Strip-split-plot of barley with fertilizer, calcium, and soil factors.
Strip-split-plot of barley with fertilizer, calcium, and soil factors.
A data frame with 96 observations on the following 5 variables.
repreplicate, 4 levels
soilsoil, 3 levels
fertfertilizer, 4 levels
calciumcalcium, 2 levels
yieldyield of winter barley
Four different fertilizer treatments are laid out in vertical strips, which are then split into subplots with different levels of calcium. Soil type is stripped across the split-plot experiment, and the entire experiment is then replicated three times.
Sometimes called a split-block design.
Comes from the notes of Gertrude Cox and A. Rotti.
SAS/STAT(R) 9.2 User's Guide, Second Edition. Example 23.5 Strip-Split Plot. https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_anova_sect030.htm
## Not run:
library(agridat)
data(cox.stripsplit)
dat <- cox.stripsplit
# Raw means
# aggregate(yield ~ calcium, data=dat, mean)
# aggregate(yield ~ soil, data=dat, mean)
# aggregate(yield ~ calcium, data=dat, mean)
libs(HH)
interaction2wt(yield ~ rep + soil + fert + calcium, dat,
x.between=0, y.between=0,
main="cox.stripsplit")
# Traditional AOV
m1 <- aov(yield~ fert*calcium*soil +
Error(rep/(fert+soil+calcium:fert+soil:fert)),
data=dat)
summary(m1)
# With balanced data, the following are all basically identical
libs(lme4)
# The 'rep:soil:fert' term causes problems...so we drop it.
m2 <- lmer(yield ~ fert*soil*calcium + (1|rep) + (1|rep:fert) +
(1|rep:soil) + (1|rep:fert:calcium), data=dat)
if(0){
# afex uses Kenword-Rogers approach for denominator d.f.
libs(afex)
mixed(yield ~ fert*soil*calcium + (1|rep) + (1|rep:fert) +
(1|rep:soil) + (1|rep:fert:calcium) + (1|rep:soil:fert), data=dat,
control=lmerControl(check.nobs.vs.rankZ="ignore"))
## Effect stat ndf ddf F.scaling p.value
## 1 (Intercept) 1350.8113 1 3.0009 1 0.0000
## 2 fert 3.5619 3 9.0000 1 0.0604
## 3 soil 3.4659 2 6.0000 1 0.0999
## 4 calcium 1.8835 1 12.0000 1 0.1950
## 5 fert:soil 1.2735 6 18.0000 1 0.3179
## 6 fert:calcium 4.4457 3 12.0000 1 0.0255
## 7 soil:calcium 0.2494 2 24.0000 1 0.7813
## 8 fert:soil:calcium 0.3504 6 24.0000 1 0.9027
}
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