I want to use bootstrap hypothesis testing to test if the mean of 1 distribution is greater than the other. With no other assumptions on the two distributions (e.g., they don't need to be gaussian).
I found this paragraph in the wikipedia article: https://en.wikipedia.org/wiki/Bootstrapping_(statistics)#Bootstrap_hypothesis_testing
I have two questions:
- Is the algorithm indicated in the link above testing for the hypothesis -- "the mean of X is greater than the mean of Y"? i.e., the null hypothesis being "the mean of X is not greater than the mean of Y". If it's not testing for this, how can we test for this?
- What is Step 2 doing?
I'm rather confused at this:
Create two new data sets whose values are: x_i^' = x_i - X + Z and y_i^' = y_i - Y + Z where Z is the mean of the combined sample.
At a high level, this seems to be "normalizing" samples with the joint mean. Why is this needed?