mcconway.turnip {agridat} | R Documentation

## 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.

### Source

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

Used with permission of Kevin McConway.

### 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

    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)

[Package agridat version 1.16 Index]