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On the History of the Correction for Grouping, 1873–1922

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  • Anders Hald

Abstract

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.

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  • Anders Hald, 2001. "On the History of the Correction for Grouping, 1873–1922," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 417-428, September.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:3:p:417-428
    DOI: 10.1111/1467-9469.00245
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    Cited by:

    1. Gunnar Taraldsen, 2011. "Analysis of rounded exponential data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 977-986, February.
    2. Dharmasena, Senarath & Bessler, David & Capps, Oral. Jr, 2016. "On the Evaluation of Probability Forecasts: An Application to Qualitative Choice Models," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235424, Agricultural and Applied Economics Association.

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