User Guide

GLM Multivariate Analysis

Contrasts are used to test whether the levels of an effect are significantly different from

one another. You can specify a contrast for each factor in the model. Contrasts

represent linear combinations of the parameters.

Hypothesis testing is based on the null hypothesis LBM = 0, where L is the contrast

coefficients matrix, M is the identity matrix, which has dimension equal to the number

of dependent variables, and B is the parameter vector. When a contrast is specified,

SPSS creates an L matrix such that the columns corresponding to the factor match the

contrast. The remaining columns are adjusted so that the L matrix is estimable.

In addition to the univariate test using F statistics and the Bonferroni-type

simultaneous confidence intervals based on Student’s t distribution for the contrast

differences across all dependent variables, the multivariate tests using Pillai’s trace,

Wilks’ lambda, Hotelling’s trace, and Roy’s largest root criteria are provided.

Available contrasts are deviation, simple, difference, Helmert, repeated, and

polynomial. For deviation contrasts and simple contrasts, you can choose whether the

reference category is the last or first category.

Contrast Types

Deviation. Compares the mean of each level (except a reference category) to the mean

of all of the levels (grand mean). The levels of the factor can be in any order.

Simple. Compares the mean of each level to the mean of a specified level. This type of

contrast is useful when there is a control group. You can choose the first or last category

as the reference.

Difference. Compares the mean of each level (except the first) to the mean of previous

levels. (Sometimes called reverse Helmert contrasts.)

Helmert. Compares the mean of each level of the factor (except the last) to the mean of

subsequent levels.

Repeated. Compares the mean of each level (except the last) to the mean of the

subsequent level.

Polynomial. Compares the linear effect, quadratic effect, cubic effect, and so on. The

first degree of freedom contains the linear effect across all categories; the second

degree of freedom, the quadratic effect; and so on. These contrasts are often used to

estimate polynomial trends.