 180 subjects.
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More efficient
n A single experiment, two factors with n = 10 subjects per
“cell” (combination of the levels of the two factors).
Motivation/Advantages
lExample2-WayANOVA
lSomeData:ReadingScores
lAdvantagesofFactorial Line Print/paper contrast
ANOVA
lMoreefficient length Low Medium High Totals
2
lReduceσ(cid:15)
lExperimentalControl 3" n = 10 n = 10 n = 10 n = 30
lGeneralityofResults n 11 12 13 1+
lGeneralityofResults
5" n = 10 n = 10 n = 10 n = 30
lGeneralityofResults 21 22 23 2+
7" n = 10 n = 10 n = 10 n = 30
Interaction
31 32 33 3+
2–FactorANOVA Totals n = 30 n = 30 n = 30 N = 90
+1 +2 +3
AsaGLM
Estimation n N = 90 & still n = 30 subject per level of each factor.
jk
StatisticalInference
Examples
UnbalancedDesigns
Higher-wayDesigns
FactorialDesigns Slide6of92
σ
Reduce 2
(cid:15)
via Experimental Control
Motivation/Advantages
lExample2-WayANOVA
n In 1-factor ANOVA, there are uncontrolled variables that
lSomeData:ReadingScores
lAdvantagesofFactorial
effect the dependent variable.
ANOVA
lMoreefficient
2
lReduceσ(cid:15)
n Uncontrolled and unsystematic variables.
lExperimentalControl
lGeneralityofResults
lGeneralityofResults
lGeneralityofResults n Source of variance due to
Interaction
u Random assignment to groups (or random sampling).
2–FactorANOVA
AsaGLM
u Individual differences (subject variables).
Estimation
StatisticalInference n These contribute to σ2.
(cid:15)
Examples
UnbalancedDesigns
Higher-wayDesigns
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Experimental Control
n Can reduce σ2 and increase power by including variable(s)
(cid:15)
that effect the dependent variable even though you aren’t
especially interested in the extra variable.
Motivation/Advantages
lExample2-WayANOVA
lSomeData:ReadingScores n For example. . . In reading experiment with contrast & line
lAdvantagesofFactorial
length as factors, reading level or achievement effects
ANOVA
lMoreefficient
2 reading scores.
lReduceσ(cid:15)
lExperimentalControl
lGeneralityofResults u To reduce σ2, use homogenous groups → subjects all
lGeneralityofResults (cid:15)
lGeneralityofResults same reading level.
Interaction
u Drawback: Results only generalize to others of the same
2–FactorANOVA
reading level.
AsaGLM
Estimation
n Alternative: use reading level as a factor:
StatisticalInference
u Randomly select individuals from each of the reading
Examples
levels and randomly assign to levels of the other factors.
UnbalancedDesigns
u Advantages of adding another factor:
Higher-wayDesigns
Gain reduction in σ2 and therefore increase power.
n
(cid:15)
Results more generalizable.
n
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Generality of Results
n Results from single factor experiments lack generality to the
Motivation/Advantages
lExample2-WayANOVA
extent to which specific values of other relevant variables are
lSomeData:ReadingScores
lAdvantagesofFactorial
held constant.
ANOVA
lMoreefficient
2
lReduceσ(cid:15)
lExperimentalControl
lGeneralityofResults n Factorial experiments allow effects of an independent
lGeneralityofResults
variable to be averaged over levels of other relevant
lGeneralityofResults
variable(s).
Interaction
2–FactorANOVA
AsaGLM
n Example: reading study. . .
Estimation
StatisticalInference
Examples
UnbalancedDesigns
Higher-wayDesigns
FactorialDesigns Slide9of92
Generality of Results
Example: reading study
Motivation/Advantages
lExample2-WayANOVA
n An overall effect of one factor is referred to as a main effect
lSomeData:ReadingScores
lAdvantagesofFactorial
— effect obtained by combining scores across levels of other
ANOVA
lMoreefficient
factor(s).
2
lReduceσ(cid:15)
lExperimentalControl
lGeneralityofResults
n Can collapse over print/paper contrast to look at main effect
lGeneralityofResults
lGeneralityofResults
of text length on reading scores.
Interaction
2–FactorANOVA n Effect of text length represents a more general effect
AsaGLM because average over 3 levels of paper/print contrast.
Estimation
n Can collapse over text length to look at main effects of
StatisticalInference
print/paper contrast.
Examples
UnbalancedDesigns
Higher-wayDesigns
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