## Output from repmes3.sas

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```                   3 Factor Design with 1 Repeated Measure                   1
Multivariate REPEATED Measure Analysis
```
```                       General Linear Models Procedure
Class Level Information

Class    Levels    Values
```
```                          A             2    1 2

B             2    1 2

Number of observations in data set = 12

```

```                   3 Factor Design with 1 Repeated Measure                   2
Multivariate REPEATED Measure Analysis
```
```                       General Linear Models Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information

Dependent Variable         T1       T2       T3       T4

Level of TRIALS          1        2        3        4

```

```                   3 Factor Design with 1 Repeated Measure                   3
Multivariate REPEATED Measure Analysis
```
```                       General Linear Models Procedure
Repeated Measures Analysis of Variance

Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r|

DF = 8            T1        T2        T3        T4
```
`              T1          1.000000  0.494934  0.189029  0.109985`
```                            0.0001    0.1755    0.6262    0.7782
```
`              T2          0.494934  1.000000  0.751921  0.583333`
```                            0.1755    0.0001    0.0195    0.0992
```
`              T3          0.189029  0.751921  1.000000  0.954820`
```                            0.6262    0.0195    0.0001    0.0001
```
`              T4          0.109985  0.583333  0.954820  1.000000`
```                            0.7782    0.0992    0.0001    0.0001

E = Error SS&CP Matrix

TRIALS.N represents the nth degree polynomial contrast for TRIALS
```
```                          TRIALS.1          TRIALS.2          TRIALS.3

TRIALS.1       31.76666667      -13.71455026       -3.96666667
TRIALS.2      -13.71455026       15.83333333       -1.34164079
TRIALS.3       -3.96666667       -1.34164079        4.56666667

```

```                   3 Factor Design with 1 Repeated Measure                   4
Multivariate REPEATED Measure Analysis
```
```                       General Linear Models Procedure
Repeated Measures Analysis of Variance

Partial Correlation Coefficients from the Error SS&CP Matrix
of the Variables Defined by the Specified Transformation / Prob > |r|```
```                   DF = 8      TRIALS.1  TRIALS.2  TRIALS.3

TRIALS.1    1.000000 -0.611518 -0.329337```
```                                 0.0001    0.0801    0.3868
```
`                   TRIALS.2   -0.611518  1.000000 -0.157779`
```                                 0.0801    0.0001    0.6852
```
`                   TRIALS.3   -0.329337 -0.157779  1.000000`
```                                 0.3868    0.6852    0.0001

Test for Sphericity: Mauchly's Criterion = 0.1874661
Chisquare Approximation = 11.254057 with 5 df   Prob > Chisquare = 0.0466

Applied to Orthogonal Components:
Test for Sphericity: Mauchly's Criterion = 0.1874661
Chisquare Approximation = 11.254057 with 5 df   Prob > Chisquare = 0.0466

H = Type III SS&CP Matrix for TRIALS
TRIALS.N represents the nth degree polynomial contrast for TRIALS
```
```                          TRIALS.1          TRIALS.2          TRIALS.3

TRIALS.1            984.15      -81.50467778              24.3
TRIALS.2      -81.50467778              6.75       -2.01246118
TRIALS.3              24.3       -2.01246118               0.6

```
```               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=2

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.01542181   127.6864         3         6  0.0001
Pillai's Trace             0.98457819   127.6864         3         6  0.0001
Hotelling-Lawley Trace    63.84321632   127.6864         3         6  0.0001
Roy's Greatest Root       63.84321632   127.6864         3         6  0.0001```

```                   3 Factor Design with 1 Repeated Measure                   5
Multivariate REPEATED Measure Analysis
```
```                       General Linear Models Procedure
Repeated Measures Analysis of Variance

H = Type III SS&CP Matrix for TRIALS*A
TRIALS.N represents the nth degree polynomial contrast for TRIALS
```
```                          TRIALS.1          TRIALS.2          TRIALS.3

TRIALS.1      1.6666666667      2.2360679775               2.5
TRIALS.2      2.2360679775                 3      3.3541019662
TRIALS.3               2.5      3.3541019662              3.75

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

S=1    M=0.5    N=2

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.24441969     6.1826         3         6  0.0289
Pillai's Trace             0.75558031     6.1826         3         6  0.0289
Hotelling-Lawley Trace     3.09132348     6.1826         3         6  0.0289
Roy's Greatest Root        3.09132348     6.1826         3         6  0.0289```
```                    H = Type III SS&CP Matrix for TRIALS*B
TRIALS.N represents the nth degree polynomial contrast for TRIALS
```
```                          TRIALS.1          TRIALS.2          TRIALS.3

TRIALS.1      10.416666667      -0.931694991      4.1666666667
TRIALS.2      -0.931694991      0.0833333333      -0.372677996
TRIALS.3      4.1666666667      -0.372677996      1.6666666667

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

S=1    M=0.5    N=2

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.36059729     3.5464         3         6  0.0875
Pillai's Trace             0.63940271     3.5464         3         6  0.0875
Hotelling-Lawley Trace     1.77317668     3.5464         3         6  0.0875
Roy's Greatest Root        1.77317668     3.5464         3         6  0.0875```

```                   3 Factor Design with 1 Repeated Measure                   6
Multivariate REPEATED Measure Analysis
```
```                       General Linear Models Procedure
Repeated Measures Analysis of Variance

H = Type III SS&CP Matrix for TRIALS*A*B
TRIALS.N represents the nth degree polynomial contrast for TRIALS
```
```                          TRIALS.1          TRIALS.2          TRIALS.3

TRIALS.1               9.6      -1.788854382               5.2
TRIALS.2      -1.788854382      0.3333333333       -0.96896279
TRIALS.3               5.2       -0.96896279      2.8166666667

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

S=1    M=0.5    N=2

Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.32790819     4.0993         3         6  0.0669
Pillai's Trace             0.67209181     4.0993         3         6  0.0669
Hotelling-Lawley Trace     2.04963411     4.0993         3         6  0.0669
Roy's Greatest Root        2.04963411     4.0993         3         6  0.0669```

```                   3 Factor Design with 1 Repeated Measure                   7
Multivariate REPEATED Measure Analysis
```
```                       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
```
```A                        1      10.0833333     10.0833333      0.98     0.3517
B                        1       8.3333333      8.3333333      0.81     0.3949
A*B                      1      80.0833333     80.0833333      7.77     0.0237

Error                    8      82.5000000     10.3125000

```

```                   3 Factor Design with 1 Repeated Measure                   8
Multivariate REPEATED Measure Analysis
```
```                       General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects

Source: TRIALS
DF      Type III SS      Mean Square   F Value   Pr > F    G - G    H - F```
```      3     991.50000000     330.50000000    152.05   0.0001   0.0001   0.0001
```
```Source: TRIALS*A
DF      Type III SS      Mean Square   F Value   Pr > F    G - G    H - F```
```      3       8.41666667       2.80555556      1.29   0.3003   0.3002   0.3015
```
```Source: TRIALS*B
DF      Type III SS      Mean Square   F Value   Pr > F    G - G    H - F```
```      3      12.16666667       4.05555556      1.87   0.1624   0.1967   0.1693
```
```Source: TRIALS*A*B
DF      Type III SS      Mean Square   F Value   Pr > F    G - G    H - F```
```      3      12.75000000       4.25000000      1.96   0.1477   0.1847   0.1550
```
```Source: Error(TRIALS)

DF      Type III SS      Mean Square```
```     24      52.16666667       2.17361111

Greenhouse-Geisser Epsilon = 0.5361
Huynh-Feldt Epsilon = 0.9023
```

```                   3 Factor Design with 1 Repeated Measure                   9
Multivariate REPEATED Measure Analysis
```
```                       General Linear Models Procedure
Repeated Measures Analysis of Variance
Analysis of Variance of Contrast Variables

TRIALS.N represents the nth degree polynomial contrast for TRIALS

Contrast Variable: TRIALS.1

Source                  DF     Type III SS    Mean Square   F Value     Pr > F
```
```MEAN                     1    984.15000000   984.15000000    247.84     0.0001
A                        1      1.66666667     1.66666667      0.42     0.5352
B                        1     10.41666667    10.41666667      2.62     0.1440
A*B                      1      9.60000000     9.60000000      2.42     0.1586

Error                    8     31.76666667     3.97083333```
```
Contrast Variable: TRIALS.2

Source                  DF     Type III SS    Mean Square   F Value     Pr > F
```
```MEAN                     1      6.75000000     6.75000000      3.41     0.1020
A                        1      3.00000000     3.00000000      1.52     0.2532
B                        1      0.08333333     0.08333333      0.04     0.8425
A*B                      1      0.33333333     0.33333333      0.17     0.6923

Error                    8     15.83333333     1.97916667```
```
Contrast Variable: TRIALS.3

Source                  DF     Type III SS    Mean Square   F Value     Pr > F
```
```MEAN                     1      0.60000000     0.60000000      1.05     0.3353
A                        1      3.75000000     3.75000000      6.57     0.0335
B                        1      1.66666667     1.66666667      2.92     0.1259
A*B                      1      2.81666667     2.81666667      4.93     0.0571

Error                    8      4.56666667     0.57083333

```

```                   3 Factor Design with 1 Repeated Measure                  10
Mixed Model Analysis
```
```                       General Linear Models Procedure
Class Level Information

Class    Levels    Values
```
```                A             2    1 2

B             2    1 2

SUBJ         12    1 2 3 4 5 6 7 8 9 10 11 12

TRIAL         4    1 2 3 4

Number of observations in data set = 48

```

```                   3 Factor Design with 1 Repeated Measure                  11
Mixed Model Analysis
```
```                       General Linear Models Procedure

Dependent Variable: RESPONSE
Sum of           Mean
Source                  DF         Squares         Square   F Value     Pr > F
```
```Model                   23     1205.833333      52.427536     24.12     0.0001

Error                   24       52.166667       2.173611

Corrected Total         47     1258.000000```
```
R-Square            C.V.       Root MSE        RESPONSE Mean
```
```                  0.958532        14.74317       1.474317             10.00000
```
```
Source                  DF     Type III SS    Mean Square   F Value     Pr > F
```
```A                        1      10.0833333     10.0833333      4.64     0.0415
B                        1       8.3333333      8.3333333      3.83     0.0620
A*B                      1      80.0833333     80.0833333     36.84     0.0001
SUBJ(A*B)                8      82.5000000     10.3125000      4.74     0.0014
TRIAL                    3     991.5000000    330.5000000    152.05     0.0001
A*TRIAL                  3       8.4166667      2.8055556      1.29     0.3003
B*TRIAL                  3      12.1666667      4.0555556      1.87     0.1624
A*B*TRIAL                3      12.7500000      4.2500000      1.96     0.1477```
```
Contrast                DF     Contrast SS    Mean Square   F Value     Pr > F
```
```T-linear                 1     984.1500000    984.1500000    452.77     0.0001
T-quad                   1       6.7500000      6.7500000      3.11     0.0908
T-cubic                  1       0.6000000      0.6000000      0.28     0.6041

```

```                   3 Factor Design with 1 Repeated Measure                  12
Mixed Model Analysis
```
```                       General Linear Models Procedure

Source      Type III Expected Mean Square
```
```A           Var(Error) + 4 Var(SUBJ(A*B)) + Q(A,A*B,A*TRIAL,A*B*TRIAL)

B           Var(Error) + 4 Var(SUBJ(A*B)) + Q(B,A*B,B*TRIAL,A*B*TRIAL)

A*B         Var(Error) + 4 Var(SUBJ(A*B)) + Q(A*B,A*B*TRIAL)

SUBJ(A*B)   Var(Error) + 4 Var(SUBJ(A*B))

TRIAL       Var(Error) + Q(TRIAL,A*TRIAL,B*TRIAL,A*B*TRIAL)

A*TRIAL     Var(Error) + Q(A*TRIAL,A*B*TRIAL)

B*TRIAL     Var(Error) + Q(B*TRIAL,A*B*TRIAL)

A*B*TRIAL   Var(Error) + Q(A*B*TRIAL)

```
`Contrast               Contrast Expected Mean Square`
```T-linear               Var(Error) + Q(TRIAL,A*TRIAL,B*TRIAL,A*B*TRIAL)

T-cubic                Var(Error) + Q(TRIAL,A*TRIAL,B*TRIAL,A*B*TRIAL)

```

```                   3 Factor Design with 1 Repeated Measure                  13
Mixed Model Analysis
```
```                       General Linear Models Procedure

Dependent Variable: RESPONSE

Tests of Hypotheses using the Type III MS for SUBJ(A*B) as an error term

Source                  DF     Type III SS    Mean Square   F Value     Pr > F
```
```A                        1     10.08333333    10.08333333      0.98     0.3517
B                        1      8.33333333     8.33333333      0.81     0.3949
A*B                      1     80.08333333    80.08333333      7.77     0.0237

```

```                   3 Factor Design with 1 Repeated Measure                  14
A * B means
```
```                 Plot of RESPONSE*A.  Symbol is value of B.

RESPONSE |
12.167 +                                               2
12.083 +
12.000 +
11.917 +
11.833 +
11.750 +
11.667 +
11.583 +
11.500 +
11.417 +
11.333 +
11.250 +
11.167 +
11.083 +
11.000 +
10.917 +
10.833 +
10.750 +
10.667 +
10.583 +
10.500 +
10.417 +  1
10.333 +
10.250 +
10.167 +
10.083 +
10.000 +
9.917 +
9.833 +
9.750 +
9.667 +
9.583 +
9.500 +
9.417 +
9.333 +
9.250 +
9.167 +
9.083 +
9.000 +
8.917 +
8.833 +
8.750 +                                               1
8.667 +  2
---+--------------------------------------------+--
1                                            2

Manifest Anxiety

```