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