A k x k Latin square experiment is one in which three experimental factors (one of
which
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.
Factor
B
|
Factor A
|
level | 1 | 2 | 3 |
| 1 | 1 | 3 | 2 | |
| 2 | 2 | 1 | 3 | |
| 3 | 3 | 2 | 1 |
Green are the levels of Factor C.
| Factor A level | Factor B level | Factor C level |
| 1 | 1 | 1 |
| 1 | 2 | 3 |
| 1 | 3 | 2 |
| 2 | 1 | 2 |
| 2 | 2 | 1 |
| 2 | 3 | 3 |
| 3 | 1 | 3 |
| 3 | 2 | 2 |
| 3 | 3 | 1 |
Notice if the green column was missing then the first two have the 3 x 3 full factorial
structure for
factors A and B.
The same is true if we dropped any of the three columns in the above table.