Multi-environment trial of corn, balanced incomplete block design

Balanced incomplete block design in corn

Format

A data frame with 52 observations on the following 3 variables.

loc

location/block, 13 levels

gen

genotype/line, 13 levels

yield

yield, pounds/plot

Details

Incomplete block design. Each loc/block has 4 genotypes/lines. The blocks are planted at different locations.

Conducted in 1943 in North Carolina.

Source

North Carolina Agricultural Experiment Station, United States Department of Agriculture.

References

Cochran, W.G. and Cox, G.M. (1957), Experimental Designs, 2nd ed., Wiley and Sons, New York, p. 448.

Examples

library(agridat)

data(cochran.bib)
dat <- cochran.bib

# Show the incomplete-block structure
libs(lattice)
redblue <- colorRampPalette(c("firebrick", "lightgray", "#375997"))
levelplot(yield~loc*gen, dat,
          col.regions=redblue,
          xlab="loc (block)", main="cochran.bib - incomplete blocks")

with(dat, table(gen,loc))
#>      loc
#> gen   B01 B02 B03 B04 B05 B06 B07 B08 B09 B10 B11 B12 B13
#>   G01   0   0   0   0   0   0   1   0   1   0   1   1   0
#>   G02   0   0   0   1   0   0   0   0   1   1   0   0   1
#>   G03   1   1   0   0   0   0   0   1   1   0   0   0   0
#>   G04   0   1   0   0   0   1   0   0   0   1   1   0   0
#>   G05   0   0   0   1   0   1   1   1   0   0   0   0   0
#>   G06   1   0   0   0   0   1   0   0   0   0   0   1   1
#>   G07   0   0   0   0   1   0   0   1   0   0   1   0   1
#>   G08   0   1   0   1   1   0   0   0   0   0   0   1   0
#>   G09   1   0   0   0   1   0   1   0   0   1   0   0   0
#>   G10   0   0   1   0   1   1   0   0   1   0   0   0   0
#>   G11   1   0   1   1   0   0   0   0   0   0   1   0   0
#>   G12   0   1   1   0   0   0   1   0   0   0   0   0   1
#>   G13   0   0   1   0   0   0   0   1   0   1   0   1   0
rowSums(as.matrix(with(dat, table(gen,loc))))
#> G01 G02 G03 G04 G05 G06 G07 G08 G09 G10 G11 G12 G13 
#>   4   4   4   4   4   4   4   4   4   4   4   4   4 
colSums(as.matrix(with(dat, table(gen,loc))))
#> B01 B02 B03 B04 B05 B06 B07 B08 B09 B10 B11 B12 B13 
#>   4   4   4   4   4   4   4   4   4   4   4   4   4 

m1 = aov(yield ~ gen + Error(loc), data=dat)
summary(m1)
#> 
#> Error: loc
#>     Df Sum Sq Mean Sq
#> gen 12  689.4   57.45
#> 
#> Error: Within
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> gen       12  328.5   27.38   1.373  0.238
#> Residuals 27  538.2   19.93               

libs(nlme)
m2 = lme(yield ~ -1 + gen, data=dat, random=~1|loc)