AGRI 2400 Lecture 29 - Split-Pot and Latin Square Designs

Split-Plot Designs - RBC Extension

• but with a second treatment factor (that is of interest) applied to each entire block (called plot)

  • giving you a whole-plot factor applied per block

  • and a subplot factor appiled to replicates within blocks

• extremely common design in field ag studies for operational and efficiency reasons

Basic Split Plot Design

• 1 treatment (whole-plot factor) applied per block (plot)

• 1 treatment (subplot factor) applied to replicates within each block

Typical Split-Plot Uses

• when it is operationally convenient to apply experimental treatments at different scales

• e.g. seeding in plots vs pesticide or fertilizer applications

Reporting Results - Split Plot

• similar to two-factor ANOVA

  • presentation of results and interpretation depends on whther there is a sig interaction between the whole-plot and subplot factors

  • since we mist treat plot/block as random

Latin Square ANOVA Design

• another extension of an RCB ANOVA design

  • with each treatment level of factor of interest represented in every row (block 1) and every columb (block 2) with a nxn square

  • need not actually be physical rows/columns, any two blocking factors can be used provided they ‘work’ within other the design constraints

• strongly represented in ag field studies

Latin Square ANOVA Assumptions

• each sample is randomly selected and indep

• interval or ratio scale measurement of dep variable

• residuals are normally distributed

• equal variances among treatment groups

• no outliers

• additivity between blocks (rows/colums) and treatments (as in RCB designs)

Latin Square Limitations

• the # of treatments, rows, and columns must be the same

  • may be impractical for many natural systems

• squares smaller than 5×5 are not practical because of the small # of df for error term

• the effect of each treatment must be similar across rows and columns

Latin Square Example

• study: effect of bowl colour on number of wild bees captured in the tallgrass prairie

  • every bowl colour present in every row and column

  • measured total number of bees captured after being deployed for one week

Latin Square Reporting Results

• similar to two-factor ANOVA, but since we can not test for interactions:

  • you can directly discuss the meain effect

  • you can perform post hoc testing for the main if there is evidence of a significant effect