Multi-environment trial of rice, split-plot design

Grain yield was measured at 3 locations with 2 reps per location. Within each rep, the main plot was 6 nitrogen fertilizer treatments and the sub plot was 2 rice varieties.

Format

A data frame with 108 observations on the following 5 variables.

loc: location, 3 levels
nitro: nitrogen in kg/ha
rep: replicate, 2 levels
gen: genotype, 2 levels
yield: yield, kg/ha

Source

Gomez, K.A. and Gomez, A.A.. 1984, Statistical Procedures for Agricultural Research. Wiley-Interscience. Page 339.

Used with permission of Kwanchai Gomez.

Examples


library(agridat)

data(gomez.multilocsplitplot)
dat <- gomez.multilocsplitplot
dat$nf <- factor(dat$nitro)

# Gomez figure 8.3
libs(lattice)
xyplot(yield~nitro, dat, group=loc, type=c('p','smooth'), auto.key=TRUE,
       main="gomez.multilocsplitplot")

# AOV
# Be careful to use the right stratum, 'nf' appears in both strata.
# Still not quite the same as Gomez table 8.21
t1 <- terms(yield ~ loc * nf * gen + Error(loc:rep:nf),
            "Error", keep.order=TRUE)
m1 <- aov(t1, data=dat)
#> Warning: Error() model is singular
summary(m1)
#> 
#> Error: loc:rep:nf
#>            Df    Sum Sq  Mean Sq
#> loc         2   4401065  2200532
#> nf          5 136849095 27369819
#> gen         1   2752683  2752683
#> loc:nf     10  18591666  1859167
#> loc:gen     2    258519   129260
#> nf:gen      5   1018467   203693
#> loc:nf:gen 10   6477080   647708
#> 
#> Error: Within
#>            Df   Sum Sq Mean Sq F value   Pr(>F)    
#> gen         1  7085791 7085791  18.326 7.67e-05 ***
#> loc:gen     2  5171261 2585630   6.687  0.00254 ** 
#> nf:gen      5  3034192  606838   1.569  0.18437    
#> loc:nf:gen 10  1487520  148752   0.385  0.94801    
#> Residuals  54 20879417  386656                     
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  # F values are somewhat similar to Gomez Table 8.21
  libs(lme4)
  m2 <- lmer(yield ~ loc*nf*gen + (1|loc/rep/nf), dat)
#> Warning: unable to evaluate scaled gradient
#> Warning:  Hessian is numerically singular: parameters are not uniquely determined
  anova(m2)
#> Analysis of Variance Table
#>            Df   Sum Sq  Mean Sq F value
#> loc         2   407688   203844  0.5271
#> nf          5 72885372 14577074 37.6944
#> gen         1  7558837  7558837 19.5462
#> loc:nf     10 10143064  1014306  2.6229
#> loc:gen     2  4268700  2134350  5.5191
#> nf:gen      5  1501333   300267  0.7765
#> loc:nf:gen 10  1503043   150304  0.3887
  ## Analysis of Variance Table
  ##            Df   Sum Sq  Mean Sq F value
  ## loc         2   117942    58971  0.1525
  ## nf          5 72841432 14568286 37.6777
  ## gen         1  7557570  7557570 19.5460
  ## loc:nf     10 10137188  1013719  2.6218
  ## loc:gen     2  4270469  2135235  5.5223
  ## nf:gen      5  1501767   300353  0.7768
  ## loc:nf:gen 10  1502273   150227  0.3885

Format

Source

Examples

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