Example 50.4: A Latin Square Design

The PLAN Procedure

Example 50.4: A Latin Square Design

All of the preceding examples involve designs with completely nested block structures, for which PROC PLAN was especially designed. However, by appropriate coordination of its facilities, a much wider class of designs can be accommodated. A Latin square design is based on experimental units that have a row-and-column block structure. The following example uses the CYCLIC option for a treatment factor tmts to generate a simple 4 ×4 Latin square. Randomizing a Latin square design involves randomly permuting the row, column, and treatment values independently. In order to do this, use the RANDOM option in the OUTPUT statement of PROC PLAN. The example also uses factor-value-settings in the OUTPUT statement. The following statements produce Output 50.4.1:

   title 'Latin Square Design';
   proc plan seed=37430;
      factors rows=4 ordered cols=4 ordered / noprint;
      treatments tmts=4 cyclic;
      output out=g
             rows cvals=('Day 1' 'Day 2' 'Day 3' 'Day 4') random
             cols cvals=('Lab 1' 'Lab 2' 'Lab 3' 'Lab 4') random
             tmts nvals=(   0      100     250     450  ) random;
   quit;

   proc tabulate;
      class rows cols;
      var tmts;
      table rows, cols*(tmts*f=6.) / rts=8;
   run;

Output 50.4.1: A Randomized Latin Square Design

Latin Square Design

	cols
	Lab 1	Lab 2	Lab 3	Lab 4
	tmts	tmts	tmts	tmts
	Sum	Sum	Sum	Sum
rows	0	250	100	450
Day 1	0	250	100	450
Day 2	250	450	0	100
Day 3	100	0	450	250
Day 4	450	100	250	0

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