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Chi-squared Test for Binned, Gaussian Samples

Hutzler, Nicholas R. (2019) Chi-squared Test for Binned, Gaussian Samples. Metrologia, 56 (5). Art. No. 055007. ISSN 0026-1394. doi:10.1088/1681-7575/ab2d53.

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We examine the χ^2 test for binned, Gaussian samples, including effects due to the fact that the experimentally available sample standard deviation and the unavailable true standard deviation have different statistical properties. For data formed by binning Gaussian samples with bin size n, we find that the expected value and standard deviation of the reduced χ^2 statistic is [(n-1)/(n-3) ± (n-1)/(n-3)√[(n-2)/(n-5)]√[2/(N-1)], where N is the total number of binned values. This is strictly larger in both mean and standard deviation than the value of 1 ± (2/(N-1))^(1/2) reported in standard treatments, which ignore the distinction between true and sample standard deviation.

Item Type:Article
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URLURL TypeDescription Paper
Hutzler, Nicholas R.0000-0002-5203-3635
Additional Information:© 2019 BIPM & IOP Publishing Ltd. Received 4 March 2019; Accepted 27 June 2019; Accepted Manuscript online 27 June 2019; Published 9 August 2019. I would like to acknowledge helpful discussions with David Watson, and many helpful discussions with the ACME Collaboration, in particular David DeMille, John M. Doyle, and Brendon O'Leary.
Issue or Number:5
Record Number:CaltechAUTHORS:20190801-134558586
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Official Citation:Nicholas R Hutzler 2019 Metrologia 56 055007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97606
Deposited By: George Porter
Deposited On:01 Aug 2019 21:29
Last Modified:12 Jul 2022 19:47

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