nisi

ME
Ni

The second DESIGN specification reguests the regression effect (X) adjusted for the factor
DRUG (Figure 1.17e).

Figure 1.17e

TESTS OF SIGNIFICANCE FOR Y USING SEOGUENTIAL SUMS OF SOVARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F
WITHINHRESIDUAL 417.20260 26 16.04625 —

CONSTANT 1872.30000 1 1872.30000 116.68144 0.0
DRUG 293.60000 2 146.80000 9.14855 -001
x 5771.89740 1 577 .89740 36.01447 0.0

The regression coefficient can be obtained from the estimate of the parameters for factor X
(Figure 1.17f).

Figure 1.171

.a

ESTIMATES FOR Y

CONSTANT
PARAMETER COEFF. STD. ERR. T-VALVE SIG. OF T LOWER .95 CL UPPER .95 CL
1 -2.6957729061 1.91108 -1.41060 -170 —6..62406 1.23252
DRUG
PARAMETER COEFF. STD. ERR. T-VALVE SIG. OF T LOWER .95 CL UPPER .95 CL
2 -1.1850365374 1.06082 -..11709 274 -3.36559 99551
3 -1.0760652052 1.04130 -1.03339 -31l —3.21648 1.06435
x
PARAMETER COEFF. STD. ERR. T-VALUE SIG. OF T LOWER .95 CL UPPER .95 CL
4 9871838111 -16450 6.00121 000 64905 1.32531

From the covariance model given above, it follows that there is a common regression
coefficient for the given X. This implies that the within-treatment regression coefficients are
homogeneous. The assumption of homogeneity of regression coefficients in the analysis of
covariance can be assessed by introducing a treatment by covariate interaction term in the model.

A test for no interaction between DRUG effects and covariate is eguivalent to testing the
hypothesis that the pooled within-treatment regression coefficient is appropriate. The test for
treatment by covariate interaction, which is referred to as the test for regression parallelism, can be
obtained in MANOVA as follows:

MANOVA Y, X BY DRUG(1,3)/

ANALYSIS - Y/
DESIGN < X, DRUG, X BY DRUG/

The analysis of variance table for this DESIGN specification is given in Figure 1.17g.
Since X BY DRUG is not significant, the hypothesis of the homogeneity of the within-
treatment regression is not rejected.

Figure 1.17g

TESTS OF SIGNIFICANCE FOR Y USING SEOVENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F
WITHINARESIDUAL 397.55795 24 16.56491

CONSTANT 1872.30000 1 1872 .30000 113.02805 0.0

x 802. 94369 1 802. 94369 48.47255 0.0
DRUG 68.55371 2 34 .27686 2.06924 -148
X BY DRUG 19.64465 2 9.82232 59296 56

1.18 Analysis of Covariance with Separate Regression Estimates

Consider a 2 x 2 (Factors A, B) design with covariate X. The model (using dummy variables) can
be written as

Yix — et B(Xia—X) o Zije A U aaa Za Ujeta

MANOVA 15