Question

R probblem statistics

Suppose you have a data set that consists of 10 numerical observations from group A, and 10 numerical observations from group B. Suppose we also randomly permute the numerical observations, so that each observation is equally likely to appear in group A and in group B (as in a permutation test). Let X denote the mean of the values in group A, and Y denote the mean of the values in group B. Find E[X −Y ].

Answer 1

rm(list=ls())
groupA=c(43,89,71,49,58,62,73,84,80,49)

groupB=c(40,70,85,64,59,60,45,78,55,68)

#x denote mean of group A.
x=mean(groupA)

#y denote mean of group B.
y=mean(groupB)

z=mean(x-y)

so here each observation appear equally likely in group A and group B.That is as in a permutation test

OUTPUT:

> x
[1] 65.8
> y
[1] 62.4
> z
[1] 3.4