User Guide

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Appendix A
Special
A user-defined contrast. Allows entry of special contrasts in the form of square matrices
with as many rows and columns as there are categories of the given independent
variable. For
MANOVA and LOGLINEAR, the first row entered is always the mean, or
constant, effect and represents the set of weights indicating how to average other
independent variables, if any, over the given variable. Generally, this contrast is a
vector of ones.
The remaining rows of the matrix contain the special contrasts indicating the desired
comparisons between categories of the variable. Usually, orthogonal contrasts are the
most useful. Orthogonal contrasts are statistically independent and are nonredundant.
Contrasts are orthogonal if:
 For each row, contrast coefficients sum to 0.
 The products of corresponding coefficients for all pairs of disjoint rows also sum
to 0.
For example, suppose that treatment has four levels and that you want to compare the
various levels of treatment with each other. An appropriate special contrast is
which you specify by means of the following
CONTRAST subcommand for MANOVA,
LOGISTIC REGRESSION, and COXREG:
/CONTRAST(TREATMNT)=SPECIAL( 1 1 1 1
3 -1 -1 -1
0 2 –1 -1
0 0 1 -1 )
For LOGLINEAR, you need to specify:
/CONTRAST(TREATMNT)=BASIS SPECIAL( 1 1 1 1
3 -1 -1 -1
0 2 -1 -1
0 0 1 -1 )
(1 1 1 1 )
weights for mean calculation
( 3 –1 –1 –1 )
compare 1st with 2nd through 4th
(0 2 –1 –1 )
compare 2nd with 3rd and 4th
(0 0 1 –1 )
compare 3rd with 4th