Maize yields for four cropping systems

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Description

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

Format

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

Details

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.

Source

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.

References

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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