Experimental Design by Kirk Chapter 5: Completely Randomized Design | SAS Textbook Examples

This page shows how to obtain the results from Kirk Chapter 5 using SAS.

Use data file cr4, page 167.

data cr4;
input y a order;
datalines;
 4  1  1 
 6  1  2 
 3  1  3 
 3  1  4 
 1  1  5 
 3  1  6 
 2  1  7 
 2  1  8 
 4  2  1 
 5  2  2 
 4  2  3 
 3  2  4 
 2  2  5 
 3  2  6 
 4  2  7 
 3  2  8 
 5  3  1 
 6  3  2 
 5  3  3 
 4  3  4 
 3  3  5 
 4  3  6 
 3  3  7 
 4  3  8 
 3  4  1 
 5  4  2 
 6  4  3 
 5  4  4 
 6  4  5 
 7  4  6 
 8  4  7 
10  4  8
;
run;

Table 5.2-1, page 167.

Note: The formchar option defines the characters used for constructing the table outlines.

options formchar='|-*+*+++*+*';

proc tabulate data=cr4;
  class order a;
  var y;
  table order, mean*y=' '*a;
run;

*----------------------+---------------------------------------------------*
|                      |                       Mean                        |
|                      +---------------------------------------------------+
|                      |                         a                         |
|                      +------------+------------+------------+------------+
|                      |     1      |     2      |     3      |     4      |
+----------------------+------------+------------+------------+------------+
|order                 |            |            |            |            |
+----------------------+            |            |            |            |
|1                     |        4.00|        4.00|        5.00|        3.00|
+----------------------+------------+------------+------------+------------+
|2                     |        6.00|        5.00|        6.00|        5.00|
+----------------------+------------+------------+------------+------------+
|3                     |        3.00|        4.00|        5.00|        6.00|
+----------------------+------------+------------+------------+------------+
|4                     |        3.00|        3.00|        4.00|        5.00|
+----------------------+------------+------------+------------+------------+
|5                     |        1.00|        2.00|        3.00|        6.00|
+----------------------+------------+------------+------------+------------+
|6                     |        3.00|        3.00|        4.00|        7.00|
+----------------------+------------+------------+------------+------------+
|7                     |        2.00|        4.00|        3.00|        8.00|
+----------------------+------------+------------+------------+------------+
|8                     |        2.00|        3.00|        4.00|       10.00|
*----------------------+------------+------------+------------+------------*

proc means mean std data=cr4;
  class a;
  var y;
run;

The MEANS Procedure

               Analysis Variable : y

                  N
           a    Obs            Mean         Std Dev
---------------------------------------------------
           1      8       3.0000000       1.5118579
           2      8       3.5000000       0.9258201
           3      8       4.2500000       1.0350983
           4      8       6.2500000       2.1213203
---------------------------------------------------

Table 5.3-2, page 172.

proc glm data=cr4;
  class a;
  model y = a;
run;

The GLM Procedure

Dependent Variable: y

                                        Sum of
Source                      DF         Squares     Mean Square    F Value    Pr > F
Model                        3      49.0000000      16.3333333       7.50    0.0008
Error                       28      61.0000000       2.1785714
Corrected Total             31     110.0000000

R-Square     Coeff Var      Root MSE        y Mean
0.445455      34.72938      1.475998      4.250000


Source                      DF       Type I SS     Mean Square    F Value    Pr > F
a                            3     49.00000000     16.33333333       7.50    0.0008

Source                      DF     Type III SS     Mean Square    F Value    Pr > F
a                            3     49.00000000     16.33333333       7.50    0.0008

3 contrasts, page 173.

Note: SAS reports contrasts as F-ratios which equal the t-values squared from the book.

proc glm data=cr4;
  class a;
  model y = a;
  contrast 'c1' a 1 -1 0 0;
  contrast 'c2' a 0 0 1 -1;
  contrast 'c3' a 1 1 -1 -1;
run;

[some output omitted]

Contrast                    DF     Contrast SS     Mean Square    F Value    Pr > F
c1                           1      1.00000000      1.00000000       0.46    0.5036
c2                           1     16.00000000     16.00000000       7.34    0.0114
c3                           1     32.00000000     32.00000000      14.69    0.0007

Table 5.4-1, page 174.

Note: We will demonstrate pairwise comparisons using the tukey option since SAS does not have Fisher-Hayter comparisons.

proc glm data=cr4;
  class a;
  model y = a;
  means a / tukey;
run;

[some output omitted]

Tukey's Studentized Range (HSD) Test for y

NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher
Type II error rate than REGWQ.

Alpha                                   0.05
Error Degrees of Freedom                  28
Error Mean Square                   2.178571
Critical Value of Studentized Range  3.86125
Minimum Significant Difference         2.015

Means with the same letter are not significantly different.

Tukey
Groupi
  ng            Mean      N    a

     A        6.2500      8    4
     A
B    A        4.2500      8    3
B
B             3.5000      8    2
B
B             3.0000      8    1

Parts of Table 5.7-4, page 196.

proc glm data=cr4;
  class a;
  model y = a;
  contrast 'linear' a -3 -1 1 3;
  contrast 'quadratic' a 1 -1 -1 1;
  contrast 'cubic' a -1 3 -3 1;
run;

[some output omitted]

Contrast                    DF     Contrast SS     Mean Square    F Value    Pr > F
linear                       1     44.10000000     44.10000000      20.24    0.0001
quadratic                    1      4.50000000      4.50000000       2.07    0.1617
cubic                        1      0.40000000      0.40000000       0.18    0.6716