Multi-environment trial of oats in India

Multi-environment trial of oats in India, 13 genotypes, 3 year, 2 loc, 5 reps

data("shaw.oats")

Format

A data frame with 390 observations on the following 5 variables.

env: environment, 2 levels
year: year, 3 levels
block: block, 5 levels
gen: genotype variety, 13 levels
yield: yield of oats, pounds per plot

Details

An oat trial in India of 11 hybrid oats compared to 2 established high-yielding varieties, labeled L and M. The trail was conducted at 2 locations. The size and exact locations of the plots varied from year to year.

At Pusa, the crop was grown without irrigation. At Karnal the crop was given 2-3 irrigations. Five blocks were used, each plot 1000 square feet. In 1932, variety L was high-yielding at Pusa, but low-yielding at Karnal.

Shaw used this data to illustrate ANOVA for a multi-environment trial.

Source

F.J.F. Shaw (1936). A Handbook of Statistics For Use In Plant Breeding and Agricultural Problems. The Imperial Council of Agricultural Research, India. https://archive.org/details/HandbookStatistics1936/page/n12 P. 126

References

None

Examples


library(agridat)
data(shaw.oats)
dat <- shaw.oats
# sum(dat$yield) # 16309 matches Shaw p. 125
# sum( (dat$yield-mean(dat$yield)) ^2) # total SS matches Shaw p. 141

dat$year <- factor(dat$year)
libs(lattice)

dotplot(yield ~ gen|env, data=dat, groups=year,
        main="shaw.oats",
        par.settings=list(superpose.symbol=list(pch=c('2','3','4'))),
        panel=function(x,y,...){
          panel.dotplot(x,y,...)
          panel.superpose(x,y,..., panel.groups=function(x,y,col.line,...) {
            dd<-aggregate(y~x,data.frame(x,y),mean)
            panel.xyplot(x=dd$x, y=dd$y, col=col.line, type="l")
          })},
        auto.key=TRUE)



# Shaw & Bose meticulously calculate the ANOVA table, p. 141
m1 <- aov(yield ~ year*env*block*gen - year:env:block:gen, dat)
anova(m1)
#> Analysis of Variance Table
#> 
#> Response: yield
#>                Df  Sum Sq Mean Sq  F value    Pr(>F)    
#> year            2 14475.3  7237.6 352.8158 < 2.2e-16 ***
#> env             1   345.4   345.4  16.8352 8.552e-05 ***
#> block           4   197.8    49.4   2.4102   0.05444 .  
#> gen            12 12297.2  1024.8  49.9546 < 2.2e-16 ***
#> year:env        2  5945.6  2972.8 144.9164 < 2.2e-16 ***
#> year:block      8  3175.2   396.9  19.3480 < 2.2e-16 ***
#> env:block       4   735.2   183.8   8.9601 3.422e-06 ***
#> year:gen       24  3839.0   160.0   7.7976 9.418e-14 ***
#> env:gen        12  1314.2   109.5   5.3386 7.617e-07 ***
#> block:gen      48  1112.5    23.2   1.1298   0.30246    
#> year:env:block  8  1012.6   126.6   6.1702 2.067e-06 ***
#> year:env:gen   24  3123.5   130.1   6.3442 2.344e-11 ***
#> year:block:gen 96  2241.1    23.3   1.1380   0.26386    
#> env:block:gen  48   897.2    18.7   0.9112   0.63336    
#> Residuals      96  1969.3    20.5                       
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1