Sample SAS Programs

General SAS Programming Issues
One-factor ANOVA
One-factor ANOVA with contrasts
One-factor ANOVA with correction for alpha inflation

All the one-factor examples use data from Keppel (1991), p. 29

Two-factor ANOVA

The two-factor example uses data from Keppel (1991), p. 214

Three-factor ANOVA

The three-factor example uses data from Keppel (1991), p. 443

Four-factor ANOVA
One-factor within-subects ANOVA

The one-factor within example uses data from Keppel(1991), p. 348

Two-factor within-subjects ANOVA

The two-factor within example uses data from Keppel (1991), p. 466

Two-factor mixed design ANOVA

The two-factor mixed example uses data from Keppel (1991), p. 374

One-factor ANOVA TO TOP

This program reads data from within the program in free format.

options nocenter ls=80 ps=60;
data a;
input y group;
16 1
18 1
10 1
12 1
19 1
4 2
6 2
8 2
10 2
2 2
2 3
10 3
9 3
13 3
11 3
;
proc glm;
class group;
model y=group;
run;
quit;

General Linear Models Procedure
Class Level Information

Class Levels Values

GROUP 3 1 2 3

Number of observations in data set = 15

General Linear Models Procedure

Dependent Variable: Y
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F

Model 2 210.00000000 105.00000000 7.41 0.0080

Error 12 170.00000000 14.16666667

Corrected Total 14 380.00000000

R-Square C.V. Root MSE Y Mean

0.552632 37.63863 3.7638633 10.000000

Source DF Type I SS Mean Square F Value Pr > F

GROUP 2 210.00000000 105.00000000 7.41 0.0080

Source DF Type III SS Mean Square F Value Pr > F

GROUP 2 210.00000000 105.00000000 7.41 0.0080

One-factor ANOVA with contrasts TO TOP

This program reads data from the file 'kep1.dat' in fixed format.
You can run as many contrasts as you want in SAS.

options nocenter ls=80 ps=60;
title 'one factor with contrasts';
data a; infile 'kep1.dat';
input y 1-2 group 4;
proc glm;
class group;
model y=group;
contrast 'group1 vs group2' group 1 -1 0;
contrast 'group2 vs group3' group 0 1 -1;
contrast 'group1+2 vs group3' group -1 -1 2;
run;
quit;

General Linear Models Procedure
Class Level Information

Class Levels Values

GROUP 3 1 2 3

Number of observations in data set = 15

one factor with contrasts 14:24 Thursday, August 27, 1998 2

General Linear Models Procedure

Dependent Variable: Y
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F

Model 2 210.00000000 105.00000000 7.41 0.0080

Error 12 170.00000000 14.16666667

Corrected Total 14 380.00000000

R-Square C.V. Root MSE Y Mean

0.552632 37.63863 3.7638633 10.000000

Source DF Type I SS Mean Square F Value Pr > F

GROUP 2 210.00000000 105.00000000 7.41 0.0080

Source DF Type III SS Mean Square F Value Pr > F

GROUP 2 210.00000000 105.00000000 7.41 0.0080

Contrast DF Contrast SS Mean Square F Value Pr > F

group1 vs group2         1     202.50000000    202.50000000     14.29     0.0026
group2 vs group3         1      22.50000000     22.50000000      1.59     0.2315
group1+2 vs group3       1       7.50000000      7.50000000      0.53     0.4808

One-factor ANOVA with correction for alpha inflation TO TOP

This program reads data from the file 'kep1.dat' in fixed format.
Note that the Dunnett correction assumes the control group is coded as "1". In this example the control group is "3" so the program specifies this fact.

options nocenter ls=80 ps=60;
title 'Corrections for experimentwise error';
data a;
infile 'kep1.dat';
input y 1-2 group 4;
proc glm;
class group;
model y=group;
means group/scheffe;
means group/tukey;
means group/dunnett ("3");
means group/lsd;
run;
quit;

Corrections for experimentwise error 10:18 Wednesday, September 30, 1998 2

General Linear Models Procedure

Dependent Variable: Y
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F

Model 2 210.00000000 105.00000000 7.41 0.0080

Error 12 170.00000000 14.16666667

Corrected Total 14 380.00000000

R-Square C.V. Root MSE Y Mean

0.552632 37.63863 3.7638633 10.000000

Source DF Type I SS Mean Square F Value Pr > F

GROUP 2 210.00000000 105.00000000 7.41 0.0080

Source DF Type III SS Mean Square F Value Pr > F

GROUP 2 210.00000000 105.00000000 7.41 0.0080

Corrections for experimentwise error 10:18 Wednesday, September 30, 1998 3

General Linear Models Procedure

Scheffe's test for variable: Y

NOTE: This test controls the type I experimentwise error rate but generally has a higher type II error rate than REGWF for all pairwise comparisons

Alpha= 0.05 df= 12 MSE= 14.16667
Critical Value of F= 3.88529
Minimum Significant Difference= 6.6358

Means with the same letter are not significantly different.

Scheffe Grouping              Mean      N GROUP

                A            15.000      5 1
                A
        B       A             9.000      5 3
        B
        B                     6.000      5 2

Corrections for experimentwise error 10:18 Wednesday, September 30, 1998 4

General Linear Models Procedure

Tukey's Studentized Range (HSD) Test for variable: Y

NOTE: This test controls the type I experimentwise error rate, but generally has a higher type II error rate than REGWQ.

Alpha= 0.05 df= 12 MSE= 14.16667
Critical Value of Studentized Range= 3.773
Minimum Significant Difference= 6.3505

Means with the same letter are not significantly different.

Tukey Grouping              Mean      N GROUP

                  A            15.000      5 1
                  A
          B       A             9.000      5 3
          B
          B                     6.000      5 2

Corrections for experimentwise error 10:18 Wednesday, September 30, 1998 5

General Linear Models Procedure

Dunnett's T tests for variable: Y

NOTE: This tests controls the type I experimentwise error for comparisons of
all treatments against a control.

Alpha= 0.05 Confidence= 0.95 df= 12 MSE= 14.16667
Critical Value of Dunnett's T= 2.502
Minimum Significant Difference= 5.9569

Comparisons significant at the 0.05 level are indicated by '***'.

               Simultaneous            Simultaneous
                   Lower    Difference     Upper
   GROUP        Confidence    Between   Confidence
Comparison        Limit       Means       Limit

1 - 3 0.043 6.000 11.957 ***
2 - 3 -8.957 -3.000 2.957

Corrections for experimentwise error 10:18 Wednesday, September 30, 1998 6

General Linear Models Procedure

T tests (LSD) for variable: Y

NOTE: This test controls the type I comparisonwise error rate not the
experimentwise error rate.

Alpha= 0.05 df= 12 MSE= 14.16667
Critical Value of T= 2.18
Least Significant Difference= 5.1866

Means with the same letter are not significantly different.

T Grouping              Mean      N GROUP

                      A            15.000      5 1

                      B             9.000      5 3
                      B
                      B             6.000      5 2

Two-factor ANOVA TO TOP

This program reads the data from the program in fixed format.
This program also asks for cell means to be printed.

options nocenter ls=80 ps=60;
title 'Two factor ANOVA';
data a;
input facta 1 factb 3 y 5-6;
cards;
1 1 1
1 1 4
1 1 0
1 1 7
2 1 13
2 1 5
2 1 7
2 1 15
3 1 9
3 1 16
3 1 18
3 1 13
1 2 15
1 2 6
1 2 10
1 2 13
2 2 6
2 2 18
2 2 9
2 2 15
3 2 14
3 2 7
3 2 6
3 2 13
;
proc glm;
class facta factb;
model y=facta factb facta*factb;
means facta*factb;
run;
quit;

Two factor ANOVA 11:28 Monday, October 5, 1998 2

General Linear Models Procedure

Dependent Variable: Y
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F

Model 5 280.00000000 56.00000000 3.05 0.0361

Error 18 330.00000000 18.33333333

Corrected Total 23 610.00000000

R-Square C.V. Root MSE Y Mean

0.459016 42.81744 4.2817442 10.000000

Source DF Type I SS Mean Square F Value Pr > F

FACTA                    2     112.00000000     56.00000000      3.05     0.0721
FACTB                    1      24.00000000     24.00000000      1.31     0.2675
FACTA*FACTB              2     144.00000000     72.00000000      3.93     0.0384

Source DF Type III SS Mean Square F Value Pr > F

Two factor ANOVA 11:28 Monday, October 5, 1998 3

General Linear Models Procedure

Level of Level of --------------Y--------------
FACTA FACTB N Mean SD

1          1          4      3.0000000       3.16227766
1          2          4     11.0000000       3.91578004
2          1          4     10.0000000       4.76095229
2          2          4     12.0000000       5.47722558
3          1          4     14.0000000       3.91578004
3          2          4     10.0000000       4.08248290

Three-factor ANOVA TO TOP

This program reads the data from the program in free format.
Note that all effects are listed, including three 2-way interactions and one 3-way interaction.

options nocenter ls=80 ps=60;
title 'Three factor between subjects design';
data a;
input facta factb factc y;
cards;
1 1 1 7
1 1 1 4
1 1 1 5
1 1 1 6
1 1 2 7
1 1 2 5
1 1 2 5
1 1 2 6
1 2 1 2
1 2 1 4
1 2 1 3
1 2 1 3
1 2 2 2
1 2 2 3
1 2 2 4
1 2 2 1
1 3 1 4
1 3 1 3
1 3 1 0
1 3 1 3
1 3 2 1
1 3 2 3
1 3 2 2
1 3 2 2
2 1 1 10
2 1 1 7
2 1 1 6
2 1 1 8
2 1 2 6
2 1 2 5
2 1 2 5
2 1 2 6
2 2 1 4
2 2 1 6
2 2 1 3
2 2 1 5
2 2 2 1
2 2 2 3
2 2 2 4
2 2 2 5
2 3 1 7
2 3 1 4
2 3 1 5
2 3 1 5
2 3 2 1
2 3 2 3
2 3 2 3
2 3 2 0
3 1 1 13
3 1 1 10
3 1 1 13
3 1 1 8
3 1 2 12
3 1 2 13
3 1 2 11
3 1 2 12
3 2 1 9
3 2 1 8
3 2 1 9
3 2 1 10
3 2 2 7
3 2 2 6
3 2 2 7
3 2 2 6
3 3 1 8
3 3 1 5
3 3 1 6
3 3 1 6
3 3 2 7
3 3 2 7
3 3 2 4
3 3 2 6
;
proc glm;
class facta factb factc;
model y=facta factb factc facta*factb facta*factc factb*factc facta*factb*factc;
means facta*factb*factc;
run;
quit;

Three factor between subjects design 18:34 Sunday, October 11, 1998 4
General Linear Models Procedure
Class Level Information
Class Levels Values

FACTA 3 1 2 3

FACTB 3 1 2 3

FACTC 2 1 2
Number of observations in data set = 72

Three factor between subjects design 18:34 Sunday, October 11, 1998 5
General Linear Models Procedure

Dependent Variable: Y
Sum of Mean
Source DF Squares Square F Value Pr > F

Model 17 593.27777778 34.89869281 19.94 0.0001

Error 54 94.50000000 1.75000000

Corrected Total 71 687.77777778

R-Square C.V. Root MSE Y Mean

0.862601 23.81176 1.3228757 5.5555556

Source DF Type I SS Mean Square F Value Pr > F

FACTA                    2     318.52777778    159.26388889     91.01     0.0001
FACTB                    2     209.02777778    104.51388889     59.72     0.0001
FACTC                    1      20.05555556     20.05555556     11.46     0.0013
FACTA*FACTB              4      12.22222222      3.05555556      1.75     0.1534
FACTA*FACTC              2      15.02777778      7.51388889      4.29     0.0186
FACTB*FACTC              2       4.69444444      2.34722222      1.34     0.2701
FACTA*FACTB*FACTC        4      13.72222222      3.43055556      1.96     0.1137

Source DF Type III SS Mean Square F Value Pr > F

Three factor between subjects design 18:34 Sunday, October 11, 1998 6
General Linear Models Procedure

Level of Level of Level of --------------Y--------------
FACTA FACTB FACTC N Mean SD

1          1          1          4      5.5000000       1.29099445
1          1          2          4      5.7500000       0.95742711
1          2          1          4      3.0000000       0.81649658
1          2          2          4      2.5000000       1.29099445
1          3          1          4      2.5000000       1.73205081
1          3          2          4      2.0000000       0.81649658
2          1          1          4      7.7500000       1.70782513
2          1          2          4      5.5000000       0.57735027
2          2          1          4      4.5000000       1.29099445
2          2          2          4      3.2500000       1.70782513
2          3          1          4      5.2500000       1.25830574
2          3          2          4      1.7500000       1.50000000
3          1          1          4     11.0000000       2.44948974
3          1          2          4     12.0000000       0.81649658
3          2          1          4      9.0000000       0.81649658
3          2          2          4      6.5000000       0.57735027
3          3          1          4      6.2500000       1.25830574
3          3          2          4      6.0000000       1.41421356

Four-factor ANOVA TO TOP

The data are read in from the program in fixed format.
Note that the pipe character ( | ) is used to request all possible interactions.

options nocenter ls=80 ps=60;
data a;
input facta 1 factb 2 factc 3 factd 4 y 5;
cards;
11113
11112
11127
11125
11212
11211
11226
11225
12119
12118
12123
12123
12217
12214
12228
12226
21111
21112
21124
21124
21217
21213
21222
21221
22116
22115
22129
22127
22215
22214
22223
22226
;
proc glm;
class facta factb factc factd;
model y=facta|factb|factc|factd;
run;
quit;

The SAS System 10:36 Monday, October 12, 1998 2

General Linear Models Procedure

Dependent Variable: Y
Sum of Mean
Source DF Squares Square F Value Pr > F

Model 15 146.50000000 9.76666667 5.79 0.0006

Error 16 27.00000000 1.68750000

Corrected Total 31 173.50000000

R-Square C.V. Root MSE Y Mean

0.844380 28.08731 1.2990381 4.6250000

Source DF Type I SS Mean Square F Value Pr > F

FACTA                    1       3.12500000      3.12500000      1.85     0.1924
FACTB                    1      45.12500000     45.12500000     26.74     0.0001
FACTA*FACTB              1       0.50000000      0.50000000      0.30     0.5937
FACTC                    1       2.00000000      2.00000000      1.19     0.2924
FACTA*FACTC              1       1.12500000      1.12500000      0.67     0.4262
FACTB*FACTC              1       1.12500000      1.12500000      0.67     0.4262
FACTA*FACTB*FACTC        1       8.00000000      8.00000000      4.74     0.0448
FACTD                    1       3.12500000      3.12500000      1.85     0.1924
FACTA*FACTD              1       0.50000000      0.50000000      0.30     0.5937
FACTB*FACTD              1       8.00000000      8.00000000      4.74     0.0448
FACTA*FACTB*FACTD        1      28.12500000     28.12500000     16.67     0.0009
FACTC*FACTD              1       0.12500000      0.12500000      0.07     0.7890
FACTA*FACTC*FACTD        1      32.00000000     32.00000000     18.96     0.0005
FACTB*FACTC*FACTD        1      12.50000000     12.50000000      7.41     0.0151
FACT*FACT*FACT*FACTD     1       1.12500000      1.12500000      0.67     0.4262

Source DF Type III SS Mean Square F Value Pr > F

One-factor within ANOVA

options nocenter ls=80 ps=60;
title 'Repeated measures with contrasts, ch16';
data a;
input score1 1-2 score2 3-4 score3 5-6;
cards;
081209
081314
091506
001812
131518
101707
;
proc glm;
model score1 score2 score3= /nouni;
repeated score 3;
repeated score 3 polynomial/summary;
repeated score 3 mean/summary printm;
run;
quit;

Repeated measures with contrasts, ch16 13:47 Wednesday, November 4, 1998 1

General Linear Models Procedure

Number of observations in data set = 6

Repeated measures with contrasts, ch16 13:47 Wednesday, November 4, 1998 2

General Linear Models Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information

Dependent Variable SCORE1 SCORE2 SCORE3

Level of SCORE 1 2 3

Manova Test Criteria and Exact F Statistics for
the Hypothesis of no SCORE Effect
H = Type III SS&CP Matrix for SCORE E = Error SS&CP Matrix

S=1 M=0 N=1

Statistic Value F Num DF Den DF Pr > F

Wilks' Lambda              0.34386529     3.8162         2         4 0.1182
Pillai's Trace             0.65613471     3.8162         2         4 0.1182
Hotelling-Lawley Trace     1.90811554     3.8162         2         4 0.1182
Roy's Greatest Root        1.90811554     3.8162         2         4 0.1182
Repeated measures with contrasts, ch16     13:47 Wednesday, November 4, 1998   3

General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects

Source: SCORE
                                                                   Adj Pr > F
     DF       Type III SS       Mean Square   F Value   Pr > F    G - G    H - F
      2      148.00000000       74.00000000      4.72   0.0360   0.0367   0.0360

Source: Error(SCORE)

DF Type III SS Mean Square
10 156.66666667 15.66666667

Greenhouse-Geisser Epsilon = 0.9875
Huynh-Feldt Epsilon = 1.6280

Repeated measures with contrasts, ch16 13:47 Wednesday, November 4, 1998 4

General Linear Models Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information

Dependent Variable SCORE1 SCORE2 SCORE3

Level of SCORE 1 2 3

Manova Test Criteria and Exact F Statistics for
the Hypothesis of no SCORE Effect
H = Type III SS&CP Matrix for SCORE E = Error SS&CP Matrix

S=1 M=0 N=1

Statistic Value F Num DF Den DF Pr > F

General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects

Source: Error(SCORE)

DF Type III SS Mean Square
10 156.66666667 15.66666667

Greenhouse-Geisser Epsilon = 0.9875
Huynh-Feldt Epsilon = 1.6280

Repeated measures with contrasts, ch16 13:47 Wednesday, November 4, 1998 6

General Linear Models Procedure
Repeated Measures Analysis of Variance
Analysis of Variance of Contrast Variables

SCORE.N represents the nth degree polynomial contrast for SCORE

Contrast Variable: SCORE.1

Source DF Type III SS Mean Square F Value Pr > F

MEAN 1 27.00000000 27.00000000 1.59 0.2632

Error 5 85.00000000 17.00000000

Contrast Variable: SCORE.2

Source DF Type III SS Mean Square F Value Pr > F

MEAN 1 121.00000000 121.00000000 8.44 0.0336

Error 5 71.66666667 14.33333333

Repeated measures with contrasts, ch16 13:47 Wednesday, November 4, 1998 7

General Linear Models Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information

Dependent Variable SCORE1 SCORE2 SCORE3

Level of SCORE 1 2 3

SCORE.N represents the contrast between the
nth level of SCORE and the mean of the other levels

M Matrix Describing Transformed Variables

SCORE1 SCORE2 SCORE3

SCORE.1       1.000000000      -0.500000000      -0.500000000
SCORE.2      -0.500000000       1.000000000      -0.500000000

Manova Test Criteria and Exact F Statistics for
the Hypothesis of no SCORE Effect
H = Type III SS&CP Matrix for SCORE E = Error SS&CP Matrix

S=1 M=0 N=1

Statistic Value F Num DF Den DF Pr > F

General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects

Source: Error(SCORE)

DF Type III SS Mean Square
10 156.66666667 15.66666667

Greenhouse-Geisser Epsilon = 0.9875
Huynh-Feldt Epsilon = 1.6280

Repeated measures with contrasts, ch16 13:47 Wednesday, November 4, 1998 9

General Linear Models Procedure
Repeated Measures Analysis of Variance
Analysis of Variance of Contrast Variables

SCORE.N represents the contrast between the
nth level of SCORE and the mean of the other levels

Contrast Variable: SCORE.1

Source DF Type III SS Mean Square F Value Pr > F

MEAN 1 150.00000000 150.00000000 5.77 0.0615

Error 5 130.00000000 26.00000000

Contrast Variable: SCORE.2

Source DF Type III SS Mean Square F Value Pr > F

MEAN 1 181.50000000 181.50000000 8.44 0.0336

Error 5 107.50000000 21.50000000

Two-factor within ANOVA

options nocenter ls=80 ps=60;
title 'Two-factor repeated measures, ch 21';
data a;
input a1b1 a1b2 a1b3 a1b4 a2b1 a2b2 a2b3 a2b4;
cards;
03 04 03 07 05 06 07 11
06 08 09 12 10 12 15 18
07 13 11 11 10 15 14 15
00 03 06 06 05 07 09 11
;
proc glm;
model a1b1 a1b2 a1b3 a1b4 a2b1 a2b2 a2b3 a2b4= /nouni;
repeated freq 2, trials 4 polynomial/summary printm printe;
run;
quit;

Two-factor repeated measures, ch 21 11:15 Wednesday, November 18, 1998 1

General Linear Models Procedure

Number of observations in data set = 4

Two-factor repeated measures, ch 21 11:15 Wednesday, November 18, 1998 2

General Linear Models Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information

Dependent Variable A1B1 A1B2 A1B3 A1B4 A2B1 A2B2

Level of FREQ 1 1 1 1 2 2
Level of TRIALS 1 2 3 4 1 2

Dependent Variable A2B3 A2B4

     Level of FREQ          2        2
   Level of TRIALS          3        4

Manova Test Criteria and Exact F Statistics for the Hypothesis of no FREQ Effect
H = Type III SS&CP Matrix for FREQ E = Error SS&CP Matrix

S=1 M=-0.5 N=0.5

Statistic Value F Num DF Den DF Pr > F

Wilks' Lambda              0.04785056    59.6952         1         3 0.0045
Pillai's Trace             0.95214944    59.6952         1         3 0.0045
Hotelling-Lawley Trace    19.89839572    59.6952         1         3 0.0045
Roy's Greatest Root       19.89839572    59.6952         1         3 0.0045

Manova Test Criteria and Exact F Statistics for
the Hypothesis of no TRIALS Effect
H = Type III SS&CP Matrix for TRIALS E = Error SS&CP Matrix

S=1 M=0.5 N=-0.5

Statistic Value F Num DF Den DF Pr > F

Wilks' Lambda              0.00768937    43.0166         3         1 0.1115
Pillai's Trace             0.99231063    43.0166         3         1 0.1115
Hotelling-Lawley Trace   129.04970414    43.0166         3         1 0.1115
Roy's Greatest Root      129.04970414    43.0166         3         1 0.1115

Manova Test Criteria and Exact F Statistics for
the Hypothesis of no FREQ*TRIALS Effect
H = Type III SS&CP Matrix for FREQ*TRIALS E = Error SS&CP Matrix

S=1 M=0.5 N=-0.5

Statistic Value F Num DF Den DF Pr > F

Wilks' Lambda              0.00000000      .             3         1 0.0001
Pillai's Trace             1.00000000      .             3         1 0.0001
Hotelling-Lawley Trace      .              .             3         1 0.0001
Roy's Greatest Root         .              .             3         1 0.0001
Two-factor repeated measures, ch 21       11:15 Wednesday, November 18, 1998   3

General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects

Source: FREQ
                                                                   Adj Pr > F
     DF       Type III SS       Mean Square   F Value   Pr > F    G - G    H - F
      1      116.28125000      116.28125000     59.70   0.0045    .        .

Source: Error(FREQ)

DF Type III SS Mean Square
3 5.84375000 1.94791667

Source: TRIALS
                                                                   Adj Pr > F
     DF       Type III SS       Mean Square   F Value   Pr > F    G - G    H - F
      3      129.59375000       43.19791667     12.23   0.0016   0.0112   0.0016

Source: Error(TRIALS)

DF Type III SS Mean Square
9 31.78125000 3.53125000

Greenhouse-Geisser Epsilon = 0.5868
Huynh-Feldt Epsilon = 1.3555

Source: FREQ*TRIALS
                                                                   Adj Pr > F
     DF       Type III SS       Mean Square   F Value   Pr > F    G - G    H - F
      3        3.34375000        1.11458333      3.31   0.0712   0.1633   0.1585

Source: Error(FREQ*TRIALS)

DF Type III SS Mean Square
9 3.03125000 0.33680556

Greenhouse-Geisser Epsilon = 0.3475
Huynh-Feldt Epsilon = 0.3696

Two-factor mixed ANOVA

options nocenter ls=80 ps=60;
title 'one within, one between --ch17';
data a;
input facta b1 b2 b3 b4;
parta=facta;
if parta=1 then parta=.;
cards;
1 13 14 17 20
1 10 11 15 14
1 13 19 18 21
1 04 12 14 15
2 05 10 17 21
2 08 15 22 24
2 14 16 23 23
2 12 21 26 26
3 13 24 28 30
3 09 22 22 24
3 14 22 28 28
3 08 18 27 28
;
proc glm;
class facta;
model b1 b2 b3 b4=facta /nouni;
repeated factb 4;
run;
quit;

one within, one between --ch17 21:46 Thursday, November 19, 1998 2

General Linear Models Procedure
Class Level Information

Class Levels Values

FACTA 3 1 2 3

Number of observations in data set = 12

one within, one between --ch17 21:46 Thursday, November 19, 1998 3

General Linear Models Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information

Dependent Variable B1 B2 B3 B4

Level of FACTB 1 2 3 4

Manova Test Criteria and Exact F Statistics for
the Hypothesis of no FACTB Effect
H = Type III SS&CP Matrix for FACTB E = Error SS&CP Matrix

S=1 M=0.5 N=2.5

Statistic Value F Num DF Den DF Pr > F

Wilks' Lambda              0.03516178    64.0266         3         7 0.0001
Pillai's Trace             0.96483822    64.0266         3         7 0.0001
Hotelling-Lawley Trace    27.43997368    64.0266         3         7 0.0001
Roy's Greatest Root       27.43997368    64.0266         3         7 0.0001

Manova Test Criteria and F Approximations for
the Hypothesis of no FACTB*FACTA Effect
H = Type III SS&CP Matrix for FACTB*FACTA E = Error SS&CP Matrix

S=2 M=0 N=2.5

Statistic Value F Num DF Den DF Pr > F

Wilks' Lambda              0.17880173     3.1848         6        14 0.0347
Pillai's Trace             1.03471392     2.8585         6        16 0.0435
Hotelling-Lawley Trace     3.39863961     3.3986         6        12 0.0339
Roy's Greatest Root        3.00068071     8.0018         3         8 0.0086

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

one within, one between --ch17 21:46 Thursday, November 19, 1998 4

General Linear Models Procedure
Repeated Measures Analysis of Variance
Tests of Hypotheses for Between Subjects Effects

Source DF Type III SS Mean Square F Value Pr > F

FACTA 2 414.1250000 207.0625000 6.17 0.0206

Error 9 302.1250000 33.5694444

one within, one between --ch17 21:46 Thursday, November 19, 1998 5

General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects

Source: FACTB
                                                                   Adj Pr > F
     DF       Type III SS       Mean Square   F Value   Pr > F    G - G    H - F
      3     1152.41666667      384.13888889    114.76   0.0001   0.0001   0.0001

Source: FACTB*FACTA
                                                                   Adj Pr > F
     DF       Type III SS       Mean Square   F Value   Pr > F    G - G    H - F
      6      130.20833333       21.70138889      6.48   0.0003   0.0007   0.0003

Source: Error(FACTB)

DF Type III SS Mean Square
27 90.37500000 3.34722222

Greenhouse-Geisser Epsilon = 0.8298
Huynh-Feldt Epsilon = 1.4270

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