Split-split plot experiment of apple trees — archbold.apple • agridat

Split-split plot experiment of apple trees with different spacing, root stock, and cultivars.

Format

A data frame with 120 observations on the following 10 variables.

rep

block, 5 levels

row

row

pos

position within each row

spacing

spacing between trees, 6,10,14 feet

stock

rootstock, 4 levels

gen

genotype, 2 levels

yield

yield total, kg/tree from 1975-1979

trt

treatment code

Details

In rep 1, the 10-foot-spacing main plot was split into two non-contiguous pieces. This also happened in rep 4. In the analysis of Cornelius and Archbold, they consider each row x within-row-spacing to be a distinct main plot. (Also true for the 14-foot row-spacing, even though the 14-foot spacing plots were contiguous.)

The treatment code is defined as 100 * spacing + 10 * stock + gen, where stock=0,1,6,7 for Seedling,MM111,MM106,M0007 and gen=1,2 for Redspur,Golden, respectively.

Source

D Archbold and G. R. Brown and P. L. Cornelius. (1987). Rootstock and in-row spacing effects on growth and yield of spur-type delicious and Golden delicious apple. Journal of the American Society for Horticultural Science, 112, 219-222.

References

Cornelius, PL and Archbold, DD, 1989. Analysis of a split-split plot experiment with missing data using mixed model equations. Applications of Mixed Models in Agriculture and Related Disciplines. Pages 55-79.

Examples

# \dontrun{

library(agridat)
data(archbold.apple)
dat <- archbold.apple

# Define main plot and subplot
dat <- transform(dat, rep=factor(rep), spacing=factor(spacing), trt=factor(trt),
                 mp = factor(paste(row,spacing,sep="")),
                 sp = factor(paste(row,spacing,stock,sep="")))

# Due to 'spacing', the plots are different sizes, but the following layout
# shows the relative position of the plots and treatments. Note that the
# 'spacing' treatments are not contiguous in some reps.
libs(desplot)
desplot(dat, spacing~row*pos,
        col=stock, cex=1, num=gen, # aspect unknown
        main="archbold.apple")


libs(lme4, lucid)
#> Loading required package: Matrix
m1 <- lmer(yield ~ -1 + trt + (1|rep/mp/sp), dat)

vc(m1)  # Variances/means on Cornelius, page 59
#>          grp        var1 var2   vcov sdcor
#>  sp:(mp:rep) (Intercept) <NA>  193.3 13.9 
#>       mp:rep (Intercept) <NA>  203.8 14.27
#>          rep (Intercept) <NA>  197.3 14.05
#>     Residual        <NA> <NA> 1015   31.86
##         grp        var1 var2   vcov sdcor
## sp:(mp:rep) (Intercept) <NA>  193.3 13.9
##      mp:rep (Intercept) <NA>  203.8 14.28
##         rep (Intercept) <NA>  197.3 14.05
##    Residual        <NA> <NA> 1015   31.86
  
# }