## Output from m1way.sas

Source
0 Graphs

```            Dog Food: One Way Completely Randomized Manova Design            1
```
`                   OBS    FORMULA    DOG    START    AMOUNT`
```                     1     OLD        1       0        100
2     OLD        2       1         97
3     OLD        3       1         88
4     OLD        4       0         92
5     NEW        1       0         95
6     NEW        2       1         85
7     NEW        3       2         82
8     NEW        4       3         89
9     MAJOR      1       1         77
10     MAJOR      2       5         84
11     MAJOR      3       3         78
12     MAJOR      4       1         89
13     ALPS       1       2         72
14     ALPS       2       3         82
15     ALPS       3       4         85
16     ALPS       4       0         74```

```            Dog Food: One Way Completely Randomized Manova Design            2
```
```             Plot of AMOUNT*START.  Symbol is value of FORMULA.

|
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100 +O
99 +
98 +
97 +              O
96 +
95 +N
94 +
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A  92 +O
m  91 +
o  90 +
u  89 +              M                           N
n  88 +              O
t  87 +
86 +
e  85 +              N                                         A
a  84 +                                                                      M
t  83 +
e  82 +                            N             A
n  81 +
80 +
79 +
78 +                                          M
77 +              M
76 +
75 +
74 +A
73 +
72 +                            A
|
-+-------------+-------------+-------------+-------------+-------------+
0             1             2             3             4             5

Time to start eating

```

```            Dog Food: One Way Completely Randomized Manova Design            3
MANOVA for equality of means
```
```                       General Linear Models Procedure
Class Level Information

Class    Levels    Values
```
```                    FORMULA       4    OLD NEW MAJOR ALPS

Number of observations in data set = 16

```

```            Dog Food: One Way Completely Randomized Manova Design            4
MANOVA for equality of means
```
```                       General Linear Models Procedure

Dependent Variable: START   Time to start eating
Sum of           Mean
Source                  DF         Squares         Square   F Value     Pr > F
```
```Model                    3      9.68750000     3.22916667      1.50     0.2634

Error                   12     25.75000000     2.14583333

Corrected Total         15     35.43750000```
```
R-Square            C.V.       Root MSE           START Mean
```
```                  0.273369        86.80689       1.464866             1.687500
```
```
Source                  DF     Type III SS    Mean Square   F Value     Pr > F
```
`FORMULA                  3      9.68750000     3.22916667      1.50     0.2634`

```            Dog Food: One Way Completely Randomized Manova Design            5
MANOVA for equality of means
```
```                       General Linear Models Procedure

Dependent Variable: AMOUNT   Amount eaten
Sum of           Mean
Source                  DF         Squares         Square   F Value     Pr > F
```
```Model                    3     585.6875000    195.2291667      6.00     0.0097

Error                   12     390.2500000     32.5208333

Corrected Total         15     975.9375000```
```
R-Square            C.V.       Root MSE          AMOUNT Mean
```
```                  0.600128        6.664957       5.702704             85.56250
```
```
Source                  DF     Type III SS    Mean Square   F Value     Pr > F
```
```FORMULA                  3     585.6875000    195.2291667      6.00     0.0097

```

```            Dog Food: One Way Completely Randomized Manova Design            6
MANOVA for equality of means
```
```                       General Linear Models Procedure

Level of       ------------START------------     ------------AMOUNT-----------
FORMULA    N       Mean              SD              Mean              SD
```
```OLD        4     0.50000000       0.57735027       94.2500000       5.31507291
NEW        4     1.50000000       1.29099445       87.7500000       5.61990510
MAJOR      4     2.50000000       1.91485422       82.0000000       5.59761854
ALPS       4     2.25000000       1.70782513       78.2500000       6.23832242```

```            Dog Food: One Way Completely Randomized Manova Design            7
MANOVA for equality of means
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

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

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
START         AMOUNT
```
```            2.03961854     98.47           -0.10279413     0.04639418
0.03174562      1.53            0.16973304     0.02111246

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

S=2    M=0    N=4.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.31886605     2.8267         6        22  0.0341
Pillai's Trace             0.70178019     2.1623         6        24  0.0829
Hotelling-Lawley Trace     2.07136416     3.4523         6        20  0.0166
Roy's Greatest Root        2.03961854     8.1585         3        12  0.0031

NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Contrast SS&CP Matrix for Equality of Groups   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
START         AMOUNT
```
```            2.03961854     98.47           -0.10279413     0.04639418
0.03174562      1.53            0.16973304     0.02111246

```

```            Dog Food: One Way Completely Randomized Manova Design            8
MANOVA for equality of means
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

Manova Test Criteria and F Approximations for
the Hypothesis of no Overall Equality of Groups Effect
H = Contrast SS&CP Matrix for Equality of Groups   E = Error SS&CP Matrix

S=2    M=0    N=4.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.31886605     2.8267         6        22  0.0341
Pillai's Trace             0.70178019     2.1623         6        24  0.0829
Hotelling-Lawley Trace     2.07136416     3.4523         6        20  0.0166
Roy's Greatest Root        2.03961854     8.1585         3        12  0.0031

NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Contrast SS&CP Matrix for Ours vs. Theirs   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
START         AMOUNT
```
```            1.66869411    100.00           -0.10378699     0.04626967
0.00000000      0.00            0.16912776     0.02138397

```
```               Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall Ours vs. Theirs Effect
H = Contrast SS&CP Matrix for Ours vs. Theirs   E = Error SS&CP Matrix

S=1    M=0    N=4.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.37471511     9.1778         2        11  0.0045
Pillai's Trace             0.62528489     9.1778         2        11  0.0045
Hotelling-Lawley Trace     1.66869411     9.1778         2        11  0.0045
Roy's Greatest Root        1.66869411     9.1778         2        11  0.0045```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Contrast SS&CP Matrix for Old - New   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
START         AMOUNT
```
```            0.32912079    100.00           -0.11606288     0.04455347
0.00000000      0.00            0.16095138     0.02476175```

```            Dog Food: One Way Completely Randomized Manova Design            9
MANOVA for equality of means
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall Old - New Effect
H = Contrast SS&CP Matrix for Old - New   E = Error SS&CP Matrix

S=1    M=0    N=4.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.75237707     1.8102         2        11  0.2091
Pillai's Trace             0.24762293     1.8102         2        11  0.2091
Hotelling-Lawley Trace     0.32912079     1.8102         2        11  0.2091
Roy's Greatest Root        0.32912079     1.8102         2        11  0.2091```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Contrast SS&CP Matrix for Major vs. Alps   E = Error SS&CP Matrix

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
START         AMOUNT
```
```            0.07354926    100.00            0.02814930     0.04926128
0.00000000      0.00            0.19642697    -0.01309513

```
```               Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall Major vs. Alps Effect
H = Contrast SS&CP Matrix for Major vs. Alps   E = Error SS&CP Matrix

S=1    M=0    N=4.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.93148963     0.4045         2        11  0.6768
Pillai's Trace             0.06851037     0.4045         2        11  0.6768
Hotelling-Lawley Trace     0.07354926     0.4045         2        11  0.6768
Roy's Greatest Root        0.07354926     0.4045         2        11  0.6768```

```            Dog Food: One Way Completely Randomized Manova Design           10
MANOVA for equality of means
```
```                       General Linear Models Procedure

Dependent Variable: START   Time to start eating

Contrast                DF     Contrast SS    Mean Square   F Value     Pr > F
```
```Equality of Groups       3      9.68750000     3.22916667      1.50     0.2634
Ours vs. Theirs          1      7.56250000     7.56250000      3.52     0.0850
Old - New                1      2.00000000     2.00000000      0.93     0.3534
Major vs. Alps           1      0.12500000     0.12500000      0.06     0.8134```

```            Dog Food: One Way Completely Randomized Manova Design           11
MANOVA for equality of means
```
```                       General Linear Models Procedure

Dependent Variable: AMOUNT   Amount eaten

Contrast                DF     Contrast SS    Mean Square   F Value     Pr > F
```
```Equality of Groups       3     585.6875000    195.2291667      6.00     0.0097
Ours vs. Theirs          1     473.0625000    473.0625000     14.55     0.0025
Old - New                1      84.5000000     84.5000000      2.60     0.1329
Major vs. Alps           1      28.1250000     28.1250000      0.86     0.3707

```