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) Advantages: Reduces more experimental error than with 1 blocking factor

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Latin Square Designs

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Latin square designs

Latin Square Designs

KNNL – Sections 28.3-28.7


Description

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

    • 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):


Latin square model

Latin Square Model


Analysis of variance

Analysis of Variance


Post hoc comparison of treatment means relative efficiency

Post-Hoc Comparison of Treatment Means & Relative Efficiency


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


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