Wireworms controlled by fumigants in a latin square

Format

A data frame with 25 observations on the following 4 variables.

row: row
col: column
trt: fumigant treatment, 5 levels
worms: count of wireworms per plot

Details

Plots were approximately 22 cm by 13 cm. Layout of the experiment was a latin square. The number of wireworms in each plot was counted, following soil fumigation the previous year.

Source

W. G. Cochran (1938). Some difficulties in the statistical analysis of replicated experiments. Empire Journal of Experimental Agriculture, 6, 157–175.

References

Ron Snee (1980). Graphical Display of Means. The American Statistician, 34, 195-199. https://www.jstor.org/stable/2684060 https://doi.org/10.1080/00031305.1980.10483028

W. Cochran (1940). The analysis of variance when experimental errors follow the Poisson or binomial laws. The Annals of Mathematical Statistics, 11, 335-347. https://www.jstor.org/stable/2235680

G W Snedecor and W G Cochran, 1980. Statistical Methods, Iowa State University Press. Page 288.

Examples

if (FALSE) { # \dontrun{

library(agridat)
data(cochran.wireworms)
dat <- cochran.wireworms

libs(desplot)
desplot(dat, worms ~ col*row,
        text=trt, cex=1, # aspect unknown
        main="cochran.wireworms")

# Trt K is effective, but not the others.  Really, this says it all.
libs(lattice)
bwplot(worms ~ trt, dat, main="cochran.wireworms", xlab="Treatment")

# Snedecor and Cochran do ANOVA on sqrt(x+1).
dat <- transform(dat, rowf=factor(row), colf=factor(col))
m1 <- aov(sqrt(worms+1) ~ rowf + colf + trt, data=dat)
anova(m1)

# Instead of transforming, use glm
m2 <- glm(worms ~ trt + rowf + colf, data=dat, family="poisson")
anova(m2)

# GLM with random blocking.
libs(lme4)
m3 <- glmer(worms ~ -1 +trt +(1|rowf) +(1|colf), data=dat, family="poisson")
summary(m3)
## Fixed effects:
##      Estimate Std. Error z value Pr(>|z|)    
## trtK   0.1393     0.4275   0.326    0.745    
## trtM   1.7814     0.2226   8.002 1.22e-15 ***
## trtN   1.9028     0.2142   8.881  < 2e-16 ***
## trtO   1.7147     0.2275   7.537 4.80e-14 ***

} # }