# Two-Way Random-Effect Model

## Newswriting Efficiency Example

### Setup

Do StatANOVAGeneral Linear Model:

#### Session Output

General Linear Model: eff versus wp, writer

Factor  Type    Levels  Values
wp      random       3  1, 2, 3
writer  random       4  1, 2, 3, 4

Analysis of Variance for eff, using Adjusted SS for Tests

wp          2   68.167   68.167  34.083  0.58  0.589
writer      3  238.667  238.667  79.556  1.35  0.344
wp*writer   6  353.167  353.167  58.861  6.54  0.000
Error      24  216.000  216.000   9.000
Total      35  876.000

S = 3   R-Sq = 75.34%   R-Sq(adj) = 64.04%

Term          Coef  SE Coef       T      P
Constant   121.333    0.500  242.67  0.000
wp
1           0.6667   0.7071    0.94  0.355
2          -1.9167   0.7071   -2.71  0.012
writer
1          -3.8889   0.8660   -4.49  0.000
2           1.4444   0.8660    1.67  0.108
3           3.0000   0.8660    3.46  0.002
wp*writer
1  1        -3.444    1.225   -2.81  0.010
1  2         1.889    1.225    1.54  0.136
1  3        -2.000    1.225   -1.63  0.116
2  1         5.472    1.225    4.47  0.000
2  2        -2.194    1.225   -1.79  0.086
2  3        -3.083    1.225   -2.52  0.019

Unusual Observations for eff

Obs      eff      Fit  SE Fit  Residual  St Resid
16  124.000  118.667   1.732     5.333      2.18 R

R denotes an observation with a large standardized residual.

Expected Mean Squares, using Adjusted SS

Source     Expected Mean Square for Each Term
1  wp         (4) + 3.0000 (3) + 12.0000 (1)
2  writer     (4) + 3.0000 (3) + 9.0000 (2)
3  wp*writer  (4) + 3.0000 (3)
4  Error      (4)

Error Terms for Tests, using Adjusted SS

Synthesis
of Error
Source     Error DF  Error MS  MS
1  wp             6.00    58.861  (3)
2  writer         6.00    58.861  (3)
3  wp*writer     24.00     9.000  (4)

Estimated
Source         Value
wp            -2.065
writer         2.299
wp*writer     16.620
Error          9.000

Least Squares Means for eff

wp*writer   Mean
1  1       114.7
1  2       125.3
1  3       123.0
1  4       125.0
2  1       121.0
2  2       118.7
2  3       119.3
2  4       118.7
3  1       116.7
3  2       124.3
3  3       130.7
3  4       118.7

#### Interaction Plot (fitted means) for eff

From the plot, the existence of variability in the interaction is apparent.