RCB experiment of turnips
RCB experiment of turnips, 2 treatments for planting date and density
A data frame with 64 observations on the following 6 variables.
gengenotype
dateplanting date, levels 21Aug1990 28Aug1990
densityplanting density, 1, 2, 4, 8 kg/ha
blockblock, 4 levels
yieldyield
This is a randomized block experiment with 16 treatments allocated at random to each of four blocks. The 16 treatments were combinations of two varieties, two planting dates, and four densities.
Lee et al (2008) proposed an analysis using mixed models with changing treatment variances.
Piepho (2009) proposed an ordinary ANOVA using transformed data.
Used with permission of Kevin McConway.
K. J. McConway, M. C. Jones, P. C. Taylor. Statistical Modelling Using Genstat.
Michael Berthold, D. J. Hand. Intelligent data analysis: an introduction, 1998. Pages 75–82.
Lee, C.J. and O Donnell, M. and O Neill, M. (2008). Statistical analysis of field trials with changing treatment variance. Agronomy Journal, 100, 484–489.
Piepho, H.P. (2009), Data transformation in statistical analysis of field trials with changing treatment variance. Agronomy Journal, 101, 865–869. https://doi.org/10.2134/agronj2008.0226x
## Not run:
library(agridat)
data(mcconway.turnip)
dat <- mcconway.turnip
dat$densf <- factor(dat$density)
# Table 2 of Lee et al.
m0 <- aov( yield ~ gen * densf * date + block, dat )
summary(m0)
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 1 84.0 83.95 8.753 0.00491 **
## densf 3 470.4 156.79 16.347 2.51e-07 ***
## date 1 233.7 233.71 24.367 1.14e-05 ***
## block 3 163.7 54.58 5.690 0.00216 **
## gen:densf 3 8.6 2.88 0.301 0.82485
## gen:date 1 36.5 36.45 3.800 0.05749 .
## densf:date 3 154.8 51.60 5.380 0.00299 **
## gen:densf:date 3 18.0 6.00 0.626 0.60224
## Residuals 45 431.6 9.59
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Boxplots suggest heteroskedasticity for date, density
libs("HH")
interaction2wt(yield ~ gen + date + densf +block, dat,
x.between=0, y.between=0,
main="mcconway.turnip - yield")
libs(nlme)
# Random block model
m1 <- lme(yield ~ gen * date * densf, random= ~1|block, data=dat)
summary(m1)
anova(m1)
# Multiplicative variance model over densities and dates
m2 <- update(m1,
weights=varComb(varIdent(form=~1|densf),
varIdent(form=~1|date)))
summary(m2)
anova(m2)
# Unstructured variance model over densities and dates
m3 <- update(m1, weights=varIdent(form=~1|densf*date))
summary(m3)
anova(m3)
# Table 3 of Piepho, using transformation
m4 <- aov( yield^.235 ~ gen * date * densf + block, dat )
summary(m4)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.