/* This example shows the analysis for the Latin Square experiment */
/* using the productivity data example we looked at in class */

/* Entering the data and defining the variables: */

DATA productivity; 
INPUT OBS MUSIC $ DAY TIME PRODUCT; 
CARDS; 
 1 A 1 1 6.3 
 2 B 1 2 9.8 
 3 C 1 3 14.3 
 4 D 1 4 12.3 
 5 E 1 5 9.1 
 6 B 2 1 7.7 
 7 C 2 2 13.5 
 8 D 2 3 13.4 
 9 E 2 4 12.6 
 10 A 2 5 9.9 
 11 C 3 1 11.7 
 12 D 3 2 10.7 
 13 E 3 3 13.8 
 14 A 3 4 9.0 
 15 B 3 5 10.3 
 16 D 4 1 9.0 
 17 E 4 2 10.5 
 18 A 4 3 9.3 
 19 B 4 4 9.8 
 20 C 4 5 12.0 
 21 E 5 1 4.5 
 22 A 5 2 5.3 
 23 B 5 3 8.4 
 24 C 5 4 9.6 
 25 D 5 5 11.0
;
run;


/*******************************************************************************/
/* The PROC GLM syntax is familiar here.  MUSIC, DAY and TIME are factors.     */
/* PRODUCT is the response variable, MUSIC is the treatment factor,            */
/* and TIME and DAY are the row and column factors. Note there is no RANDOM    */
/* statement, since the levels of TIME and DAY are not really a random sample. */

PROC GLM data=productivity;
CLASS MUSIC DAY TIME;
MODEL PRODUCT = MUSIC DAY TIME;
MEANS MUSIC / ALPHA=0.05 TUKEY;
MEANS MUSIC / ALPHA=0.05 TUKEY CLDIFF;
RUN;                 

/* From the F-tests and their P-values, there is a significant effect of music type    */
/* on mean productivity.  We also see a significant row (TIME) effect and column (DAY) */
/* effect.  Tukey's procedure tells us which pairs of music types are significantly    */
/* different.                                                                          */