## Output from mpower2.sas

Source
0 Graphs

```                    Two Way Manova Example: Power analysis                   1
```
```                  Plot of Y2*Y1.  Symbol is value of DRUG.

|
|
12.00 +                                                                  C
11.75 +
11.50 +
W 11.25 +
e 11.00 +
e 10.75 +
k 10.50 +
2 10.25 +
10.00 +
w  9.75 +
e  9.50 +
i  9.25 +
g  9.00 +
h  8.75 +            B
t  8.50 +                                                  C
8.25 +         B A
l  8.00 +
o  7.75 +
s  7.50 +
s  7.25 +
7.00 +
6.75 +
6.50 +
6.25 +    A
|
--+------------+------------+------------+------------+------------+--
6            8           10           12           14           16

Week1 weight loss

```

```                    Two Way Manova Example: Power analysis                   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

```

```                    Two Way Manova Example: Power analysis                   3
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type I 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 I 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```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Type I 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
0.06350991      1.37           -0.03619684     0.11526161

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

```                    Two Way Manova Example: Power analysis                   4
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

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.
```
```          Characteristic Roots and Vectors of: E Inverse * H, where
H = Type I 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

```
```                Manova Test Criteria and F Approximations for
the Hypothesis of no Overall SEX*DRUG Effect
H = Type I 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.
```

```                    Two Way Manova Example: Power analysis                   5
OUTSTAT= data set
```
`OBS  _NAME_  _SOURCE_  _TYPE_       Y1       Y2  DF       SS     F       PROB`
``` 1     Y1    ERROR     ERROR    94.500   76.500  18   94.500    .       .
2     Y2    ERROR     ERROR    76.500  114.000  18  114.000    .       .
3     Y1    SEX       SS1       0.667    0.667   1    0.667   0.1270  0.72572
4     Y2    SEX       SS1       0.667    0.667   1    0.667   0.1053  0.74934
5     Y1    DRUG      SS1     301.000   97.500   2  301.000  28.6667  0.00000
6     Y2    DRUG      SS1      97.500   36.333   2   36.333   2.8684  0.08292
7     Y1    SEX*DRUG  SS1      14.333   21.333   2   14.333   1.3651  0.28056
8     Y2    SEX*DRUG  SS1      21.333   32.333   2   32.333   2.5526  0.10569```

```                    Two Way Manova Example: Power analysis                   6
Retrospective power analysis
```
```                                        EFFECT      ALPHA
Power analysis for SEX SS1      0.05

ROOTS     THETA         S         M         N
0.0075192 0.0074631         1         0       7.5
0         0

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

Wilks' Lambda      0.993    0.064      2    17     0.0075    0.0639    0.0541
Pillai's Trace     0.007    0.064      2    17     0.0075    0.0639    0.0541
Lawley Trace       0.008    0.064      2    17     0.0075    0.0639    0.0541
Roy's max. Root    0.008    0.064      2    17     0.0075    0.0639    0.0541

EFFECT        ALPHA
Power analysis for DRUG SS1       0.05

ROOTS     THETA         S         M         N
4.5760267 0.8206608         2      -0.5       7.5
0.0635099 0.0597173

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

Wilks' Lambda      0.169   12.199      4    34     0.5894    24.398    0.9728
Pillai's Trace     0.880    7.077      4    36     0.4402    14.154    0.8174
Lawley Trace       4.640   18.558      4    32     0.6988    37.116    0.9983
Roy's max. Root    4.576   41.184      2    18     0.8207    82.368         1

EFFECT                ALPHA
Power analysis for SEX*DRUG SS1           0.05

ROOTS     THETA         S         M         N
0.2837227 0.2210156         2      -0.5       7.5
0.0059689 0.0059335

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

Wilks' Lambda      0.774    1.159      4    34       0.12    2.3187    0.1733
Pillai's Trace     0.227    1.152      4    36     0.1135     2.304    0.1734
Lawley Trace       0.290    1.159      4    32     0.1265    2.3175    0.1721
Roy's max. Root    0.284    2.554      2    18      0.221     5.107    0.4444
```