Sampling Techniques and Design of Experiments (New Model Paper)

 

5.4. Latin Square Design

 

Latin Square Design (LSD):

The entire experimental area is divided into relative homogeneous groups / blocks with respect to two sources of variation rows and columns, treatments are now allocated to all experimental units in rows and columns in a such a way that every treatment occurs once and only once in each row and column, such design is called Latin Square Design.

Lay out of LSD:

In LSD, the number of treatments and number of replications are equal i.e., the number of rows is equal to number of columns. Suppose we consider m treatments, then there is mxm = m² experimental units. So the whole experimental area is divided into m² experimental units and arranged in a square so that each row and column consists of m units. Then the m treatments are allocated at random to these rows and columns in such a way that every treatment occurs once and only in each row and in each column. This lay out is known as mxm LSD.

For example:

A	B	C
B	C	A
C	A	B

 

A	B	C	D
B	C	D	A
C	D	A	B
D	A	B	C

Advantages:

1. LSD controls variation in three ways i.e., row, column and treatment

2. The statistical analysis is simple even with missing value

3. More than one factor can be studied simultaneously and with fewer trials than more complicated designs.

Dis advantages:

1. The number of treatments is equal to the number of replications in LSD, this restricts the use of this design.

2. If several units are missing in LSD, the statistical analysis is more complex

3. LSD, performs only on a square field but RBD or CRD can perform rectangular fields also

4. The fundamental assumption that there is no interaction between different factors may not be true in general.