User Guide

384
Chapter 22
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-su
bjects factor). Contrasts represent linear combinations of the parameters.
Hypothesis testing is based on the null hypothesis LB =0,whereL is the contrast
coefficients matrix and B is the parameter vector. When a contrast is specified, SPSS
creates an L
matrix in which the columns 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 d
ifferences are Bonferroni-type simultaneous confidence intervals based on
Student’s t distribution.
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.
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. C
ompares 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.
Differe
nce.
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 subse
quent levels.
Repeated. Compares the mean of each level (except the last) to the mean of the
subsequent level.
Polynom
ial.
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 esti
mate polynomial trends.