options ls=75;  
 
title 'Sugar Beet Varieties';
title3 'Latin Square Design';
/*
The data for this example, which appears in the online SAS documentation
for version 8, is taken from Smith (1951). A Latin square design is used 
to evaluate six different sugar beet varieties arranged in a six-row  
by six-column square.

Smith, W.G. (1951), Dissertation Notes on Canadian Sugar Factories, Ltd., 
Alberta, Canada: Taber.

Questions:
1) Plot the yields against the rows, using a different symbol
for each variety
2) Plot the yields against the columns, using a different symbol
for each variety
3) In an analysis of variance, which factors do suspect will 
account for the most variability in yield ?
4) Carry such an ANOVA for the data from this latin-square experiment
5) Use Tukey's procedure to carry out all pairwise comparisons
among variety means, after averaging over row and column
6) What proportion of SS(variety) is explained by the contrast
comparing variety 5 with the average of the other varieties?


*/



data one;
   do row=1 to 6;
      do column=1 to 6;
         input variety y @;
         output;
      end;
   end;
   cards; 
   3 19.1 6 18.3 5 19.6 1 18.6 2 18.2 4 18.5
   6 18.1 2 19.5 4 17.6 3 18.7 1 18.7 5 19.9
   1 18.1 5 20.2 6 18.5 4 20.1 3 18.6 2 19.2
   2 19.1 3 18.8 1 18.7 5 20.2 4 18.6 6 18.5
   4 17.5 1 18.1 2 18.7 6 18.2 5 20.4 3 18.5
   5 17.7 4 17.8 3 17.4 2 17.0 6 17.6 1 17.6
;
proc gplot data=one;
   plot y*row=variety;
   plot y*column=variety;
run;

proc glm;
   class row column variety;
   model y=row column variety;
run;