A Pedagogical Note on Asymptotic Normality of a Two-Sample Approximate Pivot for Comparing Means. Issue 1 (May 2021) - Mukhopadhyay, Nitis
A two-sample pivot for comparing the means from independent populations is well known. For large sample sizes, the distribution of the pivot is routinely approximated by a standard normal distribution. The question is about the thinking process that may guide one to rationalize invoking the asymptotic theory. In this pedagogical piece, we put forward soft statistical arguments to make users feel more at ease by suitably indexing the sample sizes from a practical standpoint that would allow a valid interpretation and understanding of pointwise convergence of the pivot's cumulative distribution function (c.d.f.) to the c.d.f. of a standard normal random variable.