## Output from m1power.sas

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```              Retrospective Power Analysis: OneWay MANOVA Design             1
```
```                       General Linear Models Procedure
Class Level Information

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

Number of observations in data set = 16

```

```              Retrospective Power Analysis: OneWay MANOVA Design             2
```
```                       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 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

```

```              Retrospective Power Analysis: OneWay MANOVA Design             3
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

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```

```              Retrospective Power Analysis: OneWay MANOVA Design             4
Univariate power
```
```                                                            F Nominal Adj.
SOURCE          _NAME_ _TYPE_     START   AMOUNT  DF  Value  power  power```
```  FORMULA         START  SS3        9.6875  -70.938  3   1.50  0.063  0.050
FORMULA         AMOUNT SS3      -70.9375  585.687  3   6.00  0.868  0.693
Ours vs. Theirs START  CONTRAST   7.5625  -59.813  1   3.52  0.073  0.050
Ours vs. Theirs AMOUNT CONTRAST -59.8125  473.063  1  14.55  0.938  0.864
```
```                            Non-      Adj_Non-   Req'd  Total  Req'd
SOURCE          _NAME_ Centrality  Centrality    N      N    power  ALPHA```
```  FORMULA         START      0.30        0.00       .      .    0.8    0.05
FORMULA         AMOUNT    18.01       12.01       .      .    0.8    0.05
Ours vs. Theirs START      0.23        0.00       .      .    0.8    0.05
Ours vs. Theirs AMOUNT    14.55       11.12       .      .    0.8    0.05```

```              Retrospective Power Analysis: OneWay MANOVA Design             5
Multivariate power
```
```                                    EFFECT              ALPHA
Power analysis for FORMULA SS3          0.05

ROOTS     THETA         S         M         N
2.0396185 0.6710114         2         0       4.5
0.0317456 0.0307688

Value        F    df1   df2     Eta##2 Non-Cent.     Power

Wilks' Lambda      0.319    2.827      6    22     0.4353      8.48    0.4352
Pillai's Trace     0.702    2.162      6    24     0.3509    6.4869    0.3414
Lawley Trace       2.071    3.452      6    20     0.5088    10.357    0.5135
Roy's max. Root    2.040    8.158      3    12      0.671    24.475    0.9529

EFFECT                              ALPHA
Power analysis for Ours vs. Theirs CONTRAST             0.05

ROOTS     THETA         S         M         N
1.6686941 0.6252849         1         0       4.5
0         0

Value        F    df1   df2     Eta##2 Non-Cent.     Power

Wilks' Lambda      0.375    9.178      2    11     0.6253    9.1778    0.6509
Pillai's Trace     0.625    9.178      2    11     0.6253    9.1778    0.6509
Lawley Trace       1.669    9.178      2    11     0.6253    9.1778    0.6509
Roy's max. Root    1.669    9.178      2    11     0.6253    9.1778    0.6509
```