### Stata Textbook Examples Experimental Design by Roger Kirk Chapter 7: Randomized Block Designs

Table 7.2-1, page 260.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/rb4, clear

tabdisp s a, cellvar(y)

----------+-----------------------
|           a
s |    1     2     3     4
----------+-----------------------
1 |    3     4     4     3
2 |    2     4     4     5
3 |    2     3     3     6
4 |    3     3     3     5
5 |    1     2     4     7
6 |    3     3     6     6
7 |    4     4     5    10
8 |    6     5     5     8
----------+-----------------------
Table 7.2-2, page 261.
anova y a s

Number of obs =      32     R-squared     =  0.7318
Root MSE      = 1.18523     Adj R-squared =  0.6041

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |       80.50    10        8.05       5.73     0.0004
|
a |       49.00     3  16.3333333      11.63     0.0001
s |       31.50     7        4.50       3.20     0.0180
|
Residual |       29.50    21   1.4047619
-----------+----------------------------------------------------
Total |      110.00    31   3.5483871
Table 7.3-2, page 271.

nonadd y a s

Tukey's test of nonadditivity for randomized block designs
F (1,20) = 1.2795813   Pr > F: .27135918
Figure 7.3-1, page 272.
anova y a s, noanova  /* rerun anova without redisplaying anova table */

predict yhat  /* yhat is the fitted value */

predict e, rstandard  /* e is the standardized residual */

graph twoway scatter e yhat, ylabel(-2.5(.5)2.5) xlabel(1(1)9)
Various computations on compound symmetry, pages 274-282.
anova y a s, repeated(a)  /* anova with conservative p-values for repeated measures */

Number of obs =      32     R-squared     =  0.7318
Root MSE      = 1.18523     Adj R-squared =  0.6041

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |       80.50    10        8.05       5.73     0.0004
|
a |       49.00     3  16.3333333      11.63     0.0001
s |       31.50     7        4.50       3.20     0.0180
|
Residual |       29.50    21   1.4047619
-----------+----------------------------------------------------
Total |      110.00    31   3.5483871

Between-subjects error term:  s
Levels:  8         (7 df)
Lowest b.s.e. variable:  s

Repeated variable: a
Huynh-Feldt epsilon        =  0.8343
Greenhouse-Geisser epsilon =  0.6195
Box's conservative epsilon =  0.3333

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box
-----------+----------------------------------------------------
a |      3    11.63   0.0001   0.0003   0.0015   0.0113
Residual |     21
-----------+----------------------------------------------------

matrix list e(Srep)  /* display variance-covariance matrix */

symmetric e(Srep)[4,4]
c1         c2         c3         c4
r1  2.2857143
r2  1.1428571  .85714286
r3  .71428571  .28571429  1.0714286
r4  1.2857143  .28571429  .92857143        4.5
Table 7.8-2, page 299.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/rb3, clear

tabdisp s a, cellvar(y)

----------+-----------------
|        a
s |    1     2     3
----------+-----------------
1 |   15    12    11
2 |         11     9
3 |   13    13
----------+-----------------
Table 7.8-3, page 301.
anova y a s

Number of obs =       7     R-squared     =  0.8970
Root MSE      = 1.06458     Adj R-squared =  0.6909

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |  19.7333333     4  4.93333333       4.35     0.1954
|
a |        8.40     2        4.20       3.71     0.2125
s |  3.73333333     2  1.86666667       1.65     0.3778
|
Residual |  2.26666667     2  1.13333333
-----------+----------------------------------------------------
Total |       22.00     6  3.66666667 
Tables 7.9-1, page 305.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/grb4, clear

tabdisp id a, by(g) cellvar(y)

----------+-----------------------
|           a
g and id |    1     2     3     4
----------+-----------------------
1         |
1 |    3     4     4     3
2 |    3     3     3     5
----------+-----------------------
2         |
1 |    2     4     4     5
2 |    2     3     3     6
----------+-----------------------
3         |
1 |    6     5     5     8
2 |    3     3     6     6
----------+-----------------------
4         |
1 |    1     2     4     7
2 |    4     4     5    10
----------+-----------------------

table g a, cont(sum y)

----------+-----------------------
|           a
g |    1     2     3     4
----------+-----------------------
1 |    6     7     7     8
2 |    4     7     7    11
3 |    9     8    11    14
4 |    5     6     9    17
----------+-----------------------
Table 7.9-2, page 306.

Note: To obtain the correct F-ratio of a, a*g is used as the error term.
anova y a g a*g

Number of obs =      32     R-squared     =  0.7727
Root MSE      =    1.25     Adj R-squared =  0.5597

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |       85.00    15  5.66666667       3.63     0.0074
|
a |       49.00     3  16.3333333      10.45     0.0005
g |       16.75     3  5.58333333       3.57     0.0377
a*g |       19.25     9  2.13888889       1.37     0.2795
|
Residual |       25.00    16      1.5625
-----------+----------------------------------------------------
Total |      110.00    31   3.5483871

test a /a*g

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
a |       49.00     3  16.3333333       7.64     0.0076
a*g |       19.25     9  2.13888889

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