Balanced Incomplete Block Design Example

  Refer to our previous example on a randomized complete block design.
Suppose we modify that problem slightly. First, we'll assume that we now
have 6 age blocks, rather than 5, as shown below:

                                     Fat content
                                    --------------
Age                  Extremely Low     Fairly Low   Moderately Low
----

15-24                    .73              .67            
25-34                    .86                             .21       
35-44                                     .81            .26
45-54                   1.40                             .75
55-64                                    1.41            .78
65-74                   0.83             1.04

 However, the data is not "complete": we see each treatment (diet type)
appears in only 4 of the 6 blocks. We also see that diet is paired with
another diet exactly twice. For example, the extremely low-fat diet is
paired with the fairly low-fat diet in the 1st and 6th blocks.

 This is called a balanced incomplete block design.

 We can analyze this using SAS, but we must use PROC GLM. The following
commands were saved in the SAS program dietbibd.sas:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

title 'Balanced Incomplete Block Design: Diets';

options linesize=79;

data diet;
   infile 'dietinc.dat';


input Fat Age Lipids;

PROC PRINT;

PROC GLM;
    CLASS Fat Age;
    MODEL Lipids = Fat Age;

RUN;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

                    Balanced Incomplete Block Design: Diets

#NOTE: In the data, the . represents in missing value in SAS. So, when
the data is typed in to a file, this '.' (but not typed in quotes like
this) must be included.

                          Obs    Fat    Age    Lipids

                            1     1      1      0.73 
                            2     1      2      0.86 
                            3     1      3       .   
                            4     1      4      1.40 
                            5     1      5       .   
                            6     1      6      0.83 
                            7     2      1      0.67 
                            8     2      2       .   
                            9     2      3      0.81 
                           10     2      4       .   
                           11     2      5      1.41 
                           12     2      6      1.04 
                           13     3      1       .   
                           14     3      2      0.21 
                           15     3      3      0.26 
                           16     3      4      0.75 
                           17     3      5      0.78 
                           18     3      6       .   

                    Balanced Incomplete Block Design: Diets                   

                               The GLM Procedure

                           Class Level Information
 
                     Class         Levels    Values

                     Fat                3    1 2 3       

                     Age                6    1 2 3 4 5 6 

                         Number of observations    18

NOTE: Due to missing values, only 12 observations can be used in this analysis.

                    Balanced Incomplete Block Design: Diets       

                               The GLM Procedure
 
Dependent Variable: Lipids   

                                      Sum of
Source                     DF        Squares    Mean Square   F Value   Pr > F

Model                       7     1.43092500     0.20441786     31.57   0.0024

Error                       4     0.02590000     0.00647500                   

Corrected Total            11     1.45682500                                  

              R-Square     Coeff Var      Root MSE    Lipids Mean

              0.982222      9.903678      0.080467       0.812500


Source                     DF      Type I SS    Mean Square   F Value   Pr > F

Fat                         2     0.58745000     0.29372500     45.36   0.0018
Age                         5     0.84347500     0.16869500     26.05   0.0038


Source                     DF    Type III SS    Mean Square   F Value   Pr > F

Fat                         2     0.77015000     0.38507500     59.47   0.0011
Age                         5     0.84347500     0.16869500     26.05   0.0038