## Output from manova3.sas

Source
0 Graphs

```                      Two Way Manova Example (Morrison)                      1
```
```        Plot of Y2*Y1=DRUG.                       Plot of Y2*Y1=SEX.

15 +                     C               15 +                     M
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14 +                                     14 +
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13 +          B                          13 +          F
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12 +         B      CC                   12 +         M      FM
|                                        |
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11 +              C                      11 +              M
|                                        |
|                                        |
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W 10 +       AA   C                      W 10 +       FF   M
e    |                                   e    |
e    |                                   e    |
k    |                                   k    |
2  9 +      B  A    C                    2  9 +      F  M    F
|                                        |
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8 +      B       C                       8 +      M       F
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7 +       BBA                            7 +       MFF
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6 +     AAA                              6 +     MFM
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5 +          C                           5 +          F
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4 +     A                                4 +     M
-+---------+---------+---------+         -+---------+---------+---------+
0        10        20        30          0        10        20        30

Week1                                    Week1

NOTE: 2 obs hidden.                      NOTE: 2 obs hidden.```

```                      Two Way Manova Example (Morrison)                      2
```
```                       General Linear Models Procedure
Class Level Information

Class    Levels    Values
```
```                          SEX           2    F M

DRUG          3    A B C

Number of observations in data set = 24

```
```
E = Error SS&CP Matrix
```
```                                      Y1                Y2

Y1              94.5              76.5
Y2              76.5               114```

```                      Two Way Manova Example (Morrison)                      3
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r|```
```                        DF = 18           Y1        Y2

Y1          1.000000  0.737043```
```                                      0.0001    0.0003
```
`                        Y2          0.737043  1.000000`
```                                      0.0003    0.0001

```

```                      Two Way Manova Example (Morrison)                      4
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

H = Type III SS&CP Matrix for SEX
```
```                                      Y1                Y2

Y1      0.6666666667      0.6666666667
Y2      0.6666666667      0.6666666667

```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for SEX   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
Y1             Y2
```
```            0.00751918    100.00            0.07175780     0.03444374
0.00000000      0.00           -0.13423121     0.13423121

```
```               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=0    N=7.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.99253694     0.0639         2        17  0.9383
Pillai's Trace             0.00746306     0.0639         2        17  0.9383
Hotelling-Lawley Trace     0.00751918     0.0639         2        17  0.9383
Roy's Greatest Root        0.00751918     0.0639         2        17  0.9383
```
```
H = Type III SS&CP Matrix for DRUG
```
```                                      Y1                Y2

Y1               301              97.5
Y2              97.5      36.333333333

```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for DRUG   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
Y1             Y2
```
`            4.57602675     98.63            0.14784109    -0.07693601`

```                      Two Way Manova Example (Morrison)                      5
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for DRUG   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
Y1             Y2
```
```            0.06350991      1.37           -0.03619684     0.11526161

```
```                Manova Test Criteria and F Approximations for
the Hypothesis of no Overall DRUG Effect
H = Type III SS&CP Matrix for DRUG   E = Error SS&CP Matrix

S=2    M=-0.5    N=7.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.16862952    12.1991         4        34  0.0001
Pillai's Trace             0.88037810     7.0769         4        36  0.0003
Hotelling-Lawley Trace     4.63953666    18.5581         4        32  0.0001
Roy's Greatest Root        4.57602675    41.1842         2        18  0.0001

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

```
```
H = Type III SS&CP Matrix for SEX*DRUG
```
```                                      Y1                Y2

Y1      14.333333333      21.333333333
Y2      21.333333333      32.333333333

```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for SEX*DRUG   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
Y1             Y2
```
```            0.28372273     97.94           -0.00284433     0.09555092
0.00596889      2.06           -0.15218117     0.10037136

```

```                      Two Way Manova Example (Morrison)                      6
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

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

S=2    M=-0.5    N=7.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.77436234     1.1593         4        34  0.3459
Pillai's Trace             0.22694905     1.1520         4        36  0.3481
Hotelling-Lawley Trace     0.28969161     1.1588         4        32  0.3473
Roy's Greatest Root        0.28372273     2.5535         2        18  0.1056

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

```
```
H = Contrast SS&CP Matrix for drug C:A,B
```
```                                      Y1                Y2

Y1               300                95
Y2                95      30.083333333

```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Contrast SS&CP Matrix for drug C:A,B   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
Y1             Y2
```
```            4.57407407    100.00            0.14775192    -0.07665325
0.00000000      0.00           -0.03655912     0.11544985

```
```               Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall drug C:A,B Effect
H = Contrast SS&CP Matrix for drug C:A,B   E = Error SS&CP Matrix

S=1    M=0    N=7.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.17940199    38.8796         2        17  0.0001
Pillai's Trace             0.82059801    38.8796         2        17  0.0001
Hotelling-Lawley Trace     4.57407407    38.8796         2        17  0.0001
Roy's Greatest Root        4.57407407    38.8796         2        17  0.0001```

```                      Two Way Manova Example (Morrison)                      7
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

H = Contrast SS&CP Matrix for drug A:B
```
```                                      Y1                Y2

Y1                 1               2.5
Y2               2.5              6.25

```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Contrast SS&CP Matrix for drug A:B   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
Y1             Y2
```
```            0.06546258    100.00           -0.06135792     0.12688579
0.00000000      0.00            0.13929252    -0.05571701

```
```               Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall drug A:B Effect
H = Contrast SS&CP Matrix for drug A:B   E = Error SS&CP Matrix

S=1    M=0    N=7.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.93855947     0.5564         2        17  0.5833
Pillai's Trace             0.06144053     0.5564         2        17  0.5833
Hotelling-Lawley Trace     0.06546258     0.5564         2        17  0.5833
Roy's Greatest Root        0.06546258     0.5564         2        17  0.5833```

```                      Two Way Manova Example (Morrison)                      8
```
```                       General Linear Models Procedure

Tukey's Studentized Range (HSD) Test for variable: Y1
```
```         NOTE: This test controls the type I experimentwise error rate, but
generally has a higher type II error rate than REGWQ.```
```                        Alpha= 0.05  df= 18  MSE= 5.25
Critical Value of Studentized Range= 3.609
Minimum Significant Difference= 2.9239
```
```         Means with the same letter are not significantly different.

Tukey Grouping              Mean      N  DRUG```
```                             A            14.750      8  C

B             7.500      8  B
B
B             7.000      8  A

```

```                      Two Way Manova Example (Morrison)                      9
```
```                       General Linear Models Procedure

Tukey's Studentized Range (HSD) Test for variable: Y2
```
```         NOTE: This test controls the type I experimentwise error rate, but
generally has a higher type II error rate than REGWQ.```
```                      Alpha= 0.05  df= 18  MSE= 6.333333
Critical Value of Studentized Range= 3.609
Minimum Significant Difference= 3.2114
```
```         Means with the same letter are not significantly different.

Tukey Grouping              Mean      N  DRUG```
```                             A            10.250      8  C
A
A             8.500      8  B
A
A             7.250      8  A

```