Uncertainty estimation with a small number of measurements, part I: new insights on the t-interval method and its limitations
The conventional approach to estimating measurement uncertainty employs the t-interval when the population standard deviation is unknown and the sample size is small (
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| Veröffentlicht in: | Measurement science & technology 2018-01, Vol.29 (1), p.15004 |
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| creator | Huang, Hening |
| description | The conventional approach to estimating measurement uncertainty employs the t-interval when the population standard deviation is unknown and the sample size is small ( |
| doi_str_mv | 10.1088/1361-6501/aa96c7 |
| format | Article |
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This is because the t-interval, or t-based uncertainty, is considered to be the 'exact' solution to estimating measurement uncertainty for small samples. However, three paradoxes have been found to be attributable to the t-interval. This paper is the first one (Part I) in a series of two papers (Part I and Part II). It presents some new insights on the t-interval and explores its true underlying meaning. This paper reveals that the t-interval is a result from a distorted statistical inference in the transformed sample space. The transformation distortion is the root cause of extremely high t-scores when the sample size is very small (<5), resulting in unrealistic estimates of uncertainty. This is the fundamental limitation of the t-interval method for uncertainty estimation. Part II will propose a redefinition of uncertainty and a modification of the conventional approach to estimating measurement uncertainty.</description><identifier>ISSN: 0957-0233</identifier><identifier>EISSN: 1361-6501</identifier><identifier>DOI: 10.1088/1361-6501/aa96c7</identifier><identifier>CODEN: MSTCEP</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>interval ; small samples ; transformation distortion ; uncertainty estimation</subject><ispartof>Measurement science & technology, 2018-01, Vol.29 (1), p.15004</ispartof><rights>2017 IOP Publishing Ltd</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c280t-825a3c32e595e95cfe9ae4afe921822ce00e1fd8c96e5d0c6cac18ee5c478d413</citedby><cites>FETCH-LOGICAL-c280t-825a3c32e595e95cfe9ae4afe921822ce00e1fd8c96e5d0c6cac18ee5c478d413</cites><orcidid>0000-0003-1882-0042</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1361-6501/aa96c7/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>314,776,780,27903,27904,53824,53871</link.rule.ids></links><search><creatorcontrib>Huang, Hening</creatorcontrib><title>Uncertainty estimation with a small number of measurements, part I: new insights on the t-interval method and its limitations</title><title>Measurement science & technology</title><addtitle>MST</addtitle><addtitle>Meas. Sci. Technol</addtitle><description>The conventional approach to estimating measurement uncertainty employs the t-interval when the population standard deviation is unknown and the sample size is small (<30). This is because the t-interval, or t-based uncertainty, is considered to be the 'exact' solution to estimating measurement uncertainty for small samples. However, three paradoxes have been found to be attributable to the t-interval. This paper is the first one (Part I) in a series of two papers (Part I and Part II). It presents some new insights on the t-interval and explores its true underlying meaning. This paper reveals that the t-interval is a result from a distorted statistical inference in the transformed sample space. The transformation distortion is the root cause of extremely high t-scores when the sample size is very small (<5), resulting in unrealistic estimates of uncertainty. This is the fundamental limitation of the t-interval method for uncertainty estimation. Part II will propose a redefinition of uncertainty and a modification of the conventional approach to estimating measurement uncertainty.</description><subject>interval</subject><subject>small samples</subject><subject>transformation distortion</subject><subject>uncertainty estimation</subject><issn>0957-0233</issn><issn>1361-6501</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kM1OwzAQhC0EEqVw5-gHaOg6qVObG6r4qVSJCz1Hi7MhrhKnsl2qHnh3XIq4cRppNd_s7jB2K-BOgFJTUZQiKyWIKaIuzfyMjf5G52wEWs4zyIvikl2FsAGAOWg9Yl9rZ8hHtC4eOIVoe4x2cHxvY8uRhx67jrtd_06eDw3vCcPOU08uhgnfoo98ec8d7bl1wX60MfAEx5Z4zFIk-U_sEhTboeboam6TobO9jT9bwjW7aLALdPOrY7Z-enxbvGSr1-fl4mGVmVxBzFQusTBFTlJL0tI0pJFmmCQXKs8NAZBoamV0SbIGUxo0QhFJM5ureiaKMYNTrvFDCJ6aauvTp_5QCaiO9VXHrqpjV9WpvoRMTogdttVm2HmXDvzf_g39GnRJ</recordid><startdate>20180101</startdate><enddate>20180101</enddate><creator>Huang, Hening</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-1882-0042</orcidid></search><sort><creationdate>20180101</creationdate><title>Uncertainty estimation with a small number of measurements, part I: new insights on the t-interval method and its limitations</title><author>Huang, Hening</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c280t-825a3c32e595e95cfe9ae4afe921822ce00e1fd8c96e5d0c6cac18ee5c478d413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>interval</topic><topic>small samples</topic><topic>transformation distortion</topic><topic>uncertainty estimation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huang, Hening</creatorcontrib><collection>CrossRef</collection><jtitle>Measurement science & technology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huang, Hening</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Uncertainty estimation with a small number of measurements, part I: new insights on the t-interval method and its limitations</atitle><jtitle>Measurement science & technology</jtitle><stitle>MST</stitle><addtitle>Meas. 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The transformation distortion is the root cause of extremely high t-scores when the sample size is very small (<5), resulting in unrealistic estimates of uncertainty. This is the fundamental limitation of the t-interval method for uncertainty estimation. Part II will propose a redefinition of uncertainty and a modification of the conventional approach to estimating measurement uncertainty.</abstract><pub>IOP Publishing</pub><doi>10.1088/1361-6501/aa96c7</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0003-1882-0042</orcidid></addata></record> |
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| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | interval small samples transformation distortion uncertainty estimation |
| title | Uncertainty estimation with a small number of measurements, part I: new insights on the t-interval method and its limitations |
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