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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)

- 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):

- 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