### Stata Textbook Examples Experimental Design by Roger Kirk Chapter 12: Split-Plot Factorial Design

Table 12.2-1, page 516.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/spf2-4, clear

tabdisp s b, cellvar(y) by(a) concise

----------+-----------------------
|           b
a and s |    1     2     3     4
----------+-----------------------
1         |
1 |    3     4     7     7
2 |    6     5     8     8
3 |    3     4     7     9
4 |    3     3     6     8
----------+-----------------------
2         |
5 |    1     2     5    10
6 |    2     3     6    10
7 |    2     4     5     9
8 |    2     3     6    11
----------+-----------------------

table a b, cont(sum y) row col

----------+----------------------------------
|                 b
a |     1      2      3      4  Total
----------+----------------------------------
1 |    15     16     28     32     91
2 |     7     12     22     40     81
|
Total |    22     28     50     72    172
----------+----------------------------------
Table 12.2-2, page 517.

Note: The repeated option is used to compute the Huynh-Feldt values.
anova y a / s|a b a*b /, repeated(b)

Number of obs =      32     R-squared     =  0.9613
Root MSE      =    .712     Adj R-squared =  0.9333

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |     226.375    13  17.4134615      34.35     0.0000
|
a |       3.125     1       3.125       2.00     0.2070
s|a |       9.375     6      1.5625
-----------+----------------------------------------------------
b |      194.50     3  64.8333333     127.89     0.0000
a*b |      19.375     3  6.45833333      12.74     0.0001
|
Residual |       9.125    18  .506944444
-----------+----------------------------------------------------
Total |      235.50    31  7.59677419

Between-subjects error term:  s|a
Levels:  8         (6 df)
Lowest b.s.e. variable:  s
Covariance pooled over:  a         (for repeated variable)

Repeated variable: b
Huynh-Feldt epsilon        =  0.9432
Greenhouse-Geisser epsilon =  0.5841
Box's conservative epsilon =  0.3333

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box
-----------+----------------------------------------------------
b |      3   127.89   0.0000   0.0000   0.0000   0.0000
a*b |      3    12.74   0.0001   0.0002   0.0019   0.0118
Residual |     18
-----------+----------------------------------------------------
Figure 12.2-1, page 518.
egen ybar_a1 = mean(y) if a == 1, by(b)
egen ybar_a2 = mean(y) if a == 2, by(b)
graph twoway (scatter ybar_a1 b, connect(l) sort mlabel(a) mlabposition(12)) ///
(scatter ybar_a2 b, connect(l) sort mlabel(a) mlabposition(12))
egen ybar_b1 = mean(y) if b == 1, by(a)
egen ybar_b2 = mean(y) if b == 2, by(a)
egen ybar_b3 = mean(y) if b == 3, by(a)
egen ybar_b4 = mean(y) if b == 4, by(a)
graph twoway (scatter ybar_b1 a, connect(L) sort mlabel(b)mlabposition(12)) ///
(scatter ybar_b2 a, connect(L) sort mlabel(b)  mlabposition(12)) ///
(scatter ybar_b3 a, connect(L) sort mlabel(b)  mlabposition(12)) ///
(scatter ybar_b4 a, connect(L) sort mlabel(b)  mlabposition(12))
Omega-squareds, page 519.

omega2 2 1

omega squared = 0.0303
effect size   = 0.1768

omega2 127.89 3

omega squared = 0.9225
effect size   = 3.4490

omega2 12.74 3

omega squared = 0.5240
effect size   = 1.0491
Table 12.4-1, page 528.
anova y a / s|a b a*b /, repeated(b) noanova  /* repeat anova with no output */

matrix list e(Srep)

symmetric e(Srep)[4,4]
c1          c2          c3          c4
r1        1.25
r2   .66666667   .66666667
r3   .58333333   .33333333          .5
r4           0  -.16666667   .16666667   .66666667
Table 12.8-1, page 542.

Note: The entry for s1 a1 c1 b4 is incorrect in the book. It should have the value 7. The data file, spf22-4.dta, has the correct value.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/spf22-4, clear

tabdisp s b, cellvar(y) by(a c) concise  /* note corrected value */

----------+-----------------------
a, c and  |           b
s         |    1     2     3     4
----------+-----------------------
1         |
1         |
1 |    3     4     7     7
2 |    6     5     8     8
----------+-----------------------
1         |
2         |
3 |    3     4     7     9
4 |    3     3     6     8
----------+-----------------------
2         |
1         |
5 |    1     2     5    10
6 |    2     3     6    10
----------+-----------------------
2         |
2         |
7 |    2     4     5     9
8 |    2     3     6    11
----------+-----------------------

table a b c, cont(sum y)

----------+-------------------------------------------------
|                     c and b
| ---------- 1 ---------    ---------- 2 ---------
a |    1     2     3     4       1     2     3     4
----------+-------------------------------------------------
1 |    9     9    15    15       6     7    13    17
2 |    3     5    11    20       4     7    11    20
----------+-------------------------------------------------

table c b, cont(sum y)

----------+-----------------------
|           b
c |    1     2     3     4
----------+-----------------------
1 |   12    14    26    35
2 |   10    14    24    37
----------+-----------------------

table a b, cont(sum y) row col

----------+----------------------------------
|                 b
a |     1      2      3      4  Total
----------+----------------------------------
1 |    15     16     28     32     92
2 |     7     12     22     40     81
|
Total |    22     28     50     73    173
----------+----------------------------------

table a c, cont(sum y) row

----------+-----------
|     c
a |    1     2
----------+-----------
1 |   48    43
2 |   39    42
|
Total |   88    85
----------+-----------
Table 12.8-2, page 545.
anova y a c a*c / s|a*c b a*b b*c a*b*c /, repeated(b)

Number of obs =      32     R-squared     =  0.9798
Root MSE      = .629153     Adj R-squared =  0.9479

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |      230.75    19  12.1447368      30.68     0.0000
|
a |       3.125     1       3.125       1.72     0.2594
c |        .125     1        .125       0.07     0.8058
a*c |        2.00     1        2.00       1.10     0.3528
s|a*c |        7.25     4      1.8125
-----------+----------------------------------------------------
b |      194.50     3  64.8333333     163.79     0.0000
a*b |      19.375     3  6.45833333      16.32     0.0002
b*c |       1.375     3  .458333333       1.16     0.3660
a*b*c |        3.00     3        1.00       2.53     0.1068
|
Residual |        4.75    12  .395833333
-----------+----------------------------------------------------
Total |      235.50    31  7.59677419

Between-subjects error term:  s|a*c
Levels:  8         (4 df)
Lowest b.s.e. variable:  s
Covariance pooled over:  a*c       (for repeated variable)

Repeated variable: b
Huynh-Feldt epsilon        =  2.1181
*Huynh-Feldt epsilon reset to 1.0000
Greenhouse-Geisser epsilon =  0.6367
Box's conservative epsilon =  0.3333

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box
-----------+----------------------------------------------------
b |      3   163.79   0.0000   0.0000   0.0000   0.0002
a*b |      3    16.32   0.0002   0.0002   0.0018   0.0156
b*c |      3     1.16   0.3660   0.3660   0.3609   0.3425
a*b*c |      3     2.53   0.1068   0.1068   0.1448   0.1872
Residual |     12
-----------+----------------------------------------------------

matrix list e(Srep)

symmetric e(Srep)[4,4]
c1    c2    c3    c4
r1  1.25
r2    .5    .5
r3    .5   .25    .5
r4  .375     0    .5   .75
Figure 12.10-1, page 555.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/spf2-22, clear

tabdisp s b c, cellvar(y) by(a) concise

----------+-------------------------
|         c and b
| ---- 1 ---    ---- 2 ---
a and s |    1     2       1     2
----------+-------------------------
1         |
1 |    3     7       4     7
2 |    6     8       5     8
3 |    3     7       4     9
4 |    3     6       3     8
----------+-------------------------
2         |
5 |    1     5       2    10
6 |    2     6       3    10
7 |    2     5       4     9
8 |    2     6       3    11
----------+-------------------------

table a c b, cont(sum y)

----------+-------------------------
|         b and c
| ---- 1 ---    ---- 2 ---
a |    1     2       1     2
----------+-------------------------
1 |   15    16      28    32
2 |    7    12      22    40
----------+-------------------------

table a c b, cont(sum y)

----------+-------------------------
|         b and c
| ---- 1 ---    ---- 2 ---
a |    1     2       1     2
----------+-------------------------
1 |   15    16      28    32
2 |    7    12      22    40
----------+-------------------------
Table 12.10-2, page 559.
anova y a / s|a b a*b / b*s|a c a*c / c*s|a b*c a*b*c /, repeated(b c)

Number of obs =      32     R-squared     =  0.9920
Root MSE      = .559017     Adj R-squared =  0.9589

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |     233.625    25       9.345      29.90     0.0002
|
a |       3.125     1       3.125       2.00     0.2070
s|a |       9.375     6      1.5625
-----------+----------------------------------------------------
b |      162.00     1      162.00     199.38     0.0000
a*b |       6.125     1       6.125       7.54     0.0335
b*s|a |       4.875     6       .8125
-----------+----------------------------------------------------
c |       24.50     1       24.50      61.89     0.0002
a*c |      10.125     1      10.125      25.58     0.0023
c*s|a |       2.375     6  .395833333
-----------+----------------------------------------------------
b*c |        8.00     1        8.00      25.60     0.0023
a*b*c |       3.125     1       3.125      10.00     0.0195
|
Residual |       1.875     6       .3125
-----------+----------------------------------------------------
Total |      235.50    31  7.59677419

Between-subjects error term:  s|a
Levels:  8         (6 df)
Lowest b.s.e. variable:  s
Covariance pooled over:  a         (for repeated variables)

Repeated variable: b
Huynh-Feldt epsilon        =  1.2000
*Huynh-Feldt epsilon reset to 1.0000
Greenhouse-Geisser epsilon =  1.0000
Box's conservative epsilon =  1.0000

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box
-----------+----------------------------------------------------
b |      1   199.38   0.0000   0.0000   0.0000   0.0000
a*b |      1     7.54   0.0335   0.0335   0.0335   0.0335
b*s|a |      6
-----------+----------------------------------------------------

Repeated variable: c
Huynh-Feldt epsilon        =  1.2000
*Huynh-Feldt epsilon reset to 1.0000
Greenhouse-Geisser epsilon =  1.0000
Box's conservative epsilon =  1.0000

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box
-----------+----------------------------------------------------
c |      1    61.89   0.0002   0.0002   0.0002   0.0002
a*c |      1    25.58   0.0023   0.0023   0.0023   0.0023
c*s|a |      6
-----------+----------------------------------------------------

Repeated variables: b*c
Huynh-Feldt epsilon        =  1.2000
*Huynh-Feldt epsilon reset to 1.0000
Greenhouse-Geisser epsilon =  1.0000
Box's conservative epsilon =  1.0000

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box
-----------+----------------------------------------------------
b*c |      1    25.60   0.0023   0.0023   0.0023   0.0023
a*b*c |      1    10.00   0.0195   0.0195   0.0195   0.0195
Residual |      6
-----------+----------------------------------------------------

matrix list e(Srep)

symmetric e(Srep)[4,4]
c1          c2          c3          c4
r1        1.25
r2   .66666667   .66666667
r3   .58333333   .33333333          .5
r4           0  -.16666667   .16666667   .66666667
Table 12.14-1, page 574.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/spf2-3a, clear

tabdisp s b, cellvar(y) by(a) concise

----------+-----------------
|        b
a and s |    1     2     3
----------+-----------------
1         |
1 |    3     4     7
2 |    6     5     8
----------+-----------------
2         |
3 |    3     4     7
4 |    3     3     6
5 |    1     2     5
----------+-----------------
Table 12.14-2, page 576.
anova y a / s|a b a*b /, repeated(b)

Number of obs =      15     R-squared     =  0.9692
Root MSE      = .544331     Adj R-squared =  0.9281

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |  55.9555556     8  6.99444444      23.61     0.0005
|
a |  10.6777778     1  10.6777778       3.08     0.1774
s|a |  10.3888889     3  3.46296296
-----------+----------------------------------------------------
b |  32.3555556     2  16.1777778      54.60     0.0001
a*b |  .355555556     2  .177777778       0.60     0.5787
|
Residual |  1.77777778     6  .296296296
-----------+----------------------------------------------------
Total |  57.7333333    14  4.12380952

Between-subjects error term:  s|a
Levels:  5         (3 df)
Lowest b.s.e. variable:  s
Covariance pooled over:  a         (for repeated variable)

Repeated variable: b
Huynh-Feldt epsilon        =  0.7500
Greenhouse-Geisser epsilon =  0.5000
Box's conservative epsilon =  0.5000

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box
-----------+----------------------------------------------------
b |      2    54.60   0.0001   0.0008   0.0051   0.0051
a*b |      2     0.60   0.5787   0.5431   0.4950   0.4950
Residual |      6
-----------+----------------------------------------------------

matrix list e(Srep)

symmetric e(Srep)[3,3]
c1         c2         c3
r1  2.3888889
r2  1.1666667  .83333333
r3  1.1666667  .83333333  .83333333

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