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    Rights statement: This is the peer reviewed version of the following article: Liu, W., Han, Y., Bretz, F., Wan, F. and Yang, P. (2016), Counting by weighing: know your numbers with confidence. Journal of the Royal Statistical Society: Series C (Applied Statistics), 65: 641–648. doi: 10.1111/rssc.12142 which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/rssc.12142/abstract This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

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Counting by weighing: know your numbers with confidence

Research output: Contribution to journalJournal articlepeer-review

Published
  • Wei Liu
  • Yang Han
  • Frank Bretz
  • Fang Wan
  • Ping Yang
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<mark>Journal publication date</mark>08/2016
<mark>Journal</mark>Journal of the Royal Statistical Society: Series C (Applied Statistics)
Issue number4
Volume65
Number of pages8
Pages (from-to)641-648
Publication StatusPublished
Early online date1/03/16
<mark>Original language</mark>English

Abstract

Counting by weighing is often more efficient than counting manually, which is time consuming and prone to human errors, especially when the number of items (e.g. plant seeds, printed labels or coins) is large. Papers in the statistical literature have focused on how to count, by weighing, a random number of items that is close to a prespecified number in some sense. The paper considers the new problem, arising from a consultation with a company, of making inference about the number of 1p coins in a bag with known weight for infinitely many bags, by using the estimated distribution of coin weight from one calibration data set only. Specifically, a lower confidence bound has been constructed on the number of 1p coins for each of infinitely many future bags of 1p coins, as required by the company. As the same calibration data set is used repeatedly in the construction of all these lower confidence bounds, the interpretation of coverage frequency of the lower confidence bounds that is proposed is different from that of a usual confidence set.

Bibliographic note

This is the peer reviewed version of the following article: Liu, W., Han, Y., Bretz, F., Wan, F. and Yang, P. (2016), Counting by weighing: know your numbers with confidence. Journal of the Royal Statistical Society: Series C (Applied Statistics), 65: 641–648. doi: 10.1111/rssc.12142 which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/rssc.12142/abstract This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.