Standard error of the difference between means

Abstract

One of the two major types of hypothesis is one which is stated in difference terms, i.e. that there is a significant difference between two independent groups. This difference is essentially a difference between the two sample means. We want to know whether the difference between sample means is a real one or whether it could be reasonably attributed to chance, i.e. does the difference between the two sample means lie within the expected chance distribution of differences between the means of an infinite number of pairs of samples at some level of probability?