A few years ago I ran a workshop where I showed how to carry out a simple (bilateral) permutation test in R. Assuming you have a matrix `d`

with two columns of values, and no missing values, it reads:

```
s0 <- mean(d[,1]) - mean(d[,2]) ## observed statistic
x <- c(d[,1], d[,2])
idx <- combn(seq(along = 1:20), 10) ## {20 \choose 10}
f <- function(k) mean(x[k]) - mean(x[-k])
s <- apply(idx, 2, f) ## test statistic s
pobs <- sum(abs(s) >= abs(s0)) / length(s)
```

Using the coin package the same test is done as follows:

```
library(coin)
oneway_test(value ~ variable, data = reshape2::melt(d[1:2]),
alternative = "two.sided", distribution = "exact")
```

I also showed how to devise a bootstrap test of hypothesis in R. This time, we need to take care of correctly centering the group means, though:

```
x1 <- d[,1] - mean(d[,1]) + mean(x) ## x is c(d[,1], d[,2])
x2 <- d[,2] - mean(d[,2]) + mean(x)
B <- 999 ## no. bootstrap samples
s <- numeric(B) ## vector of test statistics
for (i in 1:B) {
x1s <- sample(x1, replace=TRUE)
x2s <- sample(x2, replace=TRUE)
s[i] <- mean(x1s) - mean(x2s)
}
pobs <- (1 + sum(abs(s) > abs(s0))) / (B+1) ## s0 is mean(d[,1]) - mean(d[,2])
```

Note that the `for`

loop can easily be replaced with a function call in a `replicate`

statement, of course. Here is some results with the ToothGrowth dataset we discussed earlier, which can be prepared as follows:

```
> data(ToothGrowth)
> d <- as.data.frame(with(ToothGrowth, split(len, supp)))
> x <- ToothGrowth$len
> s0 <- mean(d[,1]) - mean(d[,2])
--8<-- copy/paste code above ---
> pobs
[1] 0.043
```

Of course, we could compute confidence normal, percentile or BCA confidence intervals, with little effort. Stata does it smoothly, as usual:

```
. use toothgrowth, clear
. bootstrap dobs = (r(mu_1) - r(mu_2)), reps(1000) seed(101): ttest len, by(supp)
. estat bootstrap, all
Bootstrap results Number of obs = 60
Replications = 1000
command: ttest len, by(supp)
diff: r(mu_1) - r(mu_2)
------------------------------------------------------------------------------
| Observed Bootstrap
| Coef. Bias Std. Err. [95% Conf. Interval]
-------------+----------------------------------------------------------------
diff | 3.7 .0643175 1.8568749 .0605921 7.339408 (N)
| -.0248661 7.282081 (P)
| -.178198 7.126667 (BC)
------------------------------------------------------------------------------
(N) normal confidence interval
(P) percentile confidence interval
(BC) bias-corrected confidence interval
```

You can download the dataset here.

♪ Three Days Grace • *I Hate Everything About You*