implant=c(231,308287,33291,124550,17075,22955,95102,5649,840585,58924)
control=c(35324,12457,8276,44,278,840)

interleukin.6=c(implant,control)
group=c(rep("implant",length(implant)),rep("control",length(control)))

boxplot(interleukin.6~group)
library(lattice)
dotplot(interleukin.6~group)

# looks highly skewed to the right; normality not a good assumption
# also samples sizes too small to use t-test anyway (CLT)

# one solution is to try to *transform* the data so they 
# are approximately normal.
# common transformations: log(x), sqrt(x), 1/x

# is log-transformed data approximately normal?
boxplot(log(interleukin.6)~group)
dotplot(log(interleukin.6)~group)

# is log-transformed data approximately normal?
shapiro.test(log(interleukin.6[group=="implant"]))
shapiro.test(log(interleukin.6[group=="control"]))

# looks good!  a t-test on the log-transformed values is OK!
t.test(log(interleukin.6)~group)

# how about a permutation test?  Like MWW, it's *always* valid

library(DAAG)
twot.permutation(interleukin.6[group=="implant"],interleukin.6[group=="control"])
twot.permutation(log(interleukin.6[group=="implant"]),log(interleukin.6[group=="control"]))

# note that transforming data can make comparing means easier!

# What happens if we transform data and use MWW?

wilcox.test(interleukin.6[group=="implant"],interleukin.6[group=="control"])
wilcox.test(log(interleukin.6[group=="implant"]),log(interleukin.6[group=="control"]))

# Why does this happen???