Latin square design or Least square difference (LSD)

• When the experimental units is divided into rows, columns and treatment and each treatment occurs only once in the row and column, the design is called LSD.
• Used only when the F-test indicates a significant difference exists.

i.e. LSD = t √2MSE/ n

• Helps to control variations in two directions.
• Treatments are arranged in row and column.
• Most common size is 5×5 to 8×8.
• Each object appear once and only once in each row and each column.
• Also called the three-factors experiment.
• The factors are row , column and treatment.

Advantages of LSD

• You can control variations in two directions.
• Increased efficiency as compared to RCBD.
• More than one factor can be investigated simultaneously.

Disadvantages of LSD

• Number of treatments must be equal to number of replicates.
• Experimental error likely to increase with size of squares.
• Small square has few degree of freedom.
• Can’t calculate interaction between rows and columns , rows and treatments and column and treatments.

d) Factorial design

e) Split plot design

• Used when one of factors is difficult to change or randomize.

• We may use split plot design where we are interested in testing the effect of one factor over a wider variety of condition.
• Requires enough size in main-plots to be split into sub-plots.
• We first look at the effect of main plot treatment, then sub-plot treatment.
• In split plot design, the hard-to-change factors are implemented first, the fields are split in two , then the easier-to-change factors are implemented.

Advantage

• Cheaper to run
• More efficient statistically with increased precision

Disadvantage

• Implementing the design can be difficult and requires advance knowledge of a specific discipline.
• Software packages that assist with the design are hard to find.