14 SPSS UPDATE 7-9

bacilli at these sites before the experiment began. Variate Y is a similar score after several months
of treatment. Drugs 1 and 2 are antibiotics, while drug 3 is an inert drug included as a control. Ten
patients were selected for each treatment. The MANOVA commands are as follows:

MANOVA Y BY DRUG(1,3) WITH X/
PRINT PMEANS/

Inelusion of covariates in a model is indicated by the keyword WITH on the MANOVA command.
The PRINT < PMEANS (see Section 1.50) specification reguests the predicted and adjusted (for
covariate) means of treatments.

The output includes the analysis of covariance summary table shown in Figure 1.17a, which
gives the sum of sguares due to regression (adjusted for the factor DRUG), and the sum of sguares
due to DRUG adjusted for regression.

Figure 1.17a

a A a Ra E IRENE EMEA AED WAEEEEEEEEEMC,

TESTS OF SIGNIFICANCE FOR Y USING SEOUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F
WITHIN CELLS 417.20260 26 16.04625

REGRESSION 577.89740 l 577.89740 36.01447 0.0
CONSTANT 31.92864 1 31.92864 1.98979 -170
DRUG 68.55371 2 34 .2T686 2.136153 138

a a aa ER EENEEE RAME NEEEEEWEWEEEEEEWEWEEEEEEWESEEEEEEEERENO IH!

In addition, the estimated regression coefficient (B), the standardized regression coefficient
(BETA), the standard error of the regression coefficient and the t-value of the test that B — 0 are
also given (Figure 1.17b). Note that (6.00121)' — 36.014, which is the F value for the regression in
the ANOVA table.

Figure 1.17b

a a o RE EEA M AE WEEEEEEEEOWEEEEEEEEEV OREH
REGRESSION ANALYSIS FOR WITHIN CELLS ERROR TERM

DEPENDENT VARIABLE ..Y

COVARIATE B BETA STD. ERR. T-VALUE SIG. OF T MLOWER .95 CL UPPER .95 CL

x 9871838111 » T6206498B67 - 16450 6.00121 000 - 64905 i1.32531

A NEM AE RENER AENEEWWEEENI(
The adjusted and predicted means for the factor DRUG are shown in Figure 1.17c.

Figure 1.17c

a a oa o AERO E EEA A AE MASE W ETER EEEEEEEEEWAEEEEEEEROEEEEEE ROVER ERA EVER
ADJUSTED AND ESTIMATED MEANS
VARIABLE .. Y

FACTOR CODE OBS. MEAN ADJ. MEAN EST. MEAN RAW RESID. STD. RESID.
DRUG l 5.30000 6.71496 5.30000 0.0 0.0
DRUG 2 6.10000 6.82393 6.10000 0.0 0.0
DRUG 3 12.30000 10.16110 12.30000 0.0 0.0

V A RENER MEN EEII MA NNINENAKINEEEIEEEAEEEEEMEEHH

Since MANOVA allows the inclusion of interval-scaled variables in the DESIGN specification,
the analysis of covariance can also be obtained using the following MANOVA commands:

MANOVA Y,X. BY DRUG(1,3)/
ANALYSIS < Y/
DESIGN < X, DRUG/
DESIGN < DRUG,X/

The ANALYSIS subcommand is used to select Y as the dependent variable. The first DESIGN
subcommand produces the DRUG effects adjusted for the covariate (X). The output is given in
Figure 1.17d.

Figure 1.17d |
V RENEW TEVA OEEEEEEREEEEEMEEEEEE EEA EIR REEERENEN
TESTS OF SIGNIFICANCE FOR Y USING SEOUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F
WITHIN4RESIDUAL 417.20260 26 16.04625

CONSTANT 1872.30000 l 1872.530000 116.68144 0.0

X 802.94369 l ' 802.94369 50.03932 0.0
DRUG 68.55371 2 34 ..27686 2.13615 -138

a A a ME RA WE WERE AERO EEREEEE MERE EOR ER