Output from manova1.sas	Source 0 Graphs

                      Two group MANOVA / CANDISC example                     1
                      MULTIVARIATE ANALYSIS OF VARIANCE

                       General Linear Models Procedure
                           Class Level Information

                          Class    Levels    Values

                          SEX           2    F M


                   Number of observations in data set = 59

                            E = Error SS&CP Matrix

                   LENGTH          BASILAR          ZYGOMAT          POSTORB

 LENGTH       1683039.204     1430839.7517     386107.03613     74382.903263
 BASILAR     1430839.7517     1343555.1993     324249.61888     38106.472028
 ZYGOMAT     386107.03613     324249.61888     262647.62354     33070.588578
 POSTORB     74382.903263     38106.472028     33070.588578     195162.71445

                      Two group MANOVA / CANDISC example                     2
                      MULTIVARIATE ANALYSIS OF VARIANCE

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

  Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r|

              DF = 57       LENGTH   BASILAR   ZYGOMAT   POSTORB

              LENGTH      1.000000  0.951516  0.580729  0.129786

                            0.0001    0.0001    0.0001    0.3315

              BASILAR     0.951516  1.000000  0.545840  0.074417

                            0.0001    0.0001    0.0001    0.5788

              ZYGOMAT     0.580729  0.545840  1.000000  0.146069

                            0.0001    0.0001    0.0001    0.2739

              POSTORB     0.129786  0.074417  0.146069  1.000000

                            0.3315    0.5788    0.2739    0.0001

                      Two group MANOVA / CANDISC example                     3
                      MULTIVARIATE ANALYSIS OF VARIANCE

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

                      H = Type III SS&CP Matrix for SEX

                   LENGTH          BASILAR          ZYGOMAT          POSTORB

 LENGTH      47060.931631     33597.044862     1775.0655644     3013.0797874
 BASILAR     33597.044862     23985.105784     1267.2285765     2151.0533958
 ZYGOMAT     1775.0655644     1267.2285765     66.952728063     113.64871005
 POSTORB     3013.0797874     2151.0533958     113.64871005     192.91266643

                      Two group MANOVA / CANDISC example                     4
                      MULTIVARIATE ANALYSIS OF VARIANCE

                       General Linear Models Procedure
                      Multivariate Analysis of Variance
                              Canonical Analysis

          H = Type III SS&CP Matrix for SEX   E = Error SS&CP Matrix

                                Adjusted       Approx       Squared
                 Canonical      Canonical     Standard     Canonical
                Correlation    Correlation     Error      Correlation

           1      0.208067       0.090867     0.125622      0.043292

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

                 Eigenvalue    Difference    Proportion    Cumulative

            1       0.0453         .           1.0000        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    0.95670815      0.6109           4          54    0.6566

                       NOTE: The F statistic is exact.

                          Total Canonical Structure

                                                CAN1

                            LENGTH           -0.7927
                           BASILAR           -0.6365
                           ZYGOMAT           -0.0767
                           POSTORB           -0.1510

                         Between Canonical Structure

                                                CAN1

                            LENGTH           -1.0000
                           BASILAR           -1.0000
                           ZYGOMAT           -1.0000
                           POSTORB           -1.0000

                      Two group MANOVA / CANDISC example                     5
                      MULTIVARIATE ANALYSIS OF VARIANCE

                       General Linear Models Procedure
                      Multivariate Analysis of Variance
                              Canonical Analysis

                          Within Canonical Structure

                                                CAN1

                            LENGTH           -0.7861
                           BASILAR           -0.6281
                           ZYGOMAT           -0.0751
                           POSTORB           -0.1478

                     Standardized Canonical Coefficients

                                                CAN1

                            LENGTH           -2.3719
                           BASILAR            1.2966
                           ZYGOMAT            0.5863
                           POSTORB           -0.0242

                          Raw Canonical Coefficients

                                                CAN1

                            LENGTH      -0.013733139
                           BASILAR      0.0084437216
                           ZYGOMAT      0.0087111152
                           POSTORB       -0.00041649

               Manova Test Criteria and Exact F Statistics for
                   the Hypothesis of no Overall SEX Effect
          H = Type III SS&CP Matrix for SEX   E = Error SS&CP Matrix

                              S=1    M=1    N=26

 Statistic                     Value          F      Num DF    Den DF  Pr > F

 Wilks' Lambda              0.95670815     0.6109         4        54  0.6566
 Pillai's Trace             0.04329185     0.6109         4        54  0.6566
 Hotelling-Lawley Trace     0.04525085     0.6109         4        54  0.6566
 Roy's Greatest Root        0.04525085     0.6109         4        54  0.6566

                      Two group MANOVA / CANDISC example                     6
                             Output from CANDISC

                       Canonical Discriminant Analysis

                  59 Observations        58 DF Total
                   4 Variables           57 DF Within Classes
                   2 Classes              1 DF Between Classes

                           Class Level Information

             SEX          Frequency        Weight     Proportion

             F                   26       26.0000       0.440678
             M                   33       33.0000       0.559322

                      Two group MANOVA / CANDISC example                     7
                             Output from CANDISC

                       Canonical Discriminant Analysis

                Multivariate Statistics and Exact F Statistics

                              S=1    M=1    N=26

 Statistic                     Value          F      Num DF    Den DF  Pr > F

 Wilks' Lambda              0.95670815     0.6109         4        54  0.6566
 Pillai's Trace             0.04329185     0.6109         4        54  0.6566
 Hotelling-Lawley Trace     0.04525085     0.6109         4        54  0.6566
 Roy's Greatest Root        0.04525085     0.6109         4        54  0.6566

                      Two group MANOVA / CANDISC example                     8
                             Output from CANDISC

                       Canonical Discriminant Analysis

                                Adjusted       Approx       Squared
                 Canonical      Canonical     Standard     Canonical
                Correlation    Correlation     Error      Correlation

           1      0.208067       0.090867     0.125622      0.043292

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

                 Eigenvalue    Difference    Proportion    Cumulative

            1       0.0453         .           1.0000        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    0.95670815      0.6109           4          54    0.6566

                       NOTE: The F statistic is exact.

                          Total Canonical Structure

                                               CAN1

                          LENGTH          -0.792668
                          BASILAR         -0.636499
                          ZYGOMAT         -0.076725
                          POSTORB         -0.151030

                         Between Canonical Structure

                                               CAN1

                          LENGTH          -1.000000
                          BASILAR         -1.000000
                          ZYGOMAT         -1.000000
                          POSTORB         -1.000000

                      Two group MANOVA / CANDISC example                     9
                             Output from CANDISC

                       Canonical Discriminant Analysis

                      Pooled Within Canonical Structure

                                               CAN1

                          LENGTH          -0.786086
                          BASILAR         -0.628101
                          ZYGOMAT         -0.075056
                          POSTORB         -0.147798

               Total-Sample Standardized Canonical Coefficients

                                               CAN1

                          LENGTH       -2.371872975
                          BASILAR       1.296552115
                          ZYGOMAT       0.586275637
                          POSTORB      -0.024171469

           Pooled Within-Class Standardized Canonical Coefficients

                                               CAN1

                          LENGTH       -2.359823338
                          BASILAR       1.296355864
                          ZYGOMAT       0.591320682
                          POSTORB      -0.024370535

                          Raw Canonical Coefficients

                                               CAN1

                          LENGTH       -.0137331386
                          BASILAR      0.0084437216
                          ZYGOMAT      0.0087111152
                          POSTORB      -.0004164895

                      Class Means on Canonical Variables

                            SEX              CAN1

                            F        -.2355564855
                            M        0.1855899582

                      Two group MANOVA / CANDISC example                    10
                         Discriminant function scores

      OBS    SEX    LENGTH    BASILAR    ZYGOMAT    POSTORB      CAN1

        1     M      6460       4962       3286       1100      0.53144
        2     M      6252       4773       3239       1061      1.39889
        3     M      5772       4480       3200       1097      5.16206
        4     M      6264       4806       3179       1054      0.99298
        5     M      6622       5113       3365       1071      0.28193
        6     M      6656       5100       3326       1012     -0.60993
        7     M      6441       4918       3153       1061     -0.72149
        8     M      6281       4821       3133       1071      0.47838
        9     M      6606       5060       3227       1064     -1.14508
       10     M      6573       4977       3392       1110      0.02546
       11     M      6563       5025       3234       1090     -0.79993
       12     M      6552       5086       3292       1010      0.40476
       13     M      6535       4939       3261       1065     -0.89595
       14     M      6573       4962       3320       1091     -0.72048
       15     M      6537       4990       3309       1059     -0.07216
       16     M      6302       4761       3204       1135      0.27520
       17     M      6449       4921       3256       1068      0.08831
       18     M      6481       4887       3233       1124     -0.86192
       19     M      6368       4824       3258       1130      0.37325
       20     M      6372       4844       3306       1137      0.90241
       21     M      6592       5007       3284       1148     -0.93878
       22     M      6229       4746       3257       1153      1.60525
       23     M      6391       4834       3244       1169      0.00362
       24     M      6560       4981       3341       1038     -0.17651
       25     M      6787       5181       3334       1104     -1.69365
       26     M      6384       4834       3195       1064     -0.28336
       27     M      6282       4757       3180       1179      0.28869
       28     M      6340       4791       3300       1110      0.85333
       29     M      6394       4879       3272       1241      0.55632
       30     M      6153       4557       3214       1039      0.72601
       31     M      6348       4886       3160        991      0.37562
       32     M      6534       4990       3310       1028     -0.00934
       33     M      6509       4951       3282       1104     -0.27088
       34     F      6287       4845       3218        996      1.37032
       35     F      6583       4992       3300       1107     -0.78539
       36     F      6518       5023       3246       1035     -0.07139
       37     F      6432       4790       3249       1117     -0.86574
       38     F      6450       4888       3259       1060     -0.17461
       39     F      6379       4844       3266       1115      0.46699
       40     F      6424       4855       3322       1065      0.45053
       41     F      6615       5088       3280       1179     -0.61846
       42     F      6760       5206       3337       1219     -1.13353
       43     F      6521       5011       3208        989     -0.52578
       44     F      6416       4889       3200       1001     -0.18862
       45     F      6511       4910       3230       1100     -1.09585
       46     F      6540       4997       3320       1078      0.03366
       47     F      6780       5259       3358       1174     -0.75900
       48     F      6336       4781       3165       1126     -0.35884
       49     F      6472       4954       3125       1178     -1.13588
       50     F      6476       4896       3148       1066     -1.43355

                      Two group MANOVA / CANDISC example                    11
                         Discriminant function scores

      OBS    SEX    LENGTH    BASILAR    ZYGOMAT    POSTORB      CAN1

       51     F      6276       4709       3150       1134     -0.27680
       52     F      6693       5177       3236       1131     -1.30145
       53     F      6328       4792       3214       1018      0.31573
       54     F      6661       5104       3395       1141     -0.09748
       55     F      6266       4721       3257       1031      0.93685
       56     F      6660       5146       3374       1069      0.11795
       57     F      6624       5032       3384       1154     -0.29854
       58     F      6331       4819       3278       1008      1.06419
       59     F      6298       4683       3270       1150      0.24021

                      Two group MANOVA / CANDISC example                    12
                         Discriminant function scores

 OBS  SEX  _TYPE_    _NAME_        LENGTH      BASILAR    ZYGOMAT     POSTORB

   1       N                        59.00        59.00      59.00       59.00
   2   F   N                        26.00        26.00      26.00       26.00
   3   M   N                        33.00        33.00      33.00       33.00
   4       MEAN                   6454.22      4916.17    3259.92     1091.85
   5   F   MEAN                   6486.04      4938.88    3261.12     1093.88
   6   M   MEAN                   6429.15      4898.27    3258.97     1090.24
   7   F   CSSCP     LENGTH     579780.96    583803.12  164515.88   123652.12
   8   F   CSSCP     BASILAR    583803.12    631736.65  156802.35    97384.65
   9   F   CSSCP     ZYGOMAT    164515.88    156802.35  135882.65    29739.35
  10   F   CSSCP     POSTORB    123652.12     97384.65   29739.35   103980.65
  11   M   CSSCP     LENGTH    1103258.24    847036.64  221591.15   -49269.21
  12   M   CSSCP     BASILAR    847036.64    711818.55  167447.27   -59278.18
  13   M   CSSCP     ZYGOMAT    221591.15    167447.27  126764.97     3331.24
  14   M   CSSCP     POSTORB    -49269.21    -59278.18    3331.24    91182.06
  15       PSSCP     LENGTH    1683039.20   1430839.75  386107.04    74382.90
  16       PSSCP     BASILAR   1430839.75   1343555.20  324249.62    38106.47
  17       PSSCP     ZYGOMAT    386107.04    324249.62  262647.62    33070.59
  18       PSSCP     POSTORB     74382.90     38106.47   33070.59   195162.71
  19       BSSCP     LENGTH      47060.93     33597.04    1775.07     3013.08
  20       BSSCP     BASILAR     33597.04     23985.11    1267.23     2151.05
  21       BSSCP     ZYGOMAT      1775.07      1267.23      66.95      113.65
  22       BSSCP     POSTORB      3013.08      2151.05     113.65      192.91
  23       CSSCP     LENGTH    1730100.14   1464436.80  387882.10    77395.98
  24       CSSCP     BASILAR   1464436.80   1367540.31  325516.85    40257.53
  25       CSSCP     ZYGOMAT    387882.10    325516.85  262714.58    33184.24
  26       CSSCP     POSTORB     77395.98     40257.53   33184.24   195355.63
  27       RSQUARED                  0.03         0.02       0.00        0.00
  28   F   COV       LENGTH      23191.24     23352.12    6580.64     4946.08
  29   F   COV       BASILAR     23352.12     25269.47    6272.09     3895.39
  30   F   COV       ZYGOMAT      6580.64      6272.09    5435.31     1189.57
  31   F   COV       POSTORB      4946.08      3895.39    1189.57     4159.23
  32   M   COV       LENGTH      34476.82     26469.89    6924.72    -1539.66
  33   M   COV       BASILAR     26469.89     22244.33    5232.73    -1852.44
  34   M   COV       ZYGOMAT      6924.72      5232.73    3961.41      104.10
  35   M   COV       POSTORB     -1539.66     -1852.44     104.10     2849.44
  36       PCOV      LENGTH      29527.00     25102.45    6773.81     1304.96
  37       PCOV      BASILAR     25102.45     23571.14    5688.59      668.53
  38       PCOV      ZYGOMAT      6773.81      5688.59    4607.85      580.19
  39       PCOV      POSTORB      1304.96       668.53     580.19     3423.91
  40       BCOV      LENGTH       1595.29      1138.88      60.17      102.14
  41       BCOV      BASILAR      1138.88       813.05      42.96       72.92
  42       BCOV      ZYGOMAT        60.17        42.96       2.27        3.85
  43       BCOV      POSTORB       102.14        72.92       3.85        6.54
  44       COV       LENGTH      29829.31     25248.91    6687.62     1334.41
  45       COV       BASILAR     25248.91     23578.28    5612.36      694.10
  46       COV       ZYGOMAT      6687.62      5612.36    4529.56      572.14
  47       COV       POSTORB      1334.41       694.10     572.14     3368.20
  48   F   STD                     152.29       158.96      73.72       64.49
  49   M   STD                     185.68       149.15      62.94       53.38
  50       PSTD                    171.83       153.53      67.88       58.51

                      Two group MANOVA / CANDISC example                    13
                         Discriminant function scores

  OBS   SEX   _TYPE_     _NAME_      LENGTH    BASILAR    ZYGOMAT    POSTORB

   51         BSTD                   39.941     28.514     1.5065     2.5572
   52         STD                   172.712    153.552    67.3020    58.0362
   53    F    CORR       LENGTH       1.000      0.965     0.5861     0.5036
   54    F    CORR       BASILAR      0.965      1.000     0.5352     0.3800
   55    F    CORR       ZYGOMAT      0.586      0.535     1.0000     0.2502
   56    F    CORR       POSTORB      0.504      0.380     0.2502     1.0000
   57    M    CORR       LENGTH       1.000      0.956     0.5925    -0.1553
   58    M    CORR       BASILAR      0.956      1.000     0.5574    -0.2327
   59    M    CORR       ZYGOMAT      0.593      0.557     1.0000     0.0310
   60    M    CORR       POSTORB     -0.155     -0.233     0.0310     1.0000
   61         PCORR      LENGTH       1.000      0.952     0.5807     0.1298
   62         PCORR      BASILAR      0.952      1.000     0.5458     0.0744
   63         PCORR      ZYGOMAT      0.581      0.546     1.0000     0.1461
   64         PCORR      POSTORB      0.130      0.074     0.1461     1.0000
   65         BCORR      LENGTH       1.000      1.000     1.0000     1.0000
   66         BCORR      BASILAR      1.000      1.000     1.0000     1.0000
   67         BCORR      ZYGOMAT      1.000      1.000     1.0000     1.0000
   68         BCORR      POSTORB      1.000      1.000     1.0000     1.0000
   69         CORR       LENGTH       1.000      0.952     0.5753     0.1331
   70         CORR       BASILAR      0.952      1.000     0.5431     0.0779
   71         CORR       ZYGOMAT      0.575      0.543     1.0000     0.1465
   72         CORR       POSTORB      0.133      0.078     0.1465     1.0000
   73    F    STDMEAN                 0.184      0.148     0.0178     0.0351
   74    M    STDMEAN                -0.145     -0.117    -0.0140    -0.0277
   75    F    PSTDMEAN                0.185      0.148     0.0177     0.0348
   76    M    PSTDMEAN               -0.146     -0.117    -0.0139    -0.0274
   77         CANCORR    CAN1         0.208      0.208     0.2081     0.2081
   78         STRUCTUR   CAN1        -0.793     -0.636    -0.0767    -0.1510
   79         BSTRUCT    CAN1        -1.000     -1.000    -1.0000    -1.0000
   80         PSTRUCT    CAN1        -0.786     -0.628    -0.0751    -0.1478
   81         SCORE      CAN1        -2.372      1.297     0.5863    -0.0242
   82         PSCORE     CAN1        -2.360      1.296     0.5913    -0.0244
   83         RAWSCORE   CAN1        -0.014      0.008     0.0087    -0.0004
   84    F    CANMEAN    CAN1        -0.236     -0.236    -0.2356    -0.2356
   85    M    CANMEAN    CAN1         0.186      0.186     0.1856     0.1856