IJPAM: Volume 21, No. 3 (2005)

THE VARIANCE OF SAMPLE VARIANCE FROM
A FINITE POPULATION

Eungchun Cho$^1$, Moon Jung Cho$^2$, John Eltinge$^3$
$^1$Department of Mathematics and Sciences
Kentucky State University
400, E. Main Street, Frankfort, KY 40601, USA
e-mail: eccho@gwmail.kysu.edu
$^{2,3}$Office of Survey Methods Research
Bureau of Labor Statistics
Washington, DC 20212, USA
$^2$e-mail: Cho.Moon@bls.gov
$^3$e-mail: Eltinge.John@bls.gov


Abstract.A formula for the variance of variance of all the samples taken from a finite population is given in terms of the second and the fourth moments of the population. Formulae for the variance of variance of the samples from a finite population of the discrete uniform and of the binomial distribution, and numerical values of those for the populations of uniform, binomial, normal, Poisson and hypergeometric distributions are given.

Received: May 10, 2005

AMS Subject Classification: 62D05, 62J10

Key Words and Phrases: variance of sample variance, variance estimator, sampling variance, randomization variance, moments

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 3