## Output from mpower1.sas

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```               Effects of teaching methods on math performance               1
```
```                       General Linear Models Procedure
Class Level Information

Class    Levels    Values
```
```                          GROUP         4    1 2 3 4

Number of observations in data set = 80

```
```
E = Error SS&CP Matrix
```
```                                      ADD              MULT

MULT           3926.75              5411```

```               Effects of teaching methods on math performance               2
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r|```
```                        DF = 76          ADD      MULT

```                                      0.0001    0.0001
```
`                        MULT        0.565021  1.000000`
```                                      0.0001    0.0001

```

```               Effects of teaching methods on math performance               3
```
```                       General Linear Models Procedure
Multivariate Analysis of Variance

H = Type III SS&CP Matrix for GROUP
```
```                                      ADD              MULT

MULT             12860             27882

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

Characteristic   Percent        Characteristic Vector  V'EV=1
Root
```
```            5.62938867     76.99           -0.00445768     0.01598225
1.68259713     23.01            0.01202912    -0.00400567

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

S=2    M=0    N=36.5

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.05623039    80.4276         6       150  0.0001
Pillai's Trace             1.47638345    71.4296         6       152  0.0001
Hotelling-Lawley Trace     7.31198580    90.1812         6       148  0.0001
Roy's Greatest Root        5.62938867   142.6112         3        76  0.0001

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

```               Effects of teaching methods on math performance               4
```
```                                      EFFECT          ALPHA
Power analysis for GROUP SS3        0.01

ROOTS     THETA         S         M         N
5.6293887 0.8491565         2         0      36.5
1.6825971 0.6272269

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

Wilks' Lambda      0.056   80.428      6   150     0.7629    241.28         1
Pillai's Trace     1.476   71.430      6   152     0.7382    214.29         1
Lawley Trace       7.312   90.181      6   148     0.7852    270.54         1
Roy's max. Root    5.629  142.611      3    76     0.8492    427.83         1

EFFECT                    ALPHA
Power analysis for 1-2 VS 3-4 CONTRAST        0.01

ROOTS     THETA         S         M         N
4.2093541 0.8080376         1         0      36.5
0         0

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

Wilks' Lambda      0.192  157.851      2    75      0.808    157.85         1
Pillai's Trace     0.808  157.851      2    75      0.808    157.85         1
Lawley Trace       4.209  157.851      2    75      0.808    157.85         1
Roy's max. Root    4.209  157.851      2    75      0.808    157.85         1

EFFECT                    ALPHA
Power analysis for 1-3 VS 2-4 CONTRAST        0.01

ROOTS     THETA         S         M         N
0.3317695 0.2491193         1         0      36.5
0         0

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

Wilks' Lambda      0.751   12.441      2    75     0.2491    12.441    0.7063
Pillai's Trace     0.249   12.441      2    75     0.2491    12.441    0.7063
Lawley Trace       0.332   12.441      2    75     0.2491    12.441    0.7063
Roy's max. Root    0.332   12.441      2    75     0.2491    12.441    0.7063
```

```               Effects of teaching methods on math performance               5
```
`  OBS   _SOURCE_     _TYPE_     STAT     ALPHA     ETA2       NC      POWER`
```    1   GROUP        SS3        WILKS     0.01   0.76287   241.283   1.00000
2   GROUP        SS3        PILLAI    0.01   0.73819   214.289   1.00000
3   GROUP        SS3        LAWLEY    0.01   0.78522   270.543   1.00000
4   GROUP        SS3        ROY       0.01   0.84916   427.834   1.00000
5   1-2 VS 3-4   CONTRAST   WILKS     0.01   0.80804   157.851   1.00000
6   1-2 VS 3-4   CONTRAST   PILLAI    0.01   0.80804   157.851   1.00000
7   1-2 VS 3-4   CONTRAST   LAWLEY    0.01   0.80804   157.851   1.00000
8   1-2 VS 3-4   CONTRAST   ROY       0.01   0.80804   157.851   1.00000
9   1-3 VS 2-4   CONTRAST   WILKS     0.01   0.24912    12.441   0.70627
10   1-3 VS 2-4   CONTRAST   PILLAI    0.01   0.24912    12.441   0.70627
11   1-3 VS 2-4   CONTRAST   LAWLEY    0.01   0.24912    12.441   0.70627
12   1-3 VS 2-4   CONTRAST   ROY       0.01   0.24912    12.441   0.70627```