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Statistica Textbook Examples
Computer-Aided Multivariate Analysis, Afifi, Clark and May
Chapter 10: Canonical correlation analysis

Page 235 Table 10.1  Means and standard deviations for depression data set.

File
  Open - open the depression data set
Insert
  Add variables - add one variable after sex called sex1 
  and in the box at the bottom, type "= sex - 1" (without the quotes)
Statistics
  Basic statistics
    Descriptives
      Variables - select cesd, health, sex1, age, education and income
        "Advanced" tab - uncheck "Valid N" and "minimum and maximum"
          Summary
Descriptive Statistics (depress.sta)
  Mean Std.Dev.
SEX 0.62 0.49
AGE 44.41 18.09
EDUCAT 3.48 1.31
INCOME 20.57 15.29
CESD 8.88 8.82
HEALTH 1.77 0.84

Page 235 Table 10.2  Correlation matrix for depression data set.

Statistics
  Basic statistics
    Correlation matrices
      One variable list - select cesd, health, sex, age, education and income
        Summary
Correlations (depress.sta) Marked correlations are significant at p < .05000 N=294 (Casewise deletion of missing data)
  SEX AGE EDUCAT INCOME CESD HEALTH
SEX 1.000 0.044 -0.106 -0.180 0.124 0.098
AGE 0.044 1.000 -0.208 -0.192 -0.164 0.304
EDUCAT -0.106 -0.208 1.000 0.429 -0.101 -0.270
INCOME -0.180 -0.192 0.429 1.000 -0.158 -0.183
CESD 0.124 -0.164 -0.101 -0.158 1.000 0.212
HEALTH 0.098 0.304 -0.270 -0.183 0.212 1.000

Page 237 Table 10.3  Canonical correlation coefficients for first correlation (depression data set)

NOTE:  We were unable to find a way to have Statistica display the raw coefficients shown on the left-hand side of the table.

Statistics
  Multivariate exploratory techniques
    Canonical analysis
      Variables - select cesd, health, sex, age, education and income
        OK
          OK
            "Quick" tab
              Variables for canonical analysis - select cesd and health for the first variable list 
              and sex, age, education and income for the second variable list
                OK
RESULTS
  "Canonical scores" tab
    Left and right set canonical weights

These are the standardized coefficients

Canonical Weights,
right set
  Root 1 Root 2
SEX 0.025 -0.396
AGE 0.871 0.443
EDUCAT -0.383 0.448
INCOME 0.082 0.555

Page 238 Table 10.4  Computation of correlation between U(1) and V(1)

The U's and V's can easily be added to the Statistica data set.  Begin with the RESULTS from the analysis above and click on the "Save canonical scores" button.  When asked about saving other variables with the scores, you may want to click on the "Select all" button to save all of the variables into the new data set with the scores.

Page 239 The second canonical correlations give at the top of the page.

These numbers are displayed in the output shown immediately above, called "Root 2".

Page 241 Figure 10.1  Plot of 294 pairs of the canonical variables U(1) and V(1) for the depression data set (canonical correlation = 0.405)

Graphs
  2D Scatterplots
    "Advanced" tab - set "Fit" to off
      Variables - select r_fac1 for the x-axis and l_fac1 for the y-axis
        OK
          OK

Page 242 Table 10.5  Correlations between canonical variables and corresponding variables (depression data set)

The panels of the table were obtained using the results from the canonical correlation conducted above. 

RESULTS
  "Factor structures"
    Factor structures and redundancies
Factor Structure, left set
  Root 1 (U) Root 2 (V)
CESD -0.281 -0.960
HEALTH 0.878 -0.478

Factor Structure, right set
  Root 1 (U) Root 2 (V)
SEX 0.089 -0.525
AGE 0.936 0.225
EDUCAT -0.532 0.636
INCOME -0.254 0.734

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