se;
(5

Figure 1.36

MULTIVARIATE TEST FOR HOMOGENEITY OF DISPERSION MATRICES

BOXS M < — 114.53559
F WITH (36,2404) DF - 2.6772l, P <  .000 (APPROX.)
CHI-SOVARE WITH 36 DF < 9B.09416. P <  .000 (APPROX.)

1.37 Multivariate Analysis of Covariance

MANOVA will also perform a multivariate analysis of covariance. Figure 1.37a illustrates this use
of MANOVA.

Figure 1.37a
RUN NAME DENTAL CALCULUS DATA FROM FINN(1974) PAGE C-56
FILE NAME DATA FOR ANTI-CALCULUS AGENT

VARIABLE LIST YEAR,TR,RCAN,RLI,RCI,LCI,LLI,LCAN
INPUT FORMAT  FIXED(2Fl.0,6F2.0)

N OF CASES 107

MISSING VALUES YEAR TO LCAN(BLANK)

MANOVA RCAN,RLI,RCI BY YEAR(1,2),TR(1,5) WITH LCI/
READ INPUT DATA
li221221
li000210
ll004400
ll2a225322
2301534530
23101010
23010000
23016410
FINISH

EJ NK O 7 NE EN 00 9 ER

RCAN, RLT, and RCI are the response variables and LCI the covariate in this example. The
discussion of univariate analysis of covariance in Section 1.17 can be generalized.
When a covariate is specified, multivariate significance testing and parameter estimation are

"adjusted for the covariate; i.e., both S, and S, are adjusted. For the dental calculus data, the

multivariate significance tests for the TR effect, adjusted for the covariate LCI, are given in Figure
1.37b.

Figure 1.37b

O
EFFECT .. TR

MULTIVARIATE TESTS OF SIGNIFICANCE (S < 3, M — 0, N < 47 1/2)

TEST NAME VALUE APPROX. F HYPOTH. DF ERROR DF SIG. OF F
PILLAIS -18149 1.59371 12.00 297.00 092
HOTELLINGS - 2046B 1.63178 12.00 287.00 082
WILKS 82485 1.61631 12.00 256.93 087
ROYS 13641
EIGENVALUES AND CANONICAL CORRELATIONS
ROOT NO. EIGENVALUE PCT. CUM. PCT. CANON. COR.
l -15796 TT.17431 T1.1T43l 36934
2 .04095 20 .00838 9T. 18269 .19B35
3 00577 2.81731 100.00000 07572
DIMENSION REDUCTION ANALYSIS
ROOTS WILKS LAMBDA F HYPOTH. DF ERROR DF SIG. OF F
1 TO S .B2485 1.61631 12.00 256.93 -0B7
2 TO Z 95515 75412 6.00 237.72 607
3 TO 3 - 99427 28215 2.00 196.00 754
UNIVARIATE F-TESTS WITH (4,99) D. F.
VARIABLE HYPOTH. SS ERROR SS HYPOTH. MS ERROR MS F SIG. OF F
RCAN 4.20875 119.32324 1.05219 1.20529 .87298 483
RLI 4.15057 152.399B6 1.03764 1.53939 67406 -612
RCI 18.00210 123.66477 4.50052 1.24914

3.60290 009

MANOVA — 41