Elementary Statistics and Computer Application

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


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