Sample SPSS Programs

General SPSS 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.

set width=80.
data list list
/y group.
begin data
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
end data.
manova y by group (1,3).

For HP-UX 10.0 Arizona State University SPSS ID 198670

   1 0 set width=80.
   2 data list list
   3    /y group.
   4 begin data
19 end data.

Preceding task required .02 seconds CPU time; .38 seconds elapsed.

20 manova y by group (1,3).

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The default error term in MANOVA has been changed from WITHIN CELLS to
WITHIN+RESIDUAL. Note that these are the same for all full factorial
designs.
13 Oct 98 SPSS for Unix, Release 6.1 (HP9000 xxx ) Page 2
11:54:26 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e * * * * * *

        15 cases accepted.
         0 cases rejected because of out-of-range factor values.
         0 cases rejected because of missing data.
         3 non-empty cells.

1 design will be processed.

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13 Oct 98 SPSS for Unix, Release 6.1 (HP9000 xxx ) Page 3
11:54:27 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests of Significance for Y using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 170.00 12 14.17
GROUP 210.00 2 105.00 7.41 .008

(Model) 210.00 2 105.00 7.41 .008
(Total) 380.00 14 27.14

R-Squared = .553
Adjusted R-Squared = .478

One-factor ANOVA with contrasts TO TOP

This program reads data from the file 'kep1.dat' in fixed format.
In SPSS, each contrast subcommand must contain a vector of ones (one for each group) and a-1 contrasts.

set width=80.
title 'one factor with contrasts'.
data list file='kep1.dat'
   /y 1-2 group 4.
manova y by group (1,3)
    /contrast (group) = special (1 1 1, 1 -1 0, 0 1 -1)
    /design=group(1) group(2)
    /contrast (group) = special (1 1 1, -1 -1 2, 1 0 -1)
    /design=group(1) group(2).

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *
Tests of Significance for Y using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN+RESIDUAL          170.00      12     14.17
GROUP(1)                 202.50       1    202.50     14.29      .003
GROUP(2)                  22.50       1     22.50      1.59      .232

(Model) 210.00 2 105.00 7.41 .008
(Total) 380.00 14 27.14

R-Squared = .553
Adjusted R-Squared = .478
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Estimates for Y --- Individual univariate .9500 confidence intervals
GROUP(1)
Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% CL- Upper

2 9.00000000 2.38048 3.78076 .00262 3.81339 14.18661

GROUP(2)
Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% CL- Upper

        3   -3.0000000    2.38048   -1.26025     .23153   -8.18661    2.18661
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* * * * * * A n a l y s i s   o f   V a r i a n c e -- design   2 * * * * * *
Tests of Significance for Y using UNIQUE sums of squares
Source of Variation          SS      DF        MS         F Sig of F

WITHIN+RESIDUAL          170.00      12     14.17
GROUP(1)                   7.50       1      7.50       .53      .481
GROUP(2)                  90.00       1     90.00      6.35      .027

(Model) 210.00 2 105.00 7.41 .008
(Total) 380.00 14 27.14

2 -3.0000000 4.12311 -.72761 .48081 -11.98348 5.98348

GROUP(2)
Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% CL- Upper

3 6.00000000 2.38048 2.52050 .02688 .81339 11.18661
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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 correction for experimentwise error in SPSS must be done using the oneway command.

set width=80.
title 'Corrections for experimentwise error'.
data list file='kep1.dat'
/y 1-2 group 4.
oneway y by group (1,3)
/ranges=scheffe
/ranges=tukey
/ranges=lsd.

30 Sep 98 Corrections for experimentwise error Page 2
10:19:56 Arizona State University HP 9000 HP-UX 10.0

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Variable Y
By Variable GROUP

Analysis of Variance

Sum of Mean F F
Source D.F. Squares Squares Ratio Prob.

Between Groups             2      210.0000      105.0000       7.4118 .0080
Within Groups             12      170.0000       14.1667
Total                     14      380.0000
      - - - - - O N E W A Y - - - - -
      Variable Y
   By Variable GROUP

Multiple Range Tests: Scheffe test with significance level .05

The difference between two means is significant if
MEAN(J)-MEAN(I) >= 2.6615 * RANGE * SQRT(1/N(I) + 1/N(J))
with the following value(s) for RANGE: 3.94

   (*) Indicates significant differences which are shown in the lower triangle
                          G G G
                          r r r
                          p p p

2 3 1
Mean GROUP

     6.0000    Grp 2
     9.0000    Grp 3
    15.0000    Grp 1      *

Homogeneous Subsets (highest and lowest means are not significantly different)

Subset 1
Group Grp 2 Grp 3
Mean 6.0000 9.0000
- - - - - - - - - - - - - - - - -

Subset 2
Group       Grp 3         Grp 1
Mean        9.0000       15.0000
- - - - - - - - - - - - - - - - -         - - - - - O N E W A Y - - - - -
      Variable Y
   By Variable GROUP

Multiple Range Tests: Tukey-HSD test with significance level .05

The difference between two means is significant if
MEAN(J)-MEAN(I) >= 2.6615 * RANGE * SQRT(1/N(I) + 1/N(J))
with the following value(s) for RANGE: 3.77

   (*) Indicates significant differences which are shown in the lower triangle
                          G G G
                          r r r
                          p p p

2 3 1
Mean GROUP

     6.0000    Grp 2
     9.0000    Grp 3
    15.0000    Grp 1      *

Homogeneous Subsets (highest and lowest means are not significantly different)

Subset 1
Group Grp 2 Grp 3
Mean 6.0000 9.0000
- - - - - - - - - - - - - - - - -

Subset 2
Group       Grp 3         Grp 1
Mean        9.0000       15.0000
- - - - - - - - - - - - - - - - -        - - - - - O N E W A Y - - - - -
      Variable Y
   By Variable GROUP

Multiple Range Tests: LSD test with significance level .05

The difference between two means is significant if
MEAN(J)-MEAN(I) >= 2.6615 * RANGE * SQRT(1/N(I) + 1/N(J))
with the following value(s) for RANGE: 3.08

   (*) Indicates significant differences which are shown in the lower triangle
                          G G G
                          r r r
                          p p p

2 3 1
Mean GROUP

     6.0000    Grp 2
     9.0000    Grp 3
    15.0000    Grp 1      * *

Homogeneous Subsets (highest and lowest means are not significantly different)

Subset 1
Group Grp 2 Grp 3
Mean 6.0000 9.0000
- - - - - - - - - - - - - - - - -

Subset 2
Group Grp 1
Mean 15.0000
- - - - - - - - - -

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.

set width=80.
title 'Two factor ANOVA'.
data list
/facta 1 factb 3 y 5-6.
begin data
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
end data.
manova y by facta (1,3) factb (1,2)
/print=cellinfo(means).

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Cell Means and Standard Deviations
Variable .. Y
FACTOR CODE Mean Std. Dev. N

FACTA                  1
   FACTB                  1                 3.000      3.162          4
   FACTB                  2                11.000      3.916          4
FACTA                  2
   FACTB                  1                10.000      4.761          4
   FACTB                  2                12.000      5.477          4
FACTA                  3
   FACTB                  1                14.000      3.916          4
   FACTB                  2                10.000      4.082          4
For entire sample                         10.000      5.150         24

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05 Oct 98 Two factor ANOVA &nb sp; Page 3
11:27:38 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests of Significance for Y using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS             330.00      18     18.33
FACTA                    112.00       2     56.00      3.05      .072
FACTB                     24.00       1     24.00      1.31      .268
FACTA BY FACTB           144.00       2     72.00      3.93      .038

(Model) 280.00 5 56.00 3.05 .036
(Total) 610.00 23 26.52

R-Squared = .459
Adjusted R-Squared = .309

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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.

set width=80.
title 'Three factor between subjects design'.
data list list
/facta factb factc y.
begin data
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
end data.
manova y by facta (1,3) factb (1,3) factc(1,2)
/print=cellinfo(means).

* * * * * * A n a l y s i s o f V a r i a n c e * * * * * *

        72 cases accepted.
         0 cases rejected because of out-of-range factor values.
         0 cases rejected because of missing data.
        18 non-empty cells.

1 design will be processed.

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Cell Means and Standard Deviations
Variable .. Y
FACTOR CODE Mean Std. Dev. N

FACTA                  1
   FACTB                  1
    FACTC                  1                5.500      1.291          4
    FACTC                  2                5.750       .957          4
   FACTB                  2
    FACTC                  1                3.000       .816          4
    FACTC                  2                2.500      1.291          4
   FACTB                  3
    FACTC                  1                2.500      1.732          4
    FACTC                  2                2.000       .816          4
FACTA                  2
   FACTB                  1
    FACTC                  1                7.750      1.708          4
    FACTC                  2                5.500       .577          4
   FACTB                  2
    FACTC                  1                4.500      1.291          4
    FACTC                  2                3.250      1.708          4
   FACTB                  3
    FACTC                  1                5.250      1.258          4
    FACTC                  2                1.750      1.500          4
FACTA                  3
   FACTB                  1
    FACTC                  1               11.000      2.449          4
    FACTC                  2               12.000       .816          4
   FACTB                  2
    FACTC                  1                9.000       .816          4
    FACTC                  2                6.500       .577          4
   FACTB                  3
    FACTC                  1                6.250      1.258          4
    FACTC                  2                6.000      1.414          4
For entire sample                          5.556      3.112         72
13 Oct 98 Three factor between subjects design                            Page 3
12:07:33 Arizona State University       HP 9000          HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests of Significance for Y using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS              94.50      54      1.75
FACTA                    318.53       2    159.26     91.01      .000
FACTB                    209.03       2    104.51     59.72      .000
FACTC                     20.06       1     20.06     11.46      .001
FACTA BY FACTB            12.22       4      3.06      1.75      .153
FACTA BY FACTC            15.03       2      7.51      4.29      .019
FACTB BY FACTC             4.69       2      2.35      1.34      .270
FACTA BY FACTB BY FA      13.72       4      3.43      1.96      .114
CTC

(Model) 593.28 17 34.90 19.94 .000
(Total) 687.78 71 9.69

R-Squared = .863
Adjusted R-Squared = .819

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Four-factor ANOVA TO TOP

The data are read in from the program in fixed format.

set width=80.
data list
/facta 1 factb 2 factc 3 factd 4 y 5.
begin data
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
end data.
manova y by facta (1,2) factb (1,2) factc (1,2) factd (1,2).

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests of Significance for Y using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS              27.00      16      1.69
FACTA                      3.12       1      3.12      1.85      .192
FACTB                     45.13       1     45.13     26.74      .000
FACTC                      2.00       1      2.00      1.19      .292
FACTD                      3.12       1      3.12      1.85      .192
FACTA BY FACTB              .50       1       .50       .30      .594
FACTA BY FACTC             1.13       1      1.13       .67      .426
FACTA BY FACTD              .50       1       .50       .30      .594
FACTB BY FACTC             1.12       1      1.12       .67      .426
FACTB BY FACTD             8.00       1      8.00      4.74      .045
FACTC BY FACTD              .12       1       .12       .07      .789
FACTA BY FACTB BY FA       8.00       1      8.00      4.74      .045
CTC
FACTA BY FACTB BY FA      28.12       1     28.12     16.67      .001
CTD
FACTA BY FACTC BY FA      32.00       1     32.00     18.96      .000
CTD
FACTB BY FACTC BY FA      12.50       1     12.50      7.41      .015
CTD
FACTA BY FACTB BY FA       1.12       1      1.12       .67      .426
CTC BY FACTD

(Model) 146.50 15 9.77 5.79 .001
(Total) 173.50 31 5.60

R-Squared = .844
Adjusted R-Squared = .698

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9448 bytes of memory are needed for MANOVA execution.
13 Oct 98 SPSS for Unix, Release 6.1 (HP9000 xxx ) Page 4
12:11:03 Arizona State University HP 9000 HP-UX 10.0

Preceding task required .08 seconds CPU time; .11 seconds elapsed.

38

    37 command lines read.
     0 errors detected.
     0 warnings issued.
     0 seconds CPU time.
     0 seconds elapsed time.
       End of job.

One-factor within ANOVA

set width=80.
title 'Repeated measures with contrasts, ch16'.
data list
/score1 1-2 score2 3-4 score3 5-6.
begin data
081209
081314
091506
001812
131518
101707
end data.
manova score1 score2 score3
/wsfactors=score(3)
/omeans
/design.
manova score1 score2 score3
/wsfactors=score(3)
/print=signif(univ)
/contrast(score)=special(1 1 1, 1 -2 1, 1 0 -1)
/rename=mean first second
/design.
manova score1 score2 score3
/print=signif(univ)
/transform(score1 score2 score3)=special(1 1 1, 1 -2 1, 0 1 1)
/rename=mean first second
/design.

* * * * * * A n a l y s i s o f V a r i a n c e * * * * * *

         6 cases accepted.
         0 cases rejected because of out-of-range factor values.
         0 cases rejected because of missing data.
         1 non-empty cell.

1 design will be processed.

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Cell Means and Standard Deviations
Variable .. SCORE1
; Mean Std. Dev. N

For entire sample 8.000 4.336 6

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Variable .. SCORE2
; Mean Std. Dev. N

For entire sample 15.000 2.280 6

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Variable .. SCORE3
; Mean Std. Dev. N

For entire sample 11.000 4.561 6

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04 Nov 98 Repeated measures with contrasts, ch16 Page 3
12:57:11 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests of Between-Subjects Effects.

Tests of Significance for T1 using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 67.33 5 13.47
CONSTANT 2312.00 1 2312.00 171.68 .000

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04 Nov 98 Repeated measures with contrasts, ch16 Page 4
12:57:11 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'SCORE' Within-Subject Effect.

Mauchly sphericity test, W =      .98732
Chi-square approx. =              .05103 with 2 D. F.
Significance =                      .975

Greenhouse-Geisser Epsilon =      .98748
Huynh-Feldt Epsilon =            1.00000
Lower-bound Epsilon =             .50000

AVERAGED Tests of Significance that follow multivariate tests are equivalent to
univariate or split-plot or mixed-model approach to repeated measures.
Epsilons may be used to adjust d.f. for the AVERAGED results.

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04 Nov 98 Repeated measures with contrasts, ch16 Page 5
12:57:11 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

EFFECT .. SCORE
Multivariate Tests of Significance (S = 1, M = 0, N = 1 )

Test Name Value Exact F Hypoth. DF Error DF Sig. of F

Pillais          .65613    3.81623       2.00       4.00       .118
Hotellings      1.90812    3.81623       2.00       4.00       .118
Wilks            .34387    3.81623       2.00       4.00       .118
Roys             .65613
Note.. F statistics are exact.

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04 Nov 98 Repeated measures with contrasts, ch16 Page 6
12:57:11 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'SCORE' Within-Subject Effect.

AVERAGED Tests of Significance for SCORE using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 156.67 10 15.67
SCORE 148.00 2 74.00 4.72 .036

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5736 bytes of memory are needed for MANOVA execution.
04 Nov 98 Repeated measures with contrasts, ch16 Page 7
12:57:11 Arizona State University HP 9000 HP-UX 10.0

Preceding task required .05 seconds CPU time; .26 seconds elapsed.

16 manova score1 score2 score3
17    /wsfactors=score(3)
18    /print=signif(univ)
19    /contrast(score)=special(1 1 1, 1 -2 1, 1 0 -1)
20    /rename=mean first second
21    /design.

>Warning # 12252 on line 19 in column 20. Text: SPECIAL
>Special contrasts were requested for a WSFACTOR. MANOVA automatically
>orthonormalizes contrast matrices for WSFACTORS. If the special contrasts
>that were requested are nonorthogonal, the contrasts actually fitted are
>not the contrasts requested. See the transformation matrix for the actual
>contrasts fitted. Use TRANSFORM instead of WSFACTORS to produce
>nonorthogonal contrasts for within subjects factors. Multivariate and
>averaged tests remain valid.

The default error term in MANOVA has been changed from WITHIN CELLS to
WITHIN+RESIDUAL. Note that these are the same for all full factorial
designs.
04 Nov 98 Repeated measures with contrasts, ch16 Page 8
12:57:11 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e * * * * * *

         6 cases accepted.
         0 cases rejected because of out-of-range factor values.
         0 cases rejected because of missing data.
         1 non-empty cell.

1 design will be processed.

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04 Nov 98 Repeated measures with contrasts, ch16 Page 9
12:57:11 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests of Between-Subjects Effects.

Tests of Significance for MEAN using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 67.33 5 13.47
CONSTANT 2312.00 1 2312.00 171.68 .000

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Estimates for MEAN
--- Individual univariate .9500 confidence intervals

CONSTANT

Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% CL- Upper

1 19.6299092 1.49815 13.10279 .00005 15.77880 23.48102

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04 Nov 98 Repeated measures with contrasts, ch16 Page 10
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'SCORE' Within-Subject Effect.

Mauchly sphericity test, W =      .98732
Chi-square approx. =              .05103 with 2 D. F.
Significance =                      .975

Greenhouse-Geisser Epsilon =      .98748
Huynh-Feldt Epsilon =            1.00000
Lower-bound Epsilon =             .50000

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04 Nov 98 Repeated measures with contrasts, ch16 Page 11
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

EFFECT .. SCORE
Multivariate Tests of Significance (S = 1, M = 0, N = 1 )

Test Name Value Exact F Hypoth. DF Error DF Sig. of F

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EFFECT .. SCORE (Cont.)
Univariate F-tests with (1,5) D. F.

Variable Hypoth. SS Error SS Hypoth. MS Error MS F Sig. of F

FIRST 121.00000 71.66667 121.00000 14.33333 8.44186 .034
SECOND 27.00000 85.00000 27.00000 17.00000 1.58824 .263

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04 Nov 98 Repeated measures with contrasts, ch16 Page 12
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'SCORE' Within-Subject Effect.

AVERAGED Tests of Significance for SCORE using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 156.67 10 15.67
SCORE 148.00 2 74.00 4.72 .036

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Estimates for FIRST
--- Individual univariate .9500 confidence intervals

SCORE

Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% CL- Upper

1 -4.4907312 1.54560 -2.90549 .03358 -8.46383 -.51763

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Estimates for SECOND
--- Individual univariate .9500 confidence intervals

SCORE

Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% CL- Upper

1 -2.1213203 1.68325 -1.26025 .26319 -6.44825 2.20561

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04 Nov 98 Repeated measures with contrasts, ch16 Page 13
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22 manova score1 score2 score3
23    /print=signif(univ)
24    /transform(score1 score2 score3)=special(1 1 1, 1 -2 1, 0 1 1)
25    /rename=mean first second
26    /design.
The default error term in MANOVA has been changed from WITHIN CELLS to
WITHIN+RESIDUAL. Note that these are the same for all full factorial
designs.
04 Nov 98 Repeated measures with contrasts, ch16                         Page 14
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* * * * * * A n a l y s i s o f V a r i a n c e * * * * * *

         6 cases accepted.
         0 cases rejected because of out-of-range factor values.
         0 cases rejected because of missing data.
         1 non-empty cell.

1 design will be processed.

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04 Nov 98 Repeated measures with contrasts, ch16 Page 15
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

EFFECT .. CONSTANT
Multivariate Tests of Significance (S = 1, M = 1/2, N = 1/2)

Test Name Value Exact F Hypoth. DF Error DF Sig. of F

Pillais          .98885   88.67165       3.00       3.00       .002
Hotellings     88.67165   88.67165       3.00       3.00       .002
Wilks            .01115   88.67165       3.00       3.00       .002
Roys             .98885
Note.. F statistics are exact.

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EFFECT .. CONSTANT (Cont.)
Univariate F-tests with (1,5) D. F.

Variable Hypoth. SS Error SS Hypoth. MS Error MS F Sig. of F

MEAN       6936.00000 202.00000 6936.00000   40.40000 171.68317       .000
FIRST       726.00000 430.00000 726.00000   86.00000    8.44186       .034
SECOND     4056.00000 120.00000 4056.00000   24.00000 169.00000       .000

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Two-factor within ANOVA

set width=80.
title 'Two-factor within subjects, ch 21'.
data list list
/a1b1 a1b2 a1b3 a1b4 a2b1 a2b2 a2b3 a2b4.
begin data
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
end data.
manova a1b1 a1b2 a1b3 a1b4 a2b1 a2b2 a2b3 a2b4
/wsfactors=freq(2) trials(4)
/print=signif(univ)
/wsdesign
/design.

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests of Between-Subjects Effects.

Tests of Significance for T1 using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 272.59 3 90.86
CONSTANT 2432.53 1 2432.53 26.77 .014

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18 Nov 98 Two-factor within subjects, ch 21 Page 4
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'FREQ' Within-Subject Effect.

Tests of Significance for T2 using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 5.84 3 1.95
FREQ 116.28 1 116.28 59.70 .005

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18 Nov 98 Two-factor within subjects, ch 21 Page 5
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'TRIALS' Within-Subject Effect.

Mauchly sphericity test, W =      .11105
Chi-square approx. =             3.78502 with 5 D. F.
Significance =                      .581

Greenhouse-Geisser Epsilon =      .58676
Huynh-Feldt Epsilon =            1.00000
Lower-bound Epsilon =             .33333

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18 Nov 98 Two-factor within subjects, ch 21 Page 6
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

EFFECT .. TRIALS
Multivariate Tests of Significance (S = 1, M = 1/2, N = -1/2)

Test Name Value Exact F Hypoth. DF Error DF Sig. of F

Pillais          .99231   43.01657       3.00       1.00       .112
Hotellings    129.04970   43.01657       3.00       1.00       .112
Wilks            .00769   43.01657       3.00       1.00       .112
Roys             .99231
Note.. F statistics are exact.

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EFFECT .. TRIALS (Cont.)
Univariate F-tests with (1,3) D. F.

Variable Hypoth. SS Error SS Hypoth. MS Error MS F Sig. of F

T3          124.25625    7.56875 124.25625    2.52292   49.25103       .006
T4             .78125   17.84375     .78125    5.94792     .13135       .741
T5            4.55625    6.36875    4.55625    2.12292    2.14622       .239

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18 Nov 98 Two-factor within subjects, ch 21 Page 7
11:15:03 Arizona State University HP 9000 HP-UX 10.0

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'TRIALS' Within-Subject Effect.

AVERAGED Tests of Significance for MEAS.1 using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 31.78 9 3.53
TRIALS 129.59 3 43.20 12.23 .002

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18 Nov 98 Two-factor within subjects, ch 21 Page 8
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'FREQ BY TRIALS' Within-Subject Effect.

Mauchly sphericity test, W =      .00000
Chi-square approx. =              .      with 5 D. F.
Significance =                      .

Greenhouse-Geisser Epsilon =      .34752
Huynh-Feldt Epsilon =             .36956
Lower-bound Epsilon =             .33333

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* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*                   *                                          &n bsp;      *
*   W A R N I N G   * The WITHIN CELLS error matrix is SINGULAR.      *
*                   * These variables are LINEARLY DEPENDENT          *
*                   * on preceding ones ..                            *
*                   *   T8                                         ;    *
*                   * Multivariate tests will be skipped.             *
*                   *                                          &n bsp;      *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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18 Nov 98 Two-factor within subjects, ch 21 Page 9
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

EFFECT .. FREQ BY TRIALS
Univariate F-tests with (1,3) D. F.

Variable Hypoth. SS Error SS Hypoth. MS Error MS F Sig. of F

T6            2.25625    1.36875    2.25625     .45625    4.94521       .113
T7             .78125     .84375     .78125     .28125    2.77778       .194
T8             .30625     .81875     .30625     .27292    1.12214       .367

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18 Nov 98 Two-factor within subjects, ch 21 Page 10
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'FREQ BY TRIALS' Within-Subject Effect.

AVERAGED Tests of Significance for MEAS.1 using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 3.03 9 .34
FREQ BY TRIALS 3.34 3 1.11 3.31 .071

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Two-factor mixed ANOVA

set width=80.
title 'one within, one between --ch17'.
data list list
/facta b1 b2 b3 b4.
begin data
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
end data.
manova b1 b2 b3 b4 by facta(1,3)
/wsfactors=factb(4)
/print=signif(avonly)
/wsdesign
/design.

* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests of Between-Subjects Effects.

AVERAGED Tests of Significance for B using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS 302.13 9 33.57
FACTA 414.13 2 207.06 6.17 .021

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22 Nov 98 one within, one between --ch17 & nbsp; Page 4
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'FACTB' Within-Subject Effect.

Mauchly sphericity test, W =      .64018
Chi-square approx. =             3.44415 with 5 D. F.
Significance =                      .632

Greenhouse-Geisser Epsilon =      .82977
Huynh-Feldt Epsilon =            1.00000
Lower-bound Epsilon =             .33333

AVERAGED Tests of Significance that follow are equivalent to
univariate or split-plot or mixed-model approach to repeated measures.
Epsilons may be used to adjust d.f. for the AVERAGED results.

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22 Nov 98 one within, one between --ch17 & nbsp; Page 5
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* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * * * * *

Tests involving 'FACTB' Within-Subject Effect.

AVERAGED Tests of Significance for B using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F

WITHIN CELLS              90.38      27      3.35
FACTB                   1152.42       3    384.14    114.76      .000
FACTA BY FACTB           130.21       6     21.70      6.48      .000

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