RCB experiment of rice, 12 varieties with leafhopper survival

data("gomez.nonnormal3")

Format

A data frame with 36 observations on the following 3 variables.

gen: genotype/variety of rice
rep: replicate
hoppers: percentage of surviving leafhoppers

Details

For each rice variety, 75 leafhoppers were caged and the percentage of surviving insects was determined.

Gomez suggest replacing 0 values by 1/(4*75) and replacing 100 by 1-1/(4*75) where 75 is the number of insects.

In effect, this means, for example, that (1/4)th of an insect survived.

Because the data are percents, Gomez suggested using the arcsin transformation.

Source

Gomez, K.A. and Gomez, A.A.. 1984, Statistical Procedures for Agricultural Research. Wiley-Interscience. Page 307.

Used with permission of Kwanchai Gomez.

References

None.

Examples


library(agridat)
data(gomez.nonnormal3)
dat <- gomez.nonnormal3

# First, replace 0, 100 values
dat$thoppers <- dat$hoppers
dat <- transform(dat, thoppers=ifelse(thoppers==0, 1/(4*75), thoppers))
dat <- transform(dat, thoppers=ifelse(thoppers==100, 100-1/(4*75), thoppers))
# Arcsin transformation of percentage p converted to degrees
# is arcsin(sqrt(p))/(pi/2)*90
dat <- transform(dat, thoppers=asin(sqrt(thoppers/100))/(pi/2)*90)

# QQ plots for raw/transformed data
libs(reshape2, lattice)
qqmath( ~ value|variable, data=melt(dat),
       main="gomez.nonnormal3 - raw/transformed QQ plot",
       scales=list(relation="free"))
#> Using gen, rep as id variables

m1 <- lm(thoppers ~ gen, data=dat)
anova(m1) # Match Gomez table 7.25
#> Analysis of Variance Table
#> 
#> Response: thoppers
#>           Df  Sum Sq Mean Sq F value    Pr(>F)    
#> gen       11 16838.7 1530.79  16.502 1.316e-08 ***
#> Residuals 24  2226.4   92.77                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Response: thoppers
##           Df  Sum Sq Mean Sq F value    Pr(>F)    
## gen       11 16838.7 1530.79  16.502 1.316e-08 ***
## Residuals 24  2226.4   92.77