Chapter 12 Introduction to MANOVA

Chapter 12 Multivariate ANOVA (MANOVA)

Introduction to MANOVA

Independent Variable(s) t-test

One-way ANOVA

Control

Experimental

Control

Exp1

Exp2

C1 . . . Cn

E1 . . . En

C1 . . . Cn

E11 . . . En1

E12 . . . En2

Control

Exp1

Exp2

Male Two-way ANOVA Female

(M)ANOVA One-way (M)ANOVA Control

Exp1

Exp2

mDV1 mDV2 mDV3

mDV1 mDV2 mDV3

mDV1 mDV2 mDV3

MANOVA Hypotheses Ho mDV1 mDV2 mDV3

=

mDV1 mDV2 mDV3

≠

mDV1 mDV2 mDV3

=

mDV1 mDV2 mDV3

≠

mDV1 mDV2 mDV3

H1

mDV1 mDV2 mDV3

MANOVA Test Statistics t-test t-ratio ANOVA F-ratio

Ho mDV1 mDV2 mDV3

=

mDV1 mDV2 mDV3

MANOVA Pillai’s Trace Wilks’ Lambda Hotelling’s Trace Roy’s Largest Root

=

mDV1 mDV2 mDV3