Output from discralz.sas	Source 0 Graphs

               Memory Tests on Alzheimer and Depressed Patients              1
                            Descriptive statistics

                                                                      HI
                                   HI        LO                    Imagery
                         Total   Imagery   Imagery   Unreminded   Unreminded
    GROUP     _FREQ_    recall   Recall    Recall      Memory       Memory

          .     45      66.622    35.622    31.000     0.3868       0.4200
  Alzheimer     15      43.333    23.400    19.933     0.0760       0.0853
  Depressed     14      72.071    38.357    33.714     0.4546       0.4750
  Normal        16      83.688    44.688    39.000     0.6188       0.6856

                           LO
                        Imagery
                       Unreminded               Recognition
    GROUP     _FREQ_     Memory      Storage      Memory

          .     45       0.3536       0.7500       10.800
  Alzheimer     15       0.0667       0.3527        8.800
  Depressed     14       0.4343       0.8629       11.643
  Normal        16       0.5519       1.0238       11.938

               Memory Tests on Alzheimer and Depressed Patients              2
                                 Group Means

     Plot of TRECALL*GROUP='T'.               Plot of TUNREM*GROUP='T'.
     Plot of HIRECALL*GROUP='H'.              Plot of HIUNREM*GROUP='H'.
     Plot of LIRECALL*GROUP='L'.              Plot of LIUNREM*GROUP='L'.

  100 +                                  U 1.0 +
T     |                                  n     |
o     |                            T     r     |
t     |                                  e     |
a     |              T                   m     |                            H
l     |                                  i     |                            T
      |                                  n     |                            L
r  50 +                                  d 0.5 +              H
e     |T                           H     e     |              T
c     |              H             L     d     |
a     |                                        |
l     |H                                 M     |
l     |                                  e     |
      |                                  m     |T
    0 +                                  o 0.0 +
      -+-------------+-------------+-    r     -+-------------+-------------+-
   Alzheimer     Depressed     Normal    y  Alzheimer     Depressed     Normal

                   GROUP                                    GROUP

NOTE: 2 obs hidden.                      NOTE: 3 obs hidden.


     Plot of STORE*GROUP=GROUP.               Plot of RECOG*GROUP=GROUP.

  1.25 +                                 R 12 +                              N
       |                                 e    |               D
       |                                 c    |
       |                                 o    |
  1.00 +                            N    g 11 +
S      |                                 n    |
t      |              D                  i    |
o      |                                 t    |
r 0.75 +                                 i 10 +
a      |                                 o    |
g      |                                 n    |
e      |                                      |
  0.50 +                                 M  9 +
       |                                 e    |A
       |A                                m    |
       |                                 o    |
  0.25 +                                 r  8 +
       -+-------------+-------------+    y    -+--------------+--------------+
    Alzheimer     Depressed    Normal      Alzheimer      Depressed     Normal

                    GROUP                                   GROUP

               Memory Tests on Alzheimer and Depressed Patients              3
                       Canonical Discriminant Analysis

                       Canonical Discriminant Analysis

                  45 Observations        44 DF Total
                   6 Variables           42 DF Within Classes
                   3 Classes              2 DF Between Classes

                           Class Level Information

             GROUP         Frequency        Weight     Proportion

             Alzheimer            15       15.0000       0.333333
             Depressed            14       14.0000       0.311111
             Normal               16       16.0000       0.355556

               Memory Tests on Alzheimer and Depressed Patients              4
                       Canonical Discriminant Analysis

Canonical Discriminant Analysis     Pairwise Squared Distances Between Groups

                       2         _   _       -1  _   _
                      D (i|j) = (X - X )' COV   (X - X )
                                  i   j           i   j

                          Squared Distance to GROUP
            From
            GROUP          Alzheimer      Depressed         Normal

            Alzheimer              0        9.41842       16.91067
            Depressed        9.41842              0        1.95746
            Normal          16.91067        1.95746              0

                          F Statistics, NDF=6, DDF=37 for
                          Squared Distance to GROUP
            From
            GROUP          Alzheimer      Depressed         Normal

            Alzheimer              0       10.01384       19.22257
            Depressed       10.01384              0        2.14596
            Normal          19.22257        2.14596              0

                          Prob > Mahalanobis Distance for
                          Squared Distance to GROUP
            From
            GROUP          Alzheimer      Depressed         Normal

            Alzheimer         1.0000         0.0001         0.0001
            Depressed         0.0001         1.0000         0.0710
            Normal            0.0001         0.0710         1.0000

               Memory Tests on Alzheimer and Depressed Patients              5
                       Canonical Discriminant Analysis

                       Canonical Discriminant Analysis

                         Univariate Test Statistics

                   F Statistics,    Num DF= 2   Den DF= 42

                 Total        Pooled       Between                       RSQ/
Variable           STD           STD           STD     R-Squared      (1-RSQ)

HIRECALL       11.2478        6.7370       11.0459      0.657554       1.9202
LIRECALL       10.7302        7.0741        9.9402      0.585118       1.4103
HIUNREM         0.2988        0.1602        0.3083      0.725665       2.6452
LIUNREM         0.2645        0.1636        0.2553      0.634935       1.7392
STORE           0.3669        0.2276        0.3533      0.632506       1.7211
RECOG           1.9259        1.3143        1.7383      0.555442       1.2494

                    Univariate Test Statistics




Variable          F        Pr > F     Label

HIRECALL       40.3236     0.0001     HI Imagery Recall
LIRECALL       29.6168     0.0001     LO Imagery Recall
HIUNREM        55.5487     0.0001     HI Imagery Unreminded Memory
LIUNREM        36.5240     0.0001     LO Imagery Unreminded Memory
STORE          36.1437     0.0001     Storage
RECOG          26.2380     0.0001     Recognition Memory

                  Average R-Squared:  Unweighted = 0.6318701
                            Weighted by Variance = 0.6220665

                 Multivariate Statistics and F Approximations

                            S=2    M=1.5    N=17.5

 Statistic                     Value          F      Num DF    Den DF  Pr > F

 Wilks' Lambda              0.20483106     7.4588        12        74  0.0001
 Pillai's Trace             0.88861275     5.0638        12        76  0.0001
 Hotelling-Lawley Trace     3.42587275    10.2776        12        72  0.0001
 Roy's Greatest Root        3.28708746    20.8182         6        38  0.0001

         NOTE: F Statistic for Roy's Greatest Root is an upper bound.
                NOTE: F Statistic for Wilks' Lambda is exact.

               Memory Tests on Alzheimer and Depressed Patients              6
                       Canonical Discriminant Analysis

                       Canonical Discriminant Analysis

                                Adjusted       Approx       Squared
                 Canonical      Canonical     Standard     Canonical
                Correlation    Correlation     Error      Correlation

           1      0.875638       0.859529     0.035165      0.766741
           2      0.349101       0.240768     0.132383      0.121871

                                Eigenvalues of INV(E)*H
                                  = CanRsq/(1-CanRsq)

                 Eigenvalue    Difference    Proportion    Cumulative

            1       3.2871        3.1483       0.9595        0.9595
            2       0.1388         .           0.0405        1.0000

                     Test of H0: The canonical correlations in the
                       current row and all that follow are zero

               Likelihood
                  Ratio      Approx F      Num DF      Den DF    Pr > F

          1    0.20483106      7.4588          12          74    0.0001
          2    0.87812866      1.0548           5          38    0.4004

                          Total Canonical Structure

                      CAN1              CAN2

HIRECALL          0.925669         -0.067893      HI Imagery Recall
LIRECALL          0.873543         -0.017035      LO Imagery Recall
HIUNREM           0.969158         -0.212239      HI Imagery Unreminded Memory
LIUNREM           0.909619          0.065853      LO Imagery Unreminded Memory
STORE             0.907803          0.071876      Storage
RECOG             0.837971          0.373926      Recognition Memory

                         Between Canonical Structure

                      CAN1              CAN2

HIRECALL          0.999573         -0.029229      HI Imagery Recall
LIRECALL          0.999970         -0.007775      LO Imagery Recall
HIUNREM           0.996210         -0.086978      HI Imagery Unreminded Memory
LIUNREM           0.999584          0.028851      LO Imagery Unreminded Memory
STORE             0.999502          0.031550      Storage
RECOG             0.984541          0.175153      Recognition Memory

               Memory Tests on Alzheimer and Depressed Patients              7
                       Canonical Discriminant Analysis

                       Canonical Discriminant Analysis

                      Pooled Within Canonical Structure

                      CAN1              CAN2

HIRECALL          0.763974         -0.108719      HI Imagery Recall
LIRECALL          0.655000         -0.024784      LO Imagery Recall
HIUNREM           0.893661         -0.379720      HI Imagery Unreminded Memory
LIUNREM           0.727098          0.102134      LO Imagery Unreminded Memory
STORE             0.723244          0.111106      Storage
RECOG             0.606993          0.525534      Recognition Memory

               Total-Sample Standardized Canonical Coefficients

                      CAN1              CAN2

HIRECALL       0.287725860       1.939638848      HI Imagery Recall
LIRECALL       0.027900716      -0.765740473      LO Imagery Recall
HIUNREM        0.787438285      -3.014925035      HI Imagery Unreminded Memory
LIUNREM        0.406678951       0.977859365      LO Imagery Unreminded Memory
STORE          0.321111340      -0.158242520      Storage
RECOG          0.367114726       1.252497720      Recognition Memory

           Pooled Within-Class Standardized Canonical Coefficients

                      CAN1              CAN2

HIRECALL       0.172336227       1.161765720      HI Imagery Recall
LIRECALL       0.018394126      -0.504830299      LO Imagery Recall
HIUNREM        0.422142258      -1.616288269      HI Imagery Unreminded Memory
LIUNREM        0.251500337       0.604732452      LO Imagery Unreminded Memory
STORE          0.199242792      -0.098186135      Storage
RECOG          0.250534463       0.854756895      Recognition Memory

                          Raw Canonical Coefficients

                      CAN1              CAN2

HIRECALL        0.02558062        0.17244598      HI Imagery Recall
LIRECALL        0.00260021       -0.07136337      LO Imagery Recall
HIUNREM         2.63506175      -10.08906195      HI Imagery Unreminded Memory
LIUNREM         1.53729385        3.69642241      LO Imagery Unreminded Memory
STORE           0.87531112       -0.43135019      Storage
RECOG           0.19061982        0.65034410      Recognition Memory

               Memory Tests on Alzheimer and Depressed Patients              8
                       Canonical Discriminant Analysis

                       Canonical Discriminant Analysis

                      Class Means on Canonical Variables

                    GROUP              CAN1              CAN2

                Alzheimer      -2.393357537      -0.131206628
                Depressed       0.605503460       0.520906072
                Normal          1.713957163      -0.332786599

               Memory Tests on Alzheimer and Depressed Patients              9
                         Linear Discriminant Analysis

                            Discriminant Analysis

                  45 Observations        44 DF Total
                   6 Variables           42 DF Within Classes
                   3 Classes              2 DF Between Classes

                           Class Level Information

                                                                    Prior
     GROUP         Frequency        Weight     Proportion     Probability

     Alzheimer            15       15.0000       0.333333        0.333333
     Depressed            14       14.0000       0.311111        0.311111
     Normal               16       16.0000       0.355556        0.355556

               Memory Tests on Alzheimer and Depressed Patients             10
                         Linear Discriminant Analysis

        Discriminant Analysis     Pooled Covariance Matrix Information

               Covariance       Natural Log of the Determinant
               Matrix Rank      of the Covariance Matrix

                     6                    -5.6251429

               Memory Tests on Alzheimer and Depressed Patients             11
                         Linear Discriminant Analysis

                            Discriminant Analysis

            Pairwise Generalized Squared Distances Between Groups

                2         _   _       -1  _   _
               D (i|j) = (X - X )' COV   (X - X ) - 2 ln PRIOR
                           i   j           i   j              j

                          Generalized Squared Distance to GROUP
            From
            GROUP          Alzheimer      Depressed         Normal

            Alzheimer        2.19722       11.75363       18.97882
            Depressed       11.61564        2.33521        4.02561
            Normal          19.10789        4.29267        2.06815

               Memory Tests on Alzheimer and Depressed Patients             12
                         Linear Discriminant Analysis

            Discriminant Analysis     Linear Discriminant Function

                  _     -1 _                                          -1 _
   Constant = -.5 X' COV   X  + ln PRIOR      Coefficient Vector = COV   X
                   j        j           j                                 j

                                    GROUP

            Alzheimer    Depressed       Normal   Label

CONSTANT    -47.58992    -66.19240    -66.62864
HIRECALL      1.85301      2.04218      1.92332   HI Imagery Recall
LIRECALL     -0.13330     -0.17204     -0.10824   LO Imagery Recall
HIUNREM     -71.21464    -69.89166    -58.35786   HI Imagery Unreminded Memory
LIUNREM      -2.10865      4.91197      3.46038   LO Imagery Unreminded Memory
STORE        -6.12430     -3.78065     -2.44217   Storage
RECOG         6.89281      7.88855      7.54464   Recognition Memory

               Memory Tests on Alzheimer and Depressed Patients             13
                         Linear Discriminant Analysis

                            Discriminant Analysis

          Classification Summary for Calibration Data: WORK.ALZHEIM

          Resubstitution Summary using Linear Discriminant Function

              Generalized Squared Distance Function:

               2         _       -1   _
              D (X) = (X-X )' COV  (X-X ) - 2 ln PRIOR
               j          j            j              j

              Posterior Probability of Membership in each GROUP:

                                 2                    2
              Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))
                                 j        k           k

                   Number of Observations and Percent Classified into GROUP:

  From GROUP          Alzheimer      Depressed         Normal          Total

       Alzheimer             15              0              0             15
                         100.00           0.00           0.00         100.00

       Depressed              1              7              6             14
                           7.14          50.00          42.86         100.00

       Normal                 0              2             14             16
                           0.00          12.50          87.50         100.00

       Total                 16              9             20             45
       Percent            35.56          20.00          44.44         100.00

       Priors            0.3333         0.3111         0.3556

                    Error Count Estimates for GROUP:

                    Alzheimer     Depressed       Normal        Total

         Rate          0.0000        0.5000       0.1250       0.2000

         Priors        0.3333        0.3111       0.3556

               Memory Tests on Alzheimer and Depressed Patients             14
          Discriminant Analysis test Equality of Covariance Matrices

                            Discriminant Analysis

                  45 Observations        44 DF Total
                   6 Variables           42 DF Within Classes
                   3 Classes              2 DF Between Classes

                           Class Level Information

                                                                    Prior
     GROUP         Frequency        Weight     Proportion     Probability

     Alzheimer            15       15.0000       0.333333        0.333333
     Depressed            14       14.0000       0.311111        0.311111
     Normal               16       16.0000       0.355556        0.355556

               Memory Tests on Alzheimer and Depressed Patients             15
          Discriminant Analysis test Equality of Covariance Matrices

 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 =   142.095183
  with     42 DF      Prob > Chi-Sq = 0.0001


  Since the chi-square value is significant at the  0.01 level,
  the within covariance matrices will be used in the discriminant function.

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

               Memory Tests on Alzheimer and Depressed Patients             16
          Discriminant Analysis test Equality of Covariance Matrices

                            Discriminant Analysis

          Classification Summary for Calibration Data: WORK.ALZHEIM

         Resubstitution Summary using Quadratic Discriminant Function

            Generalized Squared Distance Function:

             2         _       -1   _
            D (X) = (X-X )' COV  (X-X ) + ln |COV | - 2 ln PRIOR
             j          j      j     j           j              j

            Posterior Probability of Membership in each GROUP:

                               2                    2
            Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))
                               j        k           k

                   Number of Observations and Percent Classified into GROUP:

  From GROUP          Alzheimer      Depressed         Normal          Total

       Alzheimer             14              1              0             15
                          93.33           6.67           0.00         100.00

       Depressed              0             12              2             14
                           0.00          85.71          14.29         100.00

       Normal                 0              0             16             16
                           0.00           0.00         100.00         100.00

       Total                 14             13             18             45
       Percent            31.11          28.89          40.00         100.00

       Priors            0.3333         0.3111         0.3556

                    Error Count Estimates for GROUP:

                    Alzheimer     Depressed       Normal        Total

         Rate          0.0667        0.1429       0.0000       0.0667

         Priors        0.3333        0.3111       0.3556