6.4 - Blocking in 2 Dimensions: Latin Square

The Latin Square Section

 Text Section 28.3

The fundamental idea of blocking can be extended to more dimensions. Blocking simultaneously with complete blocks in two directions is accomplished with a Latin Square design.

The limitation is that the Latin Square experimental layout will only be possible if the number of Row blocks = number of Column blocks = number of treatment levels.

The process begins with a standard Latin square (available in many texts and on the internet). These have the treatment levels ordered across the first row and first column. For example, a single factor with three levels (A,B,C), to be blocked in two directions could begin with this standard 3 × 3 square:

A B C
B C A
C A B

To randomize, first randomize the order of the rows and produce a new square.

B C A
C A B
A B C

Then randomize the order of the columns to yield the final square for the experimental layout.

C A B
A B C
B C A

This process assures that any row or column is complete, having all treatment levels.

The ANOVA for the Latin Square is a direct extension of the RCBD with random blocking effects. Now, however, we would have the SAS statement: random row column; It is assumed that there is no row by column interaction.