RCB experiment of turnips — mcconway.turnip • agridat

RCB experiment of turnips, 2 treatments for planting date and density

Format

A data frame with 64 observations on the following 6 variables.

gen: genotype
date: planting date, levels 21Aug1990 28Aug1990
density: planting density, 1, 2, 4, 8 kg/ha
block: block, 4 levels
yield: yield

Details

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.

Source

K. J. McConway, M. C. Jones, P. C. Taylor. Statistical Modelling Using Genstat.

References

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

Examples

if (FALSE) { # \dontrun{

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)

} # }