Maize yields for four cropping systems at 14 on-farm trials.

A data frame with 56 observations on the following 4 variables.

`village`

Village factor, 2 levels

`farm`

Farm factor, 14 levels

`system`

Cropping system factor, levels

`LM`

`LMF`

`CCA`

`CCAF`

`yield`

Yield, t/ha

Yields from 14 on-farm trials in Phalombe Project region of south-eastern Malawi. The farms were located near two different villages.

On each farm, four different cropping systems were tested. The systems were: LM = Local Maize, LMF = Local Maize with Fertilizer, CCA = Improved Composite, CCAF = Improved Composite with Fertilizer.

P. E. Hildebrand, 1984.
Modified Stability Analysis of Farmer Managed, On-Farm Trials.
*Agronomy Journal*, 76, 271–274.
https://www.agronomy.org/publications/aj/abstracts/76/2/AJ0760020271.

H. P. Piepho, 1998.
Methods for Comparing the Yield Stability of Cropping Systems.
*Journal of Agronomy and Crop Science*, 180, 193–213.

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data(hildebrand.systems)
dat <- hildebrand.systems
# Piepho 1998 Fig 1
require(lattice)
dotplot(yield ~ system, dat, groups=village, auto.key=TRUE,
main="hildebrand.systems", xlab="cropping system by village")
## Not run:
# Environmental variance model, unstructured correlations
require("asreml")
dat <- dat[order(dat$system, dat$farm),]
m1 <- asreml(yield ~ system, data=dat, rcov = ~us(system):farm)
# Means, table 5
p1 <- predict(m1, classify="system")$predictions$pvals
## system pred.value std.error est.stat
## CCA 1.164 0.2816 Estimable
## CCAF 2.657 0.3747 Estimable
## LM 1.35 0.1463 Estimable
## LMF 2.7 0.2561 Estimable
# Variances, table 5
require(lucid)
vc(m1)[c(2,4,7,11),]
## effect component std.error z.ratio constr
## R!system.CCA:CCA 1.11 0.4354 2.5 pos
## R!system.CCAF:CCAF 1.966 0.771 2.5 pos
## R!system.LM:LM 0.2996 0.1175 2.5 pos
## R!system.LMF:LMF 0.9185 0.3603 2.5 pos
# Stability variance model
m2 <- asreml(yield ~ system, data=dat,
random = ~ farm,
rcov = ~ at(system):units)
p2 <- predict(m2, classify="system")$predictions$pvals
# Variances, table 6
vc(m2)
## effect component std.error z.ratio constr
## farm!farm.var 0.2996 0.1175 2.5 pos
## system_CCA!variance 0.4136 0.1622 2.5 pos
## system_CCAF!variance 1.267 0.4969 2.5 pos
## system_LM!variance 0.0000002 NA NA bound
## system_LMF!variance 0.5304 0.208 2.5 pos
## End(Not run)
# Plot of risk of 'failure' of System 2 vs System 1
s11 = .30; s22 <- .92; s12 = .34
mu1 = 1.35; mu2 = 2.70
lambda <- seq(from=0, to=5, length=20)
system1 <- pnorm((lambda-mu1)/sqrt(s11))
system2 <- pnorm((lambda-mu2)/sqrt(s22))
# A simpler view
plot(lambda, system1, type="l", xlim=c(0,5), ylim=c(0,1),
xlab="Yield level", ylab="Prob(yield < level)",
main="hildebrand.systems - risk of failure for each system")
lines(lambda, system2, col="red")
# Prob of system 1 outperforming system 2. Table 8
pnorm((mu1-mu2)/sqrt(s11+s22-2*s12))
# .0331
``` |

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