, MANOVA. — 7

MANOVA Y BY CAT(1,2) DRUG(1,3)/
PARTITION(DRUG)<(1,1)/
DESIGN<CAT, DRUG( 1), DRUG(2),CAT BY DRUG/

The first component is denoted by DRUG(1), and the second by DRUG(2). The Output is given in
Figure 1.8.

Figure 1.8
O Eo

TESTS OF SIGNIFICANCE FOR Y USING SEGUENTIAL SUMS OF SOVARES

SOURCE OF VARIATION SUM OF SGUARES DF MEAN SGUARE F SIG. OF F
WITHIN CELLS 106.00000 12 8.83333

CONSTANT 882 .00000 : l 882 .00000 99. 84906 9.0
CAT 18.00000 l 18.00000 2.05774 -179
DRUG( 1) 12.00000 1 12.00000 1.35849 266
DRUG(2) 36 .00000 l 36.00000 4.07547 066
CAT BY DRUG 144.00000 2 72.00000 8. 15094 .006

ESTIMATES FOR Y

CONSTANT
PARAMETER COEFF. STD. ERR. T-VALUE SIG. OF T LOWER .95 CL UPPER .95 CL
1 7 .0000000000 70053 9.99245 .000 5.47368 8.52632
CAT
PARAMETER COEFF. STD. ERR. T-VALJE SIG. OF T LOWER .95 CL UPPER .95 CL
2 -1.0000000000 -T0053 -1.42749 -179 -2.52632 52632
DRUG(1l)
PARAMETER COEFF. STD. ERR. T-VALVUE SIG. OF T LOWER .95 CL UPPER .95 CL
3 0.0 99070 0.0 1.000 -2.15854 2.15854
DRUG (2)
PARAMETER COEFF. STD. ERR. T-VALVE SIG. OF T LOWER .95 CL ' UPPER .95 CL
4 -2.0000000000 - 99070 -2.01878 066 —-4.15854 15854
CAT BY DRUG
PARAMETER COEFF. STD. ERR. T-VALVE SIG. OF T LOWER .95 Cl. UPPER .95 CL.
5 -2.0000000000 » 99070 -2.01878 066 -4.15854 . 15854
6 4..0000000000 - 99070 4.03756 002 1.84146 6.15854

O EJ OEEO tomo

The default contrasts used for partitioning are deviation contrasts (see Section 1.89). The
deviation contrasts are not orthogonal, so the two contrasts for DRUG(1) and DRUG(2) are not
independent.

1.9 Types of Contrasts

The MANOVA procedure allows specification of six different contrast types: deviation, difference,
Helmert, simple, repeated, and polynomial. The user can also input any other contrast matrix via
the SPECIAL keyword.
For example, to specify user-supplied orthogonal contrasts for the DRUG factor, the following
commands can be used:
MANOVA Y BY CAT(1,2) DRUG(1,3)/
CONTRAST(DRUG)-SPECIAL(l 1 1 -l 2 -1 1 0 -1)/
PARTITION(DRUG)<(1,1)/

DESIGNECAT, DRUG( 1), DRUG(2),CAT BY DRUG(l),
CAT BY DRUG(2)/

The first set of coefficients (1 1 1) is always the weights for obtaining the constant term. Following
the weights vector are the contrasts. The number of contrasts should be egual to the degrees of
freedom for the factor. The first contrast (-1 2 -1) defines a contrast between level 2 and the
combination of levels 1 and 3 for factor DRUG. The second contrast (1 0-1) reguests a comparison
between levels 1 and 3 of DRUG. For most applications, the user shoud be sure that each set of
contrast coefficients sum to zero.

Since the inner product of the two contrasts is 0 and the sample sizes in all cells are egual, i.e.,
C1)(1) £ 2(0) £ (-1)(-1) < 0, the two contrasts are independent. In this example, the DRUG(1)
partition can be used to test the hypothesis B, < (B, £ B;)/2 while the second contrast tests
B, — B,. The ANOVA table is given in Figure 1.9.