Latin Square Designs - PowerPoint PPT Presentation

Latin square designs
1 / 7

  • Uploaded on
  • Presentation posted in: General

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Presentation

Latin Square Designs

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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):

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

  • Login