STAM101 :: Lecture 17 :: Latin square design – description – layout – analysis – advantages and disadvantages

Latin Square Design

When the experimental material is divided into rows and columns and the treatments are allocated such that each treatment occurs only once in each row and each column, the design is known as L S D.

In LSD the treatments are usually denoted by A B C D etc.

For a 5 x 5 LSD the arrangements may be                                        


A

B

C

D

E

B

A

E

C

D

C

D

A

E

B

D

E

B

A

C

E

C

D

B

A

Square 1

B

C

D

E

B

A

D

E

C

C

E

A

B

D

D

C

E

A

B

E

D

B

C

A

Square 2

A

B

C

D

E

B

C

D

E

A

C

D

E

A

B

D

E

A

B

C

E

A

B

C

D

Square  3

 

Analysis

The ANOVA model for LSD is

            Yijk = µ + ri + cj + tk + eijk

ri is the ith row effect
cj is the jth column effect
tk is the kth treatment effect and
eijk is the error term
The analysis of variance table for LSD is as follows:

Sources of Variation

d.f.

S S

M S

F

Rows

t-1

RSS

RMS

RMS/EMS

Columns

t-1

CSS

CMS

CMS/EMS

Treatments

t-1

TrSS

TrMS

TrMS/EMS

Error

(t-1)(t-2)

ESS

EMS

 

Total

t2-1

TSS

 

 

F table value
F [t-1),(t-1)(t-2)] degrees of freedom at 5% or 1%  level of significance

 

Steps to calculate the above Sum of Squares are as follows:

Correction Factor

Total Sum of Squares

Row sum of squares

Column sum of squares

Treatment sum of squares

Error Sum of Squares = TSS-RSS-CSS-TrSS

These results can be summarized in the form of analysis of variance table.

Calculation of SE, SE (d) and CD values

where r is the number of rows
.
CD= SE (d). t
where t = table value of t for a specified level of significance and error degrees of freedom
Using CD value the bar chart can be drawn and the conclusion may be written.

Advantages

  • LSD is more efficient than RBD or CRD. This is because of double grouping that will result in small experimental error.

 

  • When missing values are present, missing plot technique can be used and analysed.
Disadvantages
  • This design is not as flexible as RBD or CRD as the number of treatments is limited to the number of rows and columns. LSD is seldom used when the number of treatments is more than 12. LSD is not suitable for treatments less than five.

Because of the limitations on the number of treatments, LSD is not widely used in agricultural experiments.

Note: The number of sources of variation is two for CRD, three for RBD and four for LSD.

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