40  sPSS UPDATE 7-9

As an indication of how much each response variable contributes to the canonical variate,
these correlations aid in the interpretation of the canonical variables.

For the dental calculus data, a diseriminant analysis for the effect TR is reguested by specifying
PRINT<DISCRIM (RAW, STAN, ESTIM, COR) /

The resulting output is given in Figure 1.35.

Figure 1.35

pp AE A ER OE MER EEA AEEEEEE VERE REEMWEEEEEEEEEEMAEA NE

RAW DISCRIMINANT FUNCTION COEFFICIENTS
FUNCTION NO.

VARIABLE

RCAN 02507
RLI -.l4814
RCI -.4072B

STANDARDIZED DISCRIMINANT FUNCTION COEFFICIENTS

FUNCTION NO.
VARIABLE 1
RCAN .02944
RLI -.23973
RCI -.83862

ESTIMATES OF EFFECTS FOR CANONICAL VARIABLES
CANONICAL VARIABLE

PARAMETER . l
3 -.60303
4 -.67469
5 . 18246
6 -.08566

CORRELATIONS BETWEEN DEPENDENT AND CANONICAL VARIABLES
CANONICAL. VARIABLE

VARIABLE 1
RCAN -.38019
RLI -.TTl43
RCI -.98526

OO Eo oo EEA AVE OST VEOEAPEVEEV EEEVAEEEEEEEV OPV ENE EEVON OEEO PETE EVE EOR O EVEEEEEEEREVO VEC

Discriminant analysis results are reported only for those functions (or corresponding
canonical correlations; see Section 1.32) that are significant at level a. The default value of a is
0.15. In Figure 1.32a, the dimension reduction analysis for the TR effect indicates that only the
first canonical correlation is significant (the observed significance level is 0.045); hence only one
discriminant function is reported in the output displayed above. The value of a can be set by
specifying a number between 0 and 1, in parentheses, after the keyword ALPHA. Thus,

PRINT-DISCRIM(RAW, COR, ALPHA(0.5) ) /
produces discriminant function coefficients and the correlations between response variables and
canonical variables that correspond to discriminant functions with significance levels less than 0.5.
If a < 1.0 is specified, MANOVA reports all the discriminant functions.

The correlations between the response variables and the canonical variables can be rotated by

adding the ROTATE keyword to the PRINT subcommand. (The types of rotation available are
described in 1.34.) For example,

PRINT-DISCRIM( COR, ROTATE( VARIMAX), ALPHA(1.0))/

produces the correlations between the response variables and all the canonical variables and
rotates the canonical variables (using the varimax method).

1.36 Box's M Test

The assumption of homogeneous within-cells variance-covariance matrices can be assessed by
Box's M test, a multivariate analog of Bartlett's test. lf

PRINT<HOMOGENEITY ( BOXM) /

is specified, MANOVA will print Box's M statistic and an approximate F statistic with its p- value.
The results of Box's M test for the dental calculus data are given in Figure 1.36.