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Example
The effect of five different catalysts (A, B, C, D, F)
on the reaction time of a chemical process is being
studied. Each batch of new material is only large
enough to permit five runs to be made. Furthermore, each
run requires approximately 1½ hours, so that only
five runs can be made in one day.
The experimenter decides
to run the experiment as a Latin square, so that day
and batch effects may be systematically controlled. She
obtains the data that follow. Analyze these data and
draw conclusions.
| Batch |
Days |
| 1 |
2 |
3 |
4 |
5 |
| 1 |
A=8 |
B=7 |
D=1 |
C=7 |
E=3 |
| 2 |
C=11 | E=2 | A=7 | D=3 | B=8 |
| 3 |
B=4 |
A=9 |
C=10 |
E=1 |
D=5 |
| 4 |
D=6 | C=8 | E=6 | B=6 | A=10 |
| 5 |
E=4 |
D=2 |
B=3 |
A=8 |
C=8 |
Use following SAS source to analyze above problem.
Closely examine comments in the source for specific
model options.
OPTIONS LINESIZE=80;
TITLE1 'n x n Latin Square Design';
TITLE2 'Response var. : Effect of catalyst on the';
TITLE3 ' reaction of a chemical process';
TITLE4 'Treatment : Five different catalysts (batches) ';
TITLE5 'Block: Days ';
DATA PROCESS;
/* @@ means a loop in reading input variable sequence */
INPUT BATCH DAY CATALYST $ REACTIME @@;
CARDS;
1 1 A 8 1 2 B 7 1 3 D 1 1 4 C 7 1 5 E 3
2 1 C 11 2 2 E 2 2 3 A 7 2 4 D 3 2 5 B 8
3 1 B 4 3 2 A 9 3 3 C 10 3 4 E 1 3 5 D 5
4 1 D 6 4 2 C 8 4 3 E 6 4 4 B 6 4 5 A 10
5 1 E 4 5 2 D 2 5 3 B 3 5 4 A 8 5 5 C 8
;
RUN;
/* Print the original data set */
PROC PRINT;
RUN;
/* Create Table & tabulate input data set */
/* Nicety, but not absolutely necessary for */
/* the analysis - you may skip */
PROC TABULATE;
CLASS BATCH DAY ;
VAR REACTIME;
TABLE BATCH, DAY*REACTIME/CONDENSE;
KEYLABEL SUM='Y(IJ)';
RUN;
/* Analysis of Variance (ANOVA) */
PROC ANOVA;
CLASS BATCH DAY CATALYST;
MODEL REACTIME = BATCH DAY CATALYST;
RUN;
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SAS User Guide (SUG) for Procedures (PROC) used in the Source
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