Strip-split-plot of barley with fertilizer, calcium, and soil factors.

Format

A data frame with 96 observations on the following 5 variables.

rep: replicate, 4 levels
soil: soil, 3 levels
fert: fertilizer, 4 levels
calcium: calcium, 2 levels
yield: yield of winter barley

Details

Four different fertilizer treatments are laid out in vertical strips, which are then split into subplots with different levels of calcium. Soil type is stripped across the split-plot experiment, and the entire experiment is then replicated three times.

Sometimes called a split-block design.

Source

Comes from the notes of Gertrude Cox and A. Rotti.

References

SAS/STAT(R) 9.2 User's Guide, Second Edition. Example 23.5 Strip-Split Plot. https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_anova_sect030.htm

Examples

# \dontrun{

library(agridat)
data(cox.stripsplit)
dat <- cox.stripsplit

# Raw means
# aggregate(yield ~ calcium, data=dat, mean)
# aggregate(yield ~ soil, data=dat, mean)
# aggregate(yield ~ calcium, data=dat, mean)

libs(HH)
#> Loading required package: multcomp
#> Loading required package: mvtnorm
#> Loading required package: TH.data
#> 
#> Attaching package: 'TH.data'
#> The following object is masked from 'package:MASS':
#> 
#>     geyser
#> Loading required package: gridExtra
#> 
#> Attaching package: 'gridExtra'
#> The following object is masked from 'package:dplyr':
#> 
#>     combine
#> 
#> Attaching package: 'HH'
#> The following object is masked from 'package:vcd':
#> 
#>     odds
#> The following objects are masked from 'package:car':
#> 
#>     logit, vif
interaction2wt(yield ~ rep + soil + fert + calcium, dat,
               x.between=0, y.between=0,
               main="cox.stripsplit")

# Traditional AOV
m1 <- aov(yield~ fert*calcium*soil +
          Error(rep/(fert+soil+calcium:fert+soil:fert)),
          data=dat)
summary(m1)
#> 
#> Error: rep
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> Residuals  3   6.28   2.093               
#> 
#> Error: rep:fert
#>           Df Sum Sq Mean Sq F value Pr(>F)  
#> fert       3  7.221  2.4071   3.562 0.0604 .
#> Residuals  9  6.082  0.6758                 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Error: rep:soil
#>           Df Sum Sq Mean Sq F value Pr(>F)  
#> soil       2  1.927  0.9633   3.466 0.0999 .
#> Residuals  6  1.668  0.2779                 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Error: rep:fert:calcium
#>              Df Sum Sq Mean Sq F value Pr(>F)  
#> calcium       1 0.2773  0.2773   1.883 0.1950  
#> fert:calcium  3 1.9640  0.6547   4.446 0.0255 *
#> Residuals    12 1.7671  0.1473                 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Error: rep:fert:soil
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> fert:soil  6 0.6883 0.11471   1.301  0.306
#> Residuals 18 1.5870 0.08817               
#> 
#> Error: Within
#>                   Df Sum Sq Mean Sq F value Pr(>F)
#> calcium:soil       2 0.0449 0.02247   0.245  0.784
#> fert:calcium:soil  6 0.1894 0.03156   0.345  0.906
#> Residuals         24 2.1962 0.09151               

# With balanced data, the following are all basically identical

libs(lme4)
# The 'rep:soil:fert' term causes problems...so we drop it.
m2 <- lmer(yield ~ fert*soil*calcium + (1|rep) + (1|rep:fert) +
             (1|rep:soil) + (1|rep:fert:calcium), data=dat)


if(0){
  # afex uses Kenword-Rogers approach for denominator d.f.
  libs(afex)
  mixed(yield ~ fert*soil*calcium + (1|rep) + (1|rep:fert) +
          (1|rep:soil) + (1|rep:fert:calcium) + (1|rep:soil:fert), data=dat,
        control=lmerControl(check.nobs.vs.rankZ="ignore"))
  ##              Effect      stat ndf     ddf F.scaling p.value
  ## 1       (Intercept) 1350.8113   1  3.0009         1  0.0000
  ## 2              fert    3.5619   3  9.0000         1  0.0604
  ## 3              soil    3.4659   2  6.0000         1  0.0999
  ## 4           calcium    1.8835   1 12.0000         1  0.1950
  ## 5         fert:soil    1.2735   6 18.0000         1  0.3179
  ## 6      fert:calcium    4.4457   3 12.0000         1  0.0255
  ## 7      soil:calcium    0.2494   2 24.0000         1  0.7813
  ## 8 fert:soil:calcium    0.3504   6 24.0000         1  0.9027
}

# }