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```                      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

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```