# Exercise 38

## Parallel bootstrap

As we saw in Assignment 4, we can use random resampling with replacement to simulate drawing samples from a population, and then we can quantitatively assess the probability of the null hypothesis.

Assume we have the following sample of data, x:

3 5 4 3 6 7 -1 2 -3 -4 2 -5 3 2 -1


and a second sample, y:

2 7 4 7 6 9 -1 3 -2 -1 3 -1 2 4 2


The mean of the sample $$x$$ is 1.533 and the mean of sample $$y$$ is 2.933. Let's compute a statistic we'll call $$d_{samp}$$ which is the difference between means, $$\bar{y}-\bar{x}$$ which in this case is equal to $$d_{samp}=1.400$$.

The null hypothesis is that the samples were taken from a single population with the same mean, and so $$d_{pop}=0.00$$, and any departure from this in our sample statistic $$d_{samp}$$ is due to random sampling error.

Question 1

Use bootstrapping to compute the probability of the null hypothesis, with one million bootstrap (re)samples.

Question 2

Rewrite your solution to question 1, to parallelize the bootstrap. In other words execute the one million bootstrap iterations in parallel, with the work spread over your available compute cores.

Paul Gribble | fall 2014