agridat (version 1.16)

mcconway.turnip: Yields of turnips grown for winter fodder

Description

Yields of turnips grown for winter fodder with two treatments for planting date and density, planted as RCB.

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.

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.

Examples

# NOT RUN {
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
if(require("HH")){
  interaction2wt(yield ~ gen + date + densf +block, dat,
                 x.between=0, y.between=0,
                 main="mcconway.turnip - yield")
}

require(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)

# }