### Stata Textbook Examples Experimental Design by Roger Kirk Chapter 14: Fractional Factorial Designs

Use data file crff24-1, page 596.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/crff24-1, clear

list

a         b         c         d         y
1.        0         0         0         0         3
2.        0         0         0         0         6
3.        0         0         1         1         4
4.        0         0         1         1         3
5.        0         1         0         1         7
6.        0         1         0         1         6
7.        0         1         1         0         7
8.        0         1         1         0         8
9.        1         0         0         1         2
10.        1         0         0         1         2
11.        1         0         1         0         2
12.        1         0         1         0         3
13.        1         1         0         0         5
14.        1         1         0         0         6
15.        1         1         1         1         9
16.        1         1         1         1        11 
Parts of Table 14.3-1, page 672.
table a c b, cont(sum y)

----------+-------------------------
|         b and c
| ---- 0 ---    ---- 1 ---
a |    0     1       0     1
----------+-------------------------
0 |    9     7      13    15
1 |    4     5      11    20
----------+-------------------------

table a b, cont(sum y) row col

----------+--------------------
|          b
a |     0      1  Total
----------+--------------------
0 |    16     28     44
1 |     9     31     40
|
Total |    25     59     84
----------+--------------------

table a c, cont(sum y) row

----------+-----------
|     c
a |    0     1
----------+-----------
0 |   22    22
1 |   15    25
|
Total |   37    47
----------+-----------

table b c, cont(sum y)

----------+-----------
|     c
b |    0     1
----------+-----------
0 |   13    12
1 |   24    35
----------+-----------
Table 14.3-2, page 674.
anova y a b c d a*b a*c b*c

Number of obs =      16     R-squared     =  0.9189
Root MSE      = 1.06066     Adj R-squared =  0.8480

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |      102.00     7  14.5714286      12.95     0.0009
|
a |        1.00     1        1.00       0.89     0.3734
b |       72.25     1       72.25      64.22     0.0000
c |        6.25     1        6.25       5.56     0.0462
d |        1.00     1        1.00       0.89     0.3734
a*b |        6.25     1        6.25       5.56     0.0462
a*c |        6.25     1        6.25       5.56     0.0462
b*c |        9.00     1        9.00       8.00     0.0222
|
Residual |        9.00     8       1.125
-----------+----------------------------------------------------
Total |      111.00    15        7.40
Use data file lsff33-2, page 688.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/lsff33-2, clear

list

a         b         c         s         y
1.        0         0         0         0         3
2.        0         1         1         0         4
3.        0         2         2         0         6
4.        0         0         0         1         1
5.        0         1         1         1         4
6.        0         2         2         1         6
7.        1         0         2         2         7
8.        1         1         0         2         3
9.        1         2         1         2         3
10.        1         0         2         3         5
11.        1         1         0         3         2
12.        1         2         1         3         3
13.        2         0         1         4         4
14.        2         1         2         4         7
15.        2         2         0         4         3
16.        2         0         1         5         2
17.        2         1         2         5         5
18.        2         2         0         5         2 
Table 14.8-1, pages 688 and 689.
tabdisp s b, cellvar(y) by(a) concise

----------+-----------------
|        b
a and s |    0     1     2
----------+-----------------
0         |
0 |    3     4     6
1 |    1     4     6
----------+-----------------
1         |
2 |    7     3     3
3 |    5     2     3
----------+-----------------
2         |
4 |    4     7     3
5 |    2     5     2
----------+-----------------

table b c, cont(sum y) by(a)

----------+-----------------
|        c
a and b |    0     1     2
----------+-----------------
0         |
0 |    4
1 |          8
2 |               12
----------+-----------------
1         |
0 |               12
1 |    5
2 |          6
----------+-----------------
2         |
0 |          6
1 |               12
2 |    5
----------+-----------------

table c b, cont(sum y) row col

----------+---------------------------
|             b
c |     0      1      2  Total
----------+---------------------------
0 |     4      5      5     14
1 |     6      8      6     20
2 |    12     12     12     36
|
Total |    22     25     23     70
----------+--------------------------- 
Table 14.8-2, page 690.

Note: Kirk calls a*b*c residual and calls the Residual b*c*s|a.
anova y a / s|a b c b*c*a

Number of obs =      18     R-squared     =  0.9504
Root MSE      = .666667     Adj R-squared =  0.8595

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |  51.1111111    11  4.64646465      10.45     0.0046
|
a |  .111111111     2  .055555556       0.03     0.9742
s|a |  6.33333333     3  2.11111111
-----------+----------------------------------------------------
b |  .777777778     2  .388888889       0.88     0.4640
c |  43.1111111     2  21.5555556      48.50     0.0002
b*c*a |  .777777778     2  .388888889       0.87     0.4640
|
Residual |  2.66666667     6  .444444444
-----------+----------------------------------------------------
Total |  53.7777778    17  3.16339869 
Use data file lsff43-2, page 693.
use http://www.ats.ucla.edu/stat/stata/examples/kirk/lsff43-2, clear

list

a         b         c         d         y
1.        0         0         0         0         2
2.        0         1         3         0         3
3.        0         2         2         0         3
4.        0         3         1         0         6
5.        1         0         1         0         2
6.        1         1         0         0         4
7.        1         2         3         0         5
8.        1         3         2         0         4
9.        2         0         2         0         5
10.        2         1         1         0         8
11.        2         2         0         0         7
12.        2         3         3         0         6
13.        3         0         3         0         9
14.        3         1         2         0         9
15.        3         2         1         0        11
16.        3         3         0         0        10
17.        0         0         0         1         1
18.        0         1         3         1         2
19.        0         2         2         1         2
20.        0         3         1         1         3
21.        1         0         1         1         3
22.        1         1         0         1         3
23.        1         2         3         1         4
24.        1         3         2         1         3
25.        2         0         2         1         6
26.        2         1         1         1         6
27.        2         2         0         1         5
28.        2         3         3         1         7
29.        3         0         3         1         8
30.        3         1         2         1         8
31.        3         2         1         1        10
32.        3         3         0         1         7  
Table 14.9-1, page 693.
tabdisp a b, cellvar(y) by(d)

----------+-----------------------
|           b
d and a |    0     1     2     3
----------+-----------------------
0         |
0 |    2     3     3     6
1 |    2     4     5     4
2 |    5     8     7     6
3 |    9     9    11    10
----------+-----------------------
1         |
0 |    1     2     2     3
1 |    3     3     4     3
2 |    6     6     5     7
3 |    8     8    10     7
----------+-----------------------

table a d, cont(sum y) col

----------+--------------------
|          d
a |     0      1  Total
----------+--------------------
0 |    14      8     22
1 |    15     13     28
2 |    26     24     50
3 |    39     33     72
----------+--------------------

table b d, cont(sum y) col

----------+--------------------
|          d
b |     0      1  Total
----------+--------------------
0 |    18     18     36
1 |    24     19     43
2 |    26     21     47
3 |    26     20     46
----------+--------------------
Table 14.9-2, page 695.
anova y a b c d a*d b*d c*d

Number of obs =      32     R-squared     =  0.9618
Root MSE      = .866025     Adj R-squared =  0.9013

Source |  Partial SS    df       MS           F     Prob > F
-----------+----------------------------------------------------
Model |      226.50    19  11.9210526      15.89     0.0000
|
a |      194.50     3  64.8333333      86.44     0.0000
b |        9.25     3  3.08333333       4.11     0.0320
c |        7.75     3  2.58333333       3.44     0.0517
d |        8.00     1        8.00      10.67     0.0068
a*d |        2.00     3  .666666667       0.89     0.4747
b*d |        2.75     3  .916666667       1.22     0.3441
c*d |        2.25     3         .75       1.00     0.4262
|
Residual |        9.00    12         .75
-----------+----------------------------------------------------
Total |      235.50    31  7.59677419

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