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

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

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.

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

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 | ```
data(student.barley)
dat <- student.barley
require(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$farmer=="Mulhall","loc"] <- "3"
dat <- transform(dat, loc=factor(paste(place,loc,sep="")))
if(require(reshape2)){
datm <- melt(dat, measure.var='yield')
# Kempton Table 9.5
round(acast(datm, loc+gen~year),2)
# Kempton Table 9.6
d2 <- dcast(datm, year+loc~gen)
mean(d2$Archer)
mean(d2$Goldthorpe)
mean(d2$Archer-d2$Goldthorpe)
sqrt(var(d2$Archer-d2$Goldthorpe)/51)
cor(d2$Archer,d2$Goldthorpe)
}
## Not run:
# Kempton Table 9.6b
require(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"))
## End(Not run)
``` |

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