Question: Reanalysis of insecticide data.

See background attachment and insect data attachment

Instead of using the survival time Yijk (in hours,

divided by 10), use the reciprocal rate Rijk = 1=Yijk. Obviously, higher \death

rates" are better.

(a) Obtain an interaction plot; are the mean profiles approximately parallel?

(b) Fit the model with main effects and interaction; formally test that the interaction is zero at the 10% level.

(c) Fit the additive model. Obtain Tukey 95% CI's for comparing the three doses with an overall FER· 0:05.

(i) Are there significant differences in death rates across doses?

(ii)Are there significant differences among insecticide types? (iii)Group the insecticides according to the results of the pairwise comparisons. Are there pairs that are not significantly different?

(iv) Which insecticide has the best “death rate?"

(d) Check the additive modeling assumptions:

(i) look at the residuals rijk versus fitted values E(Rijk);

(ii) Print histogram of the residuals rijk and comment

(c) Comment on the spread of the residuals versus both type and dose. The R code for these might look something like:

d=read.table("http://www.biostat.umn.edu/~hanson/FundBiostat/insect.txt",header=F)

dose=factor(d[,1]); type=factor(d[,2]); time=d[,3]; rate=1/time

fit=aov(rate~dose+type+dose*type); summary(fit)

interaction.plot(rate,dose,type)

fit=aov(rate~dose+type); summary(fit)

TukeyHSD(fit)

plot(fit$fit,fit$res)

hist(fit$res)

plot(type,fit$res)

plot(dose,fit$res)