ON CONTRASTS FOR DISCRIMINATING THE OPTIMAL SEMI-LATIN SQUARES WITH SIDE SIX AND BLOCK SIZE TWO

Abstract

In  this  work,  we  investigate  the  contrasts  properties  of  the  optimal semiLatin squares with side six and block size two with a view to discriminating
amongst  them.  The  Variances,  as  well  as  the  average  Variance  of  the
estimate  of  elementary  contrasts  of  treatments  was  computed  for  each
square with the aid of MATLAB and the results compared with each other.
From the results, the average variance of elementary treatment contrasts
for the three squares   1,   2  and   3  is approximately the same. Again, the
squares  2 and  3 have the same and minimal number of distinct variances
of  elementary  contrasts  compared  to   1,  hence  preferable  to   1.
Furthermore,   3  has  a  minimal  value  of  the  maximum  variances  of
contrasts amongst these squares. Thus,   3  becomes the most preferable
square amongst all of them; while  2 is preferable to  1