A k x k Latin square experiment is one in which three experimental factors (one of
is a primary experimental factor) have k levels each. It is an incomplete block experiment
with k x k experimental combination with only one treatment run in each block (which is
constructed by the two non primary experimental factors in the form of a square). In
these k x k experimental combination there is a full factorial structur in every pair of the
factor see Factor level combination table below. Any row (i.e., fixed level of a non
primary experimental factor) or column (i.e., fixed level of another non primary
experimental factor) has all the levels of the primary experimental variable.
Green are the levels of Factor C.
|Factor A level||Factor B level||Factor C level|
Notice if the green column was missing then the first two have the 3 x 3 full factorial
factors A and B.
The same is true if we dropped any of the three columns in the above table.