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Media type:
E-Article
Title:
On the History of the Correction for Grouping, 1873-1922
Contributor:
Hald, Anders
Published:
Blackwell Publishers, 2001
Published in:
Scandinavian Journal of Statistics, 28 (2001) 3, Seite 417-428
Language:
English
ISSN:
1467-9469;
0303-6898
Origination:
Footnote:
Description:
The correction for grouping is a sum of two terms, the first depending on the length of the grouping interval, the second being a periodic function of the position. Thiele (1873) studied the second term, but missed the first. Sheppard (1898) studied the first term, but missed the second. Bruns (1906) derived the first term as the aperiodic term of a Fourier series and the second as the sum of the periodic terms. He found the correction to the coefficients of the Gram-Charlier series and proved that the second term is negligible for a grouped normal distribution with at least eight groups. Independently, Fisher (1922) used the same method to derive the correction to the moments. For the normal distribution with a grouping interval less than the standard deviation Fisher proved that the second term is negligible compared with the first and with the standard error of the first four moments. Moreover, he proved that the estimates of the mean and the standard deviation obtained by the method of moments for a grouped sample with Sheppard's corrections have nearly the same variances as the maximum likelihood estimates, thus providing a new and compelling reason for using Sheppard's corrections.