[Home] [Syllabus] [Statnotes] [Links] [Lab] [Instructor] [Home]

SPSS Canonical Correlation Output

Notes: Canonical correlation is part of MANOVA in SPSS, in which one has to refer to one set of variables as "dependent" and the other as "covariates." This example uses the MANOVA procedure in SPSS 7.5 for the file "gss 93 subset.sav". To obtain this output:

  1. File, Open, point to gss 93 subset.sav.
  2. Open a syntax edit window with File, New, Syntax.
  3. Enter this syntax: 
    manova blugrass country folk with educ rincom91 scitest4 
   /discrim all alpha(1) 
   /print=sig(eigen dim).
    Note: Line 1 invokes the MANOVA procedure and tells SPSS which variables are in the "Dependent" set (the music variables before the "with") and which are "covariates" (the variables listed after the "with"). Line 2 invokes the DISCRIM option which creates the canonical variables and canonical correlations (canonical functions). Then "all" in line two tells SPSS that we want all of the output. The "alpha(1) tells SPSS we want to see all the canonical correlations regardless of their significance level. These parameters can be changed, of course. In the third line the output is specified, asking for significance levels of the eigenvalues {sig(eigen)} and of the canonical correlations {sig(dim)}.
  4. Select Run, All.
Comments in blue are by the instructor and are not part of SPSS output.

Notes
Output Created 12 Mar 98 15:10:04
Comments
Input Data Y:\PC\spss95\GSS93 subset.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 1500
Syntax manova blugrass country folk with educ rincom91 scitest4
/discrim all alpha(1)
/print=sig(eigen dim).
Resources Elapsed Time 0:00:01.60 

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The default error term in MANOVA has been changed from WITHIN CELLS to
WITHIN+RESIDUAL.  Note that these are the same for all full factorial
designs.



* * * * * * A n a l y s i s   o f   V a r i a n c e * * * * * *


       750 cases accepted.
         0 cases rejected because of out-of-range factor values.
       750 cases rejected because of missing data.
         1 non-empty cell.

         1 design will be processed.

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The ANOVA table below provides alternative tests of significance. The usual one is Wilks's lambda, which tests the significance of the first canonical correlation. If p < .05, which it is here, the two sets of variables are significantly associated by canonical correlation. This test establishes the significance of the first canonical correlation but not necessarily the second or later ones. If the first canonical correlation is not significant, the later ones won't be either. This is also called the greatest characteristic root test. 

* * * * * * A n a l y s i s   o f   V a r i a n c e -- design   1 * * * * * *

 EFFECT .. WITHIN CELLS Regression
 Multivariate Tests of Significance (S = 3, M = -1/2, N = 371 )

 Test Name         Value  Approx. F Hypoth. DF   Error DF  Sig. of F

 Pillais          .11452    9.86947       9.00    2238.00       .000
 Hotellings       .12574   10.37605       9.00    2228.00       .000
 Wilks            .88697   10.16418       9.00    1810.85       .000
 Roys             .09973

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The ratio of the eigenvalues below is the ratio of explanatory importance of the three canonical correlations (labeled "roots") which are extracted for these data. As usual the first canonical correlation is far more important than the others. For these data, however, for the first canonical correlation the "covariate" canonical variable explains only about 10% (.316*.316) of the variance in the "dependent" (music) canonical variable. 
 Eigenvalues and Canonical Correlations

 Root No.    Eigenvalue        Pct.   Cum. Pct.  Canon Cor.     Sq. Cor

        1          .111      88.096      88.096        .316        .100
        2          .013      10.377      98.473        .113        .013
        3          .002       1.527     100.000        .044        .002

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The F test below shows the first two canonical correlations are significant but the third is not. 

 Dimension Reduction Analysis

 Roots        Wilks L.          F Hypoth. DF   Error DF  Sig. of F

 1 TO 3         .88697   10.16418       9.00    1810.85       .000
 2 TO 3         .98523    2.78212       4.00    1490.00       .026
 3 TO 3         .99808    1.43266       1.00     746.00       .232

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -


 EFFECT .. WITHIN CELLS Regression (Cont.)
 Univariate F-tests with (3,746) D. F.

 Variable    Sq. Mul. R  Adj. R-sq.  Hypoth. MS    Error MS           F

 BLUGRASS        .01021      .00623     2.40976      .93930     2.56548
 COUNTRY         .06391      .06015    18.51740     1.09068    16.97784
 FOLK            .02363      .01970     6.04638     1.00469     6.01815

 Variable     Sig. of F

 BLUGRASS          .054
 COUNTRY           .000
 FOLK              .000
The raw canonical coefficients below are used in calculating the case scores on the canonical variables (the "dependent" ones) for each of the three canonical correlations which were extracted. The standardized canonical coefficients show the ratio of importance of each of the original variables in calculating the canonical score for each of the canonical variables. Note: the music variables were coded so that low corresponded to liking that type, so a negative correlation is actually one with liking that type. 

* * * * * * A n a l y s i s   o f   V a r i a n c e -- design   1 * * * * * *

 Raw canonical coefficients for DEPENDENT variables
           Function No.

 Variable            1          2          3

 BLUGRASS        -.130     -1.084       .413
 COUNTRY         -.792       .543       .263
 FOLK             .643       .545       .645

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 Standardized canonical coefficients for DEPENDENT variables
           Function No.

 Variable            1          2          3

 BLUGRASS        -.126     -1.054       .401
 COUNTRY         -.853       .584       .283
 FOLK             .651       .552       .653

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The correlations below are the structure correlations, which show how the original music variables load on each of the three canonical variables for the dependent set of variables in the three canonical correlations. Here, the "dependent" canonical variable in the first canonical correlation is most related to country (negatively) and folk (positively). For the second canonical correlation, the "dependent" canonical variable is most related (negatively) to bluegrass. The third canonical correlation is not significant and should be ignored. Note: the music variables were coded so that low corresponded to liking that type, so a negative correlation is actually one with liking that type. 

 Correlations between DEPENDENT and canonical variables
           Function No.

 Variable            1          2          3

 BLUGRASS        -.196      -.644       .740
 COUNTRY         -.790       .298       .536
 FOLK             .463       .266       .846

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 Variance in dependent variables explained by canonical variables

 CAN. VAR.  Pct Var DE Cum Pct DE Pct Var CO Cum Pct CO

        1       29.208     29.208      2.913      2.913
        2       19.153     48.360       .247      3.159
        3       51.640    100.000       .099      3.258

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SPSS now creates similar tables for the set of "covariate" variables, which for this case were educ, rincom91, and scitest4. These had to do with highest year of school completed, respondent's income, and belief in evolution. 

 Raw canonical coefficients for COVARIATES
           Function No.

 COVARIATE           1          2          3

 EDUC            -.321      -.109       .199
 RINCOM91        -.032      -.035      -.185
 SCITEST4         .101      -.913       .156




* * * * * * A n a l y s i s   o f   V a r i a n c e -- design   1 * * * * * *

 Standardized canonical coefficients for COVARIATES
           CAN. VAR.

 COVARIATE           1          2          3

 EDUC            -.893      -.304       .553
 RINCOM91        -.175      -.195     -1.020
 SCITEST4         .113     -1.021       .174

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 Correlations between COVARIATES and canonical variables
           CAN. VAR.

 Covariate           1          2          3

 EDUC            -.980      -.077       .183
 RINCOM91        -.466      -.199      -.862
 SCITEST4         .380      -.918       .110

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 Variance in covariates explained by canonical variables

 CAN. VAR.  Pct Var DE Cum Pct DE Pct Var CO Cum Pct CO

        1        4.396      4.396     44.083     44.083
        2         .381      4.778     29.612     73.695
        3         .050      4.828     26.305    100.000

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SPSS then regresses each "dependent" variable on the set of "covariate variables." This is discussed in the section on multiple regression. 

 Regression analysis for WITHIN CELLS error term
 --- Individual Univariate .9500 confidence intervals
 Dependent variable .. BLUGRASS          Bluegrass Music

 COVARIATE            B        Beta   Std. Err.     t-Value   Sig. of t

 EDUC            .03332      .09532        .014       2.393        .017
 RINCOM91       -.00140     -.00793        .007       -.207        .836
 SCITEST4        .06374      .07332        .033       1.931        .054

 COVARIATE   Lower -95%  CL- Upper

 EDUC              .006        .061
 RINCOM91         -.015        .012
 SCITEST4         -.001        .129



* * * * * * A n a l y s i s   o f   V a r i a n c e -- design   1 * * * * * *

 Regression analysis for WITHIN CELLS error term  (Cont.)
 Dependent variable .. COUNTRY           Country Western Music

 COVARIATE            B        Beta   Std. Err.     t-Value   Sig. of t

 EDUC            .08734      .22548        .015       5.821        .000
 RINCOM91        .00258      .01317        .007        .353        .724
 SCITEST4       -.05646     -.05862        .036      -1.587        .113

 COVARIATE   Lower -95%  CL- Upper

 EDUC              .058        .117
 RINCOM91         -.012        .017
 SCITEST4         -.126        .013
 Dependent variable .. FOLK              Folk Music

 COVARIATE            B        Beta   Std. Err.     t-Value   Sig. of t

 EDUC           -.04340     -.11923        .014      -3.014        .003
 RINCOM91       -.01275     -.06927        .007      -1.818        .069
 SCITEST4       -.00721     -.00796        .034       -.211        .833

 COVARIATE   Lower -95%  CL- Upper

 EDUC             -.072       -.015
 RINCOM91         -.027        .001
 SCITEST4         -.074        .060

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SPSS also prints out a section of output for Effect=CONSTANT, but that is omitted here as it is normally not used in canonical correlation. 

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -