mixed anova - wofford college
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Mixed ANOVA
Chapter 11
Partitioning the Variance in Factorial ANOVA
2-way ANOVA
Total Variability
Between-treatments
variability
Within-treatments
variability
Factor A
variability
Factor B
variability
Interaction
variability
atmentwithin tre
AxB)or Bor (A reatment
MS
MSF
t
Degrees of freedom
dftotal = N – 1
dfbetween = k – 1 (# groups -1)
dfwithin = N – k (or n-1)
dfA = k – 1 (# levels for factor A-1)
dfB = k – 1 (# levels for factor B-1)
dfAxB = dfbetween – dfA - dfB
dftotal = 30 – 1 = 29
dfbetween = 6 -1 = 5
dfwithin = 4+4+4+4+4+4 = 24
dfA = 2 – 1 = 1
dfB = 3 – 1 = 2
dfAxB = 5 – 1 – 2 = 2
Disability and gender effects
on play time with fathers
Dyer, McBride, & Jeans (2009). A longitudinal examination of father involvement with children with developmental delays. Journal of Early Intervention, 31, 265-281.
IV: Disability status of child 3 levels: typically developing, physical disability,
mental retardation
n = 20 per disability group
IV: Gender of child 2 levels: male, female
n = 29 male; n = 31 female
DV: # hours of play time with child per week
Disability and gender effects
on play time with fathers
Between
treatments
Main effect
Interaction
Within
treatments
dftotal = N – 1 dfbetweeen treatments = cells – 1 dfwithin = dfeach treatment
dffactor A = rows -1 dffactorB= columns – 1 dfA*B = dfbetweeen – dfA – dfB
n = 20 per grp
Disability and gender effects
on play time with fathers
Tests of Between-Subjects Effects
Dependent Variable: PLAY
182.278a 5 36.456 11.081 .000
1276.571 1 1276.571 388.025 .000
178.579 2 89.289 27.140 .000
.763 1 .763 .232 .632
4.294 2 2.147 .653 .525
177.656 54 3.290
1648.000 60
359.933 59
Source
Corrected Model
Intercept
DISABLE
GENDER
DISABLE * GENDER
Error
Total
Corrected Total
Type III Sum
of Squares df Mean Square F Sig.
R Squared = .506 (Adjus ted R Squared = .461)a.
Between
treatments
Main effect
Interaction
Within
treatments
dftotal = N – 1 dfbetweeen treatments = cells – 1 dfwithin = dfeach treatment
dffactor A = rows -1 dffactorB= columns – 1 dfA*B = dfbetweeen – dfA – dfB
60-1 = 59 6-1 = 5 60-6 = 54
3-1 = 2 2-1 = 1 5-1-2 = 2
n = 20 per grp
Disability and gender effects on play
0
2
4
6
8
typical physical mental
male
female
typical physical mental
male 7.3 3 3.2 13.5
female 6.8 3.4 4 14.2
14.1 6.4 7.2
Disability and gender effects on play
Marginal means
Disability and gender effects on play
0
2
4
6
8
typical physical mental
male
female
typical physical mental
male 7.3 3 3.2 4.5
female 6.8 3.4 4 4.733333
7.05 3.2 3.6
Disability and gender effects on play
ANOVA
PLAY
177.233 2 88.617 27.647 .000
182.700 57 3.205
359.933 59
Between Groups
Within Groups
Total
Sum of
Squares df Mean Square F Sig.
Multiple Comparisons
Dependent Variable: PLAY
Bonferroni
3.85* .566 .000 2.45 5.25
3.40* .566 .000 2.00 4.80
-3.85* .566 .000 -5.25 -2.45
-.45 .566 1.000 -1.85 .95
-3.40* .566 .000 -4.80 -2.00
.45 .566 1.000 -.95 1.85
(J) Disability status
of the child
Phys ical Disability
Mental Retardation
Typically Developing
Mental Retardation
Typically Developing
Phys ical Disability
(I) Disability status
of the child
Typically Developing
Phys ical Disability
Mental Retardation
Mean
Difference
(I-J) Std. Error Sig. Lower Bound Upper Bound
95% Confidence Interval
The mean difference is significant at the .05 level.*.
Disability and gender effects on play
If there were interactions…
typical physical mental
male 7.3 6 6.2 19.5
female 6.8 3.4 4 14.2
14.1 9.4 10.2
0
2
4
6
8
typical physical mental
male
female
typical physical mental
male 7.3 3 3.2 13.5
female 4 6.8 7 17.8
11.3 9.8 10.2
0
2
4
6
8
typical physical mental
male
female
Repeated and Mixed ANOVAs
Repeated-measures ANOVA
Within-participant or matched-participant design
Similar interpretation as 2-way ANOVAs – examine main effects and interactions
df are calculated differently; more power!
Mixed ANOVAs
Combo of between and within-participant design
Examine main effects and interactions, but some are bet-Ss and some are w/in-Ss
3-way ANOVAs (or 4-way … etc.!)
3 factors (or IVs): e.g. 3 x 3 x 2
Mixed ANOVA: LOP example
Condition (3) x Gender (2) mixed ANOVA
DV: test accuracy
Is there a M.E. of condition?
Is there a M.E. of gender?
Is there an interaction of condition x gender?
Mixed ANOVA: LOP example Means ↓
Three-way mixed ANOVA: LOP 3 (condition) x 4 (degree) x 2 (gender)
Three-way ANOVA: LOP
Condition x
TypeDegree
x Gender
Condition x
TypeDegree Condition x
Gender