, Volume 69, Issue 2, pp 175-183

Examples of non-normal observations for which a studentized sample mean has a student’s T-distribution

Purchase on Springer.com

$39.95 / €34.95 / £29.95*

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Summary

Statistical methodologies and their practice often rely upon tests and confidence interval procedures based on Studentized sample means of independent observations from a normal parent population and their Student’s t distributions. This is specially so when the sample size n is small. An unmistakable impression one is left with, whether implied or not, is that such exact Student’s t distributions may not be valid when the observations are dependent or non-normal. We show that one cannot discard the possibility of an exact Student’s t distribution for a Studentized sample mean, or its suitable multiple, simply because the observations may be dependent or non-normal. In arriving at this conclusion, we have uncovered a very interesting and seemingly unknown feature (Theorem 2.1) of an n-dimensional multivariate t distribution with equi-correlation p, arbitrary degree of freedom v, and arbitrary n.