Bessel's Correction

Bessel's correction is the factor  in the relationship between the variance  and the expectation values of the sample variance,

(1)

where

(2)

As noted by Kenney and Keeping (1951, p. 161), the correction factor is probably more properly attributed to Gauss, who used it in this connection as early as 1823 (Gauss 1823).

For two samples,

(3)

(Kenney and Keeping 1951, p. 162).

REFERENCES:

Farebrother, R. W. Fitting Linear Relationships: A History of the Calculus of Observations 1750-1900. New York: Springer-Verlag, 1999.

Gauss, C. F. "Theoria combinationis obsevationum erroribus minimis obnoxiae." Werke, Vol. 4. Göttingen, Germany: p. 1, 1823.

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, 1951.