4 SPSS UPDATE 7-9

Figure 1.2 shows SPSS commands to accomplish the analysis of variance of the data. The
MANOVA specification defines Y to be the dependent variable and CAT and DRUG the factor
variables with two and three levels respectively. Since only one dependent variable (Y) is
indicated, a univariate analysis of variance is reguested.

Figure 1.2
a V NANESE NEENAKO
RUN NAME A UNIVARIATE 2"3 EXAMPLE.
COMMENT THE DATA ARE TAKEN FROM WINER(197l) PAGE 436.

Y : THE DEPENDENT VARIABLE.
CAT  : FACTOR WITH 2 LEVELS.
DRUG : FACTOR WITH 3 LEVELS.

VARIABLE LIST (CAT DRUG Y

INPUT FORMAT  FREEFIELD

INPUT MEDIUM CARD

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

READ INPUT DATA

-
ONDBOOBKRODONOCOOBO

-e

15
12
9

NDUNUNUNNUNNNE EH EE-E -E —- HE E—
MONAANNINE EEA OVNNE--E—

END INPUT DATA
FINISH

an
The default model generated from the MANOVA specifications is a full factorial. For this
example the model is .
YačktatB,t (aB);;  €ijx
where a, is the main effect of category i, B; is the main effect of drug j, and (aB);; is the interaction

of patient category i and drug j. For the various tests, it is necessary to assume that the error terms,
€. are independently identically distributed as normal with mean 0 and variance o".

1.3 Default Output
The default output (without any PRINT subcommand) from a MANOVA run includes
1 Ananalysis of variance (ANOVA) table. As shown in Figure 1.3a, it gives the sum of sguares,

degrees of freedom, mean sguare, F value, and the probabilities of each F value. The
within-cells error term (default error-term if it exists) is used to obtain all the F values.

Figure 1.3a
a nn—————

TESTS OF SIGNIFICANCE FOR Y USING SEGUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F
WITHIN CELLS 106.00000 12 8.83333

CONSTANT 882 .00000 l 892 .00000 99.B4906 0.0
CAT 18.00000 l 18.00000 2.05774 -179
DRUG 48.00000 2 24 .00000 2.71698 -106
CAT BY DRUG 144.00000 2 T2.00000 8.15094 006

A a ARA ANA EINE EEA EEA OEEO OSE ANINA

2 Statistics for parameter estimation (Figure 1.3b). These consist of estimates of the parameters
(COEFF), the standard errors of the estimates (STD. ERR.), the t-value for testing that the

. parameter is zero, the two-tailed significance of the test, and 95% confidence intervals for the
parameters. (Note that the parameters estimated here are not the original a;, B;, or (aB);;
instead, contrasts of the parameters are estimated. See Section 1.52 for detailed information.)