The SAS System

The GLM Procedure

Class Level
Information

Class

Levels

Values

r

3

1 2 3

a

2

1 2

b

3

1 2 3

Number of Observations Read

18

Number of Observations Used

18

The SAS System

The GLM Procedure

Dependent Variable: y

Source

DF

Sum of Squares

Mean Square

F Value

Pr > F

Model

9

34.40722222

3.82302469

404.79

<.0001

Error

8

0.07555556

0.00944444

Corrected Total

17

34.48277778

R-Square

Coeff Var

Root MSE

y Mean

0.997809

1.636376

0.097183

5.938889

Source

DF

Type III SS

Mean Square

F Value

Pr > F

r

2

0.04111111

0.02055556

2.18

0.1759

a

1

22.44500000

22.44500000

2376.53

<.0001

r*a

2

0.00333333

0.00166667

0.18

0.8414

b

2

11.27444444

5.63722222

596.88

<.0001

a*b

2

0.64333333

0.32166667

34.06

0.0001

Tests of Hypotheses Using
the Type III MS for r*a as an Error Term

Source

DF

Type III SS

Mean Square

F Value

Pr > F

a

1

22.44500000

22.44500000

13467.0

<.0001

The SAS System

The GLM Procedure

The SAS System

The GLM Procedure

Duncan's Multiple Range Test for y

Note:

This test controls the Type I comparisonwise
error rate, not the experimentwise error rate.

Alpha

0.01

Error Degrees of Freedom

2

Error Mean Square

0.001667

Number of Means

2

Critical Range

.1910

Means with the same
letter
are not significantly different.

Duncan Grouping

Mean

N

a

A

7.05556

9

2

B

4.82222

9

1

The SAS System

The GLM Procedure

The SAS System

The GLM Procedure

Duncan's Multiple Range Test for y

Note:

This test controls the Type I comparisonwise
error rate, not the experimentwise error rate.

Alpha

0.01

Error Degrees of Freedom

8

Error Mean Square

0.009444

Number of Means

2

3

Critical Range

.1883

.1959

Means with the same
letter
are not significantly different.

Duncan Grouping

Mean

N

b

A

7.00000

6

3

B

5.71667

6

2

C

5.10000

6

1

The SAS System

The GLM Procedure

Least Squares Means

a

b

y LSMEAN

LSMEAN Number

1

1

4.10000000

1

1

2

4.33333333

2

1

3

6.03333333

3

2

1

6.10000000

4

2

2

7.10000000

5

2

3

7.96666667

6

Least Squares Means for
effect a*b
Pr > |t| for H0: LSMean(i)=LSMean(j)
Dependent
Variable: y

i/j

1

2

3

4

5

6

1

0.0187

<.0001

<.0001

<.0001

<.0001

2

0.0187

<.0001

<.0001

<.0001

<.0001

3

<.0001

<.0001

0.4252

<.0001

<.0001

4

<.0001

<.0001

0.4252

<.0001

<.0001

5

<.0001

<.0001

<.0001

<.0001

<.0001

6

<.0001

<.0001

<.0001

<.0001

<.0001

T Grouping for LS-Means of a*b

LS-means with the same
letter
are not significantly different.

y LSMEAN

a

b

LSMEAN Number

A

7.9666667

2

3

6

B

7.1000000

2

2

5

C

6.1000000

2

1

4

C

C

6.0333333

1

3

3

D

4.3333333

1

2

2

E

4.1000000

1

1

1

Note:

To ensure overall protection level, only
probabilities associated with pre-planned comparisons should be
used.