mixed anova - wofford college
TRANSCRIPT
![Page 1: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/1.jpg)
Mixed ANOVA
Chapter 11
![Page 2: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/2.jpg)
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
![Page 3: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/3.jpg)
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
![Page 4: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/4.jpg)
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
![Page 5: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/5.jpg)
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
![Page 6: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/6.jpg)
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
![Page 7: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/7.jpg)
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
![Page 8: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/8.jpg)
Disability and gender effects on play
Marginal means
![Page 9: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/9.jpg)
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
![Page 10: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/10.jpg)
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.*.
![Page 11: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/11.jpg)
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
![Page 12: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/12.jpg)
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
![Page 13: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/13.jpg)
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?
![Page 14: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/14.jpg)
Mixed ANOVA: LOP example Means ↓
![Page 15: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/15.jpg)
Three-way mixed ANOVA: LOP 3 (condition) x 4 (degree) x 2 (gender)
![Page 16: Mixed ANOVA - Wofford College](https://reader033.vdocuments.us/reader033/viewer/2022060710/629779ffef94201e7c3d423b/html5/thumbnails/16.jpg)
Three-way ANOVA: LOP
Condition x
TypeDegree
x Gender
Condition x
TypeDegree Condition x
Gender