Latin Square Designs

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					Latin Square Designs

KNNL – Sections 28.3-28.7
• Experiment with r treatments, and 2 blocking factors:
  rows (r levels) and columns (r levels)
• Advantages:
   § Reduces more experimental error than with 1 blocking factor
   § Small-scale studies can isolate important treatment effects
   § Repeated Measures designs can remove order effects
• Disadvantages
   §   Each blocking factor must have r levels
   §   Assumes no interactions among factors
   §   With small r, very few Error degrees of freedom; many with big r
   §   Randomization more complex than Completely Randomized
       Design and Randomized Block Design (but not too complex)
            Randomization in Latin Square
• Determine r , the number of treatments, row blocks, and
  column blocks
• Select a Standard Latin Square (Table B.14, p. 1344)
• Use Capital Letters to represent treatments (A,B,C,…) and
  randomly assign treatments to labels
• Randomly assign Row Block levels to Square Rows
• Randomly assign Column Block levels to Square Columns
• 4x4 Latin Squares (all treatments appear in each row/col):
Latin Square Model
Analysis of Variance
Post-Hoc Comparison of Treatment Means &
            Relative Efficiency
          Comments and Extensions
• Treatments can be Factorial Treatment Structures
  with Main Effects and Interactions
• Row, Column, and Treatment Effects can be Fixed or
  Random, without changing F-test for treatments
• Can have more than one replicate per cell to
  increase error degrees of freedom
• Can use multiple squares with respect to row or
  column blocking factors, each square must be r x r.
  This builds up error degrees of freedom (power)
• Can model carryover effects when rows or columns
  represent order of treatments

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