Example:

A laboratory is interested in examining the leaves of apple trees to detect deficiencies using three different laboratory
procedures (is there a difference in mean readings for apple leaves utilizing
three different lab. Procedures). Assume we use three analyst for leaf assays (not one). Randomly assign three
apple leaves to each analyst. Suppose
that each leaf assay takes a long time and only one procedure can be done by
each analyst per day. By modifying the randomized block design as follows

Must restrict our randomization to ensure that each treatment appears in
each row ( day ) and in each column ( analyst )

Analyst

Day |
1 |
2 |
3 |

1 |
A |
B |
C |

2 |
B |
C |
A |

3 |
C |
A |
B |

**Latin square design can be used to compare t treatment means in the
presence of two extraneous sources of variability, which are blocked off into t
rows and t columns. The t treatments are then randomly assigned to the rows and
columns so that each treatment appears in every row and every column of the
design **