Multi-environment trial of barley — student.barley • agridat

Yield for two varieties of barley grown at 51 locations in the years 1901 to 1906.

Format

A data frame with 102 observations on the following 7 variables.

year: year, 1901-1906
farmer: farmer name
place: place (nearest town)
district: district, geographical area
gen: genotype, Archer and Goldthorpe
yield: yield, 'stones' per acre (1 stone = 14 pounds)
income: income per acre in shillings, based on yield and quality

Details

Experiments were conducted for six years by the Department of Agriculture in Ireland. A total of seven varieties were tested, but only Archer and Goldthorpe were tested in all six years (others were dropped after being found inferior, or were added later). Plots were two acres in size. The value of the grain depended on the yield and quality. Quality varied much from farm to farm, but not so much within the same farm.

The phrase "analysis of variance" first appears in the abstract (only) of a 1918 paper by Fisher. The 1923 paper by Student contained the first analysis of variance table (but not for this data).

One stone is 14 pounds. To convert lb/ac to tonnes/ha, multiply by 0.00112085116

Note: The analysis of Student cannot be reproduced exactly. For example, Student states that the maximum income of Goldthorpe is 230 shillings. A quick glance at Table I of Student shows that the maximum income for Goldthorpe is 220 shillings (11 pounds, 0 shillings) in 1901 at Thurles. Also, the results of Kempton could not be reproduced exactly, perhaps due to rounding or the conversion factor that was used.

Source

Student. 1923. On Testing Varieties of Cereals. Biometrika, 15, 271--293. https://doi.org/10.1093/biomet/15.3-4.271

References

R A Kempton and P N Fox, 1997. Statistical Methods for Plant Variety Evaluation.

Examples

# \dontrun{
  
  library(agridat)
  data(student.barley)
  dat <- student.barley

  libs(lattice)
  bwplot(yield ~ gen|district, dat, main="student.barley - yield")

  dat$year <- factor(dat$year)
  dat$income <- NULL
  
  # convert to tons/ha
  dat <- transform(dat, yield=yield*14 * 0.00112085116)
  
  # Define 'loc' the way that Kempton does
  dat$loc <- rep("",nrow(dat))
  dat[is.element(dat$farmer, c("Allardyce","Roche","Quinn")),"loc"] <- "1"
  dat[is.element(dat$farmer, c("Luttrell","Dooley")), "loc"] <- "2"
  dat[is.element(dat$year, c("1904","1905","1906")) & dat$farmer=="Kearney","loc"] <- "2"
  dat[dat$farmer=="Mulhall","loc"] <- "3"
  
  dat <- transform(dat, loc=factor(paste(place,loc,sep="")))
  
  libs(reshape2)
  datm <- melt(dat, measure.var='yield')

  # Kempton Table 9.5
  round(acast(datm, loc+gen~year),2)
#>                          1901 1902 1903 1904 1905 1906
#> Arnestown_Archer           NA   NA 1.33   NA   NA   NA
#> Arnestown_Goldthorpe       NA   NA 1.93   NA   NA   NA
#> Bagnalstown_Archer         NA   NA   NA   NA   NA 3.83
#> Bagnalstown_Goldthorpe     NA   NA   NA   NA   NA 3.48
#> Ballinacurra_Archer      2.82 3.11 1.66 2.57 3.14 2.48
#> Ballinacurra_Goldthorpe  1.76 2.98 1.82 2.98 3.28 2.43
#> Birr_Archer                NA 3.11 2.46 2.81 3.69 2.75
#> Birr_Goldthorpe            NA 2.31 2.01 2.98 3.39 2.50
#> Carlingford1_Archer        NA   NA 2.95   NA   NA   NA
#> Carlingford1_Goldthorpe    NA   NA 2.31   NA   NA   NA
#> Carlingford2_Archer        NA   NA   NA 2.01 3.61 2.93
#> Carlingford2_Goldthorpe    NA   NA   NA 2.37 2.82 3.20
#> Castlebridge_Archer        NA 2.81 3.12 2.29 2.86 2.92
#> Castlebridge_Goldthorpe    NA 2.82 2.50 1.57 2.86 2.65
#> Dunleer_Archer             NA   NA   NA 3.03 3.62 3.61
#> Dunleer_Goldthorpe         NA   NA   NA 2.87 3.14 3.36
#> Enniscorthy_Archer         NA 2.84   NA   NA   NA   NA
#> Enniscorthy_Goldthorpe     NA 2.98   NA   NA   NA   NA
#> Greenore_Archer            NA   NA 2.81   NA   NA   NA
#> Greenore_Goldthorpe        NA   NA 1.96   NA   NA   NA
#> Monasterevan1_Archer       NA   NA   NA 2.62   NA   NA
#> Monasterevan1_Goldthorpe   NA   NA   NA 2.59   NA   NA
#> Monasterevan2_Archer       NA   NA   NA   NA 3.64 2.42
#> Monasterevan2_Goldthorpe   NA   NA   NA   NA 3.22 2.65
#> Monasterevan3_Archer       NA   NA   NA   NA   NA 3.14
#> Monasterevan3_Goldthorpe   NA   NA   NA   NA   NA 3.48
#> Nenagh_Archer            2.76 3.04 2.04 3.31 3.61 2.95
#> Nenagh_Goldthorpe        2.51 3.36 2.12 2.89 3.92 2.21
#> NewRoss1_Archer            NA   NA   NA 2.04   NA   NA
#> NewRoss1_Goldthorpe        NA   NA   NA 1.76   NA   NA
#> NewRoss2_Archer            NA   NA   NA   NA 3.26 3.56
#> NewRoss2_Goldthorpe        NA   NA   NA   NA 3.42 3.09
#> Portarlington_Archer       NA   NA   NA 3.03 3.03   NA
#> Portarlington_Goldthorpe   NA   NA   NA 2.81 2.64   NA
#> Thurles_Archer           3.80   NA   NA   NA   NA   NA
#> Thurles_Goldthorpe       3.48   NA   NA   NA   NA   NA
#> Tullamore_Archer           NA   NA   NA   NA 3.45 2.23
#> Tullamore_Goldthorpe       NA   NA   NA   NA 2.67 2.18
#> Whitegate_Archer         2.56 3.51 2.20 2.68 2.93 2.65
#> Whitegate_Goldthorpe     1.95 3.26 1.84 2.57 2.84 2.23

  # Kempton Table 9.6
  d2 <- dcast(datm, year+loc~gen)
  mean(d2$Archer)
#> [1] 2.895005
  mean(d2$Goldthorpe)
#> [1] 2.685164
  mean(d2$Archer-d2$Goldthorpe)
#> [1] 0.2098409
  sqrt(var(d2$Archer-d2$Goldthorpe)/51)
#> [1] 0.05336873
  cor(d2$Archer,d2$Goldthorpe)
#> [1] 0.7652551


if(0){
  # Kempton Table 9.6b
  libs(lme4)
  m2 <- lmer(yield~1 + (1|loc) + (1|year) +
               (1|loc:year) + (1|gen:loc) + (1|gen:year), data=dat,
             control=lmerControl(check.nobs.vs.rankZ="ignore"))
}

# }