# GLM Contrasts

Contrasts are used to test for differences among the levels of a factor. You can specify a contrast for each factor in the model (in a repeated measures model, for each between-subjects factor). Contrasts represent linear combinations of the parameters.

**GLM Univariate.** Hypothesis testing is based on the null
hypothesis **LB** = 0, where **L** is the contrast coefficients
matrix and **B** is the parameter vector. When a contrast is specified,
an **L** matrix is created. The columns of the **L** matrix
corresponding to the factor match the contrast. The remaining columns
are adjusted so that the **L** matrix is estimable.

The output includes an *F* statistic for each set of contrasts.
Also displayed for the contrast differences are Bonferroni-type simultaneous
confidence intervals based on Student's *t* distribution.

**GLM Multivariate.** 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, an **L** matrix
is created. The columns of the **L** matrix 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
test using Pillai's trace, Wilks' lambda, Hotelling's trace, and Roy's
largest root criteria are provided.

**GLM Repeated
Measures.** Hypothesis testing is based on the null hypothesis **LBM** =
0, where **L** is the contrast coefficients matrix, **B** is
the parameter vector, and **M** is the average matrix that corresponds
to the average transformation for the dependent variable. You can
display this transformation matrix by selecting Transformation
matrix in the GLM Repeated Measures Options dialog box.
For example, if there are four dependent variables, a within-subjects
factor of four levels, and polynomial contrasts (the default) are
used for within-subjects factors, the **M** matrix will be (0.5
0.5 0.5 0.5)'. When a contrast is specified, an **L** matrix is
created. The columns of the **L** matrix corresponding to the between-subjects
factor match the contrast. The remaining columns are adjusted so that
the **L** matrix is estimable.

A contrast other than None must be selected for within-subjects factors.

GLM Multivariate and GLM Repeated Measures are available only if you have the Advanced Statistics option installed.

Available Contrasts

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.

Specifying Contrasts for GLM

- From the
menus choose:
- Choose Univariate, Multivariate, or Repeated Measures.
- In the dialog box, click Contrasts.
- Select the factors and contrast specifications.

GLM Multivariate and GLM Repeated Measures are available only if you have the Advanced Statistics option installed.