Multiple variables Bootstrap Example 2: Difference between two population means

See also: The Bootstrap, Analyzing and using data introduction, The parametric Bootstrap, The non-parametric Bootstrap, VoseNBoot,

We offer two models to analyse the difference between two means. The first model considers random samples for two populations and analyses what we can infer about the difference between their means. The second model considers before and after effects of some experiment, to analyse the mean effect.

Model 1: Difference between two population means

If the two populations are randomly sampled, we simply estimate the mean of each population separately, and then create a model that randomly draws from the uniform distribution for each mean, and subtracts one from the other to give us our uncertainty about the difference between the means.

Model 2: Difference between two population means

Consider an experiment where individuals are randomly selected in some fashion (human volunteers or captured animals, for example), and some experiment is performed (e.g. administer a drug and look at the concentration of some compound before Bi and some time after Ai the drug administration for each of the n individuals. The random variable is the individuals selected, so in a non-parametric Bootstrap we need to randomise that selection process, but keep the paired nature of the observations. We could create Bootstrap replicates {Bi*,Ai*} for each of the n individuals, but that is simply equivalent to Bootstrapping the difference { Bi*-Ai* }, so this is in fact a univariate non-parametric analysis.

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