o Mao

BE SEJO S A MRI NEON NJE SKA

Chapter 1

MANOVA:
Multivariate Analysis of Variance

SPSS MANOVA is a generalized multivariate analysis of variance and covariance program which
will perform univariate and multivariate linear estimation and tests of hypotheses for any crossed
and/or nested design with or without covariates. The user has complete control of the model
specification. For example, several effects can be lumped together into a single term. Also,
interaction between factors and covariates is allowed:

The sections beginning with 1.2 present univariate analysis of variance models, which include
balanced incomplete block designs, confounding designs, nested designs, and split-plot designs.
Special features such as coilapsing error terms, specifying multiple error terms, partitioning
degrees of freedom, contrasts, orthogonal polynomials and analysis of covariance are also
discussed.

Tests of significance for a multivariate analysis of variance model include hypotheses and error
matrices, four multivariate test criteria, dimension reduction analysis, univariate F tests, and
step-down analysis. In addition, principal components analysis and discriminant analysis can be
reguested. They are documented beginning in Section 1.31.

The sections beginning with 1.38 present multivariate multiple linear regression analysis,
which can be considered a special case of multivariate analysis of covariance in which all the

' independent variables are covariates. Canonical correlation analysis is also discussed.

MANOVA enables the user to analyze a large class of repeated measures designs. The
observation can be either single-valued or vector-valued. Covariates, varying or constant across
the repeated measures, can also appear in the model. These facilities are described beginning in

Section 1.43.

Section 1.51 describes the graphics features available in MANOVA.
MANOVA mav reguire an additional scrateh file for which provision must be made in the job
setup. See Appendix L for information for the IBM/OS version.

1.1 OVERVIEW

MANOVA specifications are entered via toe MANOVA command itself and a number of optional

subcommands that fali into the three categories outlined below. For more detail on these, see
Section 1.52.
The MANOVA command has the following general format:

MANOVA <dependent variable list> BY <factor list> WITH
<covariate list>/

The MANOVA command, with no subcommands, is the only reguired specification. A dependent
variable list of one variable activates univariate analysis; more than one dependent variable
activates multivariate analysis of variance.

Subcommands in the first category specify the factor and data structures of the design.
WSFACTOR provides the within-subjects factors for a repeated measures design.

WSFACTOR - < factor list>/