As a teeny-tiny follow-up to the previous post I realised boot-strapping is also a great way to compare the power of statisitical tests. It is generally accepted that Mood’s Median is lower power than Mann-Whitney-Wilcoxon, but you can demonstrate this quite easily with boot-strapping.

First of all, we need to define a Mood’s Median test in R:

```
#This matches Minitab's definition (which might not be the best idea, but...)
minitab.moods.median.test <- function(x,y){
z <- c(x,y)
g <- rep(1:2, c(length(x),length(y)))
m <- median(z)
chisq.test(z<=m,g, correct=FALSE)
}
```

*The above was inspired by this implementation, which is wrong as far as the definition on Wikipedia goes (and also how Minitab does things). However, I appreciate that any person picked at random from the R mailing list is likely to know more about statistics than I do and hence that approach is proabably still valid*.

We can then define separate power functions for each test. Running these with the same data as last time shows that the Mood’s Median test needs ~43 sample points to get 80% power, whereas the Wilcoxon only needs 24 points.