Latin Square Designs

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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)
§ Reduces more experimental error than with 1 blocking factor
§ Small-scale studies can isolate important treatment effects
§ Repeated Measures designs can remove order effects
§   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
• 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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