Output from poolscpg.sas	Source 2 Graphs

                        Within and Between Group SSCP                        1

                  Plot of X2*X1.  Symbol is value of GROUP.

X2 |
35 +
   |               1 11
   |
   |                 1
   |        1    1    1
   |        11     1 1
30 +          1  1  11 1
   |    1    11    1
   |     1     1
   |      1  1
   |      1
   |        1
25 +       1
   |     1                                    2   2
   |                                            2
   |                                  2  22
   |                                  2  2     2
   |                                 22 22
20 +                                  2222
   |                            2    2 22  2
   |
   |                                 22
   |                                22
   |
15 +
   |
   |                                                        3      3  3
   |                                                              3  3 3
   |                                                        3 3
   |                                                           3  33 3
10 +                                                   3   333       3
   |                                                        3      3
   |                                                        3 3
   |
   |                                                    3  3  3
   |                                                       3
 5 +
   |
   |                                               3  3
   |
   |
   |
 0 +
   |
   -+-----------+-----------+-----------+-----------+-----------+-----------+-
    5          10          15          20          25          30          35

                                        X1

NOTE: 9 obs hidden.

                        Within and Between Group SSCP                        2
                          Total Sample Correlations

                             Correlation Analysis

                      2 'VAR' Variables:  X1       X2

                 Pearson Correlation Coefficients  / N = 90

                                      X1                X2

                    X1           1.00000          -0.88591

                    X2          -0.88591           1.00000

                        Within and Between Group SSCP                        3
                          Within Sample Correlations

---------------------------------- GROUP=1 -----------------------------------

                             Correlation Analysis

                      2 'VAR' Variables:  X1       X2

                 Pearson Correlation Coefficients  / N = 30

                                      X1                X2

                    X1           1.00000           0.65414

                    X2           0.65414           1.00000

                        Within and Between Group SSCP                        4
                          Within Sample Correlations

---------------------------------- GROUP=2 -----------------------------------

                             Correlation Analysis

                      2 'VAR' Variables:  X1       X2

                 Pearson Correlation Coefficients  / N = 30

                                      X1                X2

                    X1           1.00000           0.71811

                    X2           0.71811           1.00000

                        Within and Between Group SSCP                        5
                          Within Sample Correlations

---------------------------------- GROUP=3 -----------------------------------

                             Correlation Analysis

                      2 'VAR' Variables:  X1       X2

                 Pearson Correlation Coefficients  / N = 30

                                      X1                X2

                    X1           1.00000           0.71464

                    X2           0.71464           1.00000

                        Within and Between Group SSCP                        6
                      Pooled Within-Sample Correlations

                             Correlation Analysis

                      2 'VAR' Variables:  X1       X2

                              Simple Statistics

  Variable          N       Mean    Std Dev        Sum    Minimum    Maximum

  X1               90          0     1.9052          0    -5.0002     4.3771
  X2               90          0     2.4314          0    -6.5800     4.2801

                 Pearson Correlation Coefficients  / N = 90

                                      X1                X2

                    X1           1.00000           0.69480

                    X2           0.69480           1.00000

                        Within and Between Group SSCP                        7
                      Pooled Within-Sample Correlations

                OBS    _TYPE_    _NAME_       X1         X2

                 1      MEAN                0.0000     0.0000
                 2      STD                 1.9052     2.4314
                 3      N                  90.0000    90.0000
                 4      CORR       X1       1.0000     0.6948
                 5      CORR       X2       0.6948     1.0000

                        Within and Between Group SSCP                        8
                      Pooled Within-Sample Correlations

                  Plot of X2*X1.  Symbol is value of GROUP.

X2 |
 6 +
   |
   |
   |
   |
   |                                              1    1          2
 4 +                                                   1
   |
   |                                               3      3
   |                              3             3      3
   |                                                        2
   |                               2         2         13   3
 2 +                            1 3   3    2 1
   |                           1    2                   1 2
   |                           1        3       31   1
   |                              2        2   3       3
   |                             1   1     2      1 3 1
   |               3          3 2  2    2  2           3
 0 +                              3      2 1               1
   |                             311  2
   |                  1               2    2     13
   |                             23     2       2
   |                 2 1                1
   |                            3     31
-2 +
   |                     1        1
   |                             2 2
   |                   3         2
   |                      1    2
   |                         2         3
-4 +                           1
   |                          3
   |                         1
   |
   |
   |
-6 +                   1
   |               3
   |      3
   |
   |
   |
-8 +
   -+-----------+-----------+-----------+-----------+-----------+-----------+-
   -6          -4          -2           0           2           4           6

                                        X1

NOTE: 5 obs hidden.

                        Within and Between Group SSCP                        9
                 Within Sample and Total Data 68% Ellipsoids

                            Discriminant Analysis

                  90 Observations        89 DF Total
                   2 Variables           87 DF Within Classes
                   3 Classes              2 DF Between Classes

                           Class Level Information

                                                                     Prior
          GROUP     Frequency        Weight     Proportion     Probability

              1            30       30.0000       0.333333        0.333333
              2            30       30.0000       0.333333        0.333333
              3            30       30.0000       0.333333        0.333333

                        Within and Between Group SSCP                       10
                 Within Sample and Total Data 68% Ellipsoids

                            Discriminant Analysis

         Pooled Within-Class Correlation Coefficients  /  Prob > |R|

                 Variable                X1                X2

                 X1                 1.00000           0.69480
                                     0.0               0.0001

                 X2                 0.69480           1.00000
                                     0.0001            0.0

             Total-Sample Correlation Coefficients  /  Prob > |R|

                 Variable                X1                X2

                 X1                 1.00000          -0.88591
                                     0.0               0.0001

                 X2                -0.88591           1.00000
                                     0.0001            0.0

                        Within and Between Group SSCP                       11
                 Within Sample and Total Data 68% Ellipsoids

 Discriminant Analysis     Test of Homogeneity of Within Covariance Matrices

       Notation: K    = Number of Groups

                 P    = Number of Variables

                 N    = Total Number of Observations - Number of Groups

                 N(i) = Number of Observations in the i'th Group - 1

                          __                       N(i)/2
                          ||  |Within SS Matrix(i)|
                 V    = -----------------------------------
                                                 N/2
                              |Pooled SS Matrix|

                               _                  _     2
                              |       1        1   |  2P + 3P - 1
                 RHO  = 1.0 - | SUM -----  -  ---  | -------------
                              |_     N(i)      N  _|  6(P+1)(K-1)


                 DF   = .5(K-1)P(P+1)

                                      _                  _
                                     |    PN/2            |
                                     |   N        V       |
   Under null hypothesis:  -2 RHO ln | ------------------ |
                                     |   __      PN(i)/2  |
                                     |_  ||  N(i)        _|

   is distributed approximately as chi-square(DF)


   Test Chi-Square Value =     4.506765
   with      6 DF      Prob > Chi-Sq = 0.6084


   Since the chi-square value is not significant at the  0.05 level,
   a pooled covariance matrix will be used in the discriminant function.

   Reference: Morrison, D.F. (1976)    Multivariate Statistical Methods p252.

                                                                            12

Graphic output from poolscpg.sas

PLOT OF X2 * X1 = GROUP [CONTOUR 09/24/99 ]
PLOT OF X2 * X1 = GROUP [CONTOUR1 09/24/99 ]