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Latin Square Designs. KNNL – Sections 28.3-28.7. Description. 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

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latin square designs

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
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):
comments and extensions
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