{"id":697,"date":"2019-07-11T17:03:07","date_gmt":"2019-07-11T16:03:07","guid":{"rendered":"http:\/\/35.193.178.118\/?page_id=697"},"modified":"2019-07-29T16:21:52","modified_gmt":"2019-07-29T15:21:52","slug":"introduction-to-sensitivity-coefficients","status":"publish","type":"page","link":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/","title":{"rendered":"Introduction to sensitivity coefficients"},"content":{"rendered":"\r\n<h2 class=\"wp-block-heading\">Introduction to sensitivity coefficients<\/h2>\r\n\r\n\r\n\r\n<p>Sensitivity coefficients provide a measure of how sensitive the measurand (<span class=\"katex-eq\" data-katex-display=\"false\">Y<\/span>) is to a change in given input quantity <span class=\"katex-eq\" data-katex-display=\"false\">(X_i)<\/span>.<\/p>\r\n\r\n\r\n\r\n<p>Simply put, a sensitivity coefficient answers the question: \u201c<em>How much does a change in this input quantity change the final measured value<\/em>\u201d?<\/p>\r\n\r\n\r\n\r\n<p>In the process of uncertainty evaluation, sensitivity coefficients are used to translate the standard uncertainty associated with a given effect, <span class=\"katex-eq\" data-katex-display=\"false\">u(x_i)<\/span>, into an uncertainty associated with the measurand. This is done by multiplying the standard uncertainty by the sensitivity coefficient. Note that the unit of a sensitivity coefficient is such that when the input quantity (with its associated unit) is multiplied by the sensitivity coefficient, then the result has the unit of the measurand. If the output quantity and the input quantity have the same unit, then the sensitivity coefficient will be dimensionless.<\/p>\r\n\r\n\r\n\r\n<p>There are three ways in which sensitivity coefficients can be determined:<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>Mathematically<\/li>\r\n<li>Numerically<\/li>\r\n<li>Experimentally<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>All three of these methods are equally valid and are all approved by the \u2018Guide to the Expression of Uncertainty in Measurement\u2019 (the GUM). Consequently, in a real-life uncertainty evaluation, it is possible that all three methods will be used. Each of these methods is examined in detail on the next page.<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Introduction to sensitivity coefficients Sensitivity coefficients provide a measure of how sensitive the measurand () is to a change in given input quantity . Simply put, a sensitivity coefficient answers&#8230;<a class=\"read-more\" href=\"&#104;&#116;&#116;&#112;&#115;&#58;&#47;&#47;&#114;&#101;&#115;&#101;&#97;&#114;&#99;&#104;&#46;&#114;&#101;&#97;&#100;&#105;&#110;&#103;&#46;&#97;&#99;&#46;&#117;&#107;&#47;&#102;&#105;&#100;&#117;&#99;&#101;&#111;&#47;&#97;&#114;&#99;&#104;&#105;&#118;&#101;&#47;&#116;&#117;&#116;&#111;&#114;&#105;&#97;&#108;&#115;&#47;&#115;&#101;&#110;&#115;&#105;&#116;&#105;&#118;&#105;&#116;&#121;&#45;&#99;&#111;&#101;&#102;&#102;&#105;&#99;&#105;&#101;&#110;&#116;&#115;&#45;&#101;&#114;&#114;&#111;&#114;&#115;&#45;&#97;&#110;&#100;&#45;&#117;&#110;&#99;&#101;&#114;&#116;&#97;&#105;&#110;&#116;&#121;&#47;&#105;&#110;&#116;&#114;&#111;&#100;&#117;&#99;&#116;&#105;&#111;&#110;&#45;&#116;&#111;&#45;&#115;&#101;&#110;&#115;&#105;&#116;&#105;&#118;&#105;&#116;&#121;&#45;&#99;&#111;&#101;&#102;&#102;&#105;&#99;&#105;&#101;&#110;&#116;&#115;&#47;\">Read More ><\/a><\/p>\n","protected":false},"author":219,"featured_media":0,"parent":689,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"__cvm_playback_settings":[],"__cvm_video_id":"","footnotes":""},"coauthors":[6],"class_list":["post-697","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.8.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Introduction to sensitivity coefficients - Fiduceo<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Introduction to sensitivity coefficients - Fiduceo\" \/>\n<meta property=\"og:description\" content=\"Introduction to sensitivity coefficients Sensitivity coefficients provide a measure of how sensitive the measurand () is to a change in given input quantity . Simply put, a sensitivity coefficient answers...Read More &gt;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/\" \/>\n<meta property=\"og:site_name\" content=\"Fiduceo\" \/>\n<meta property=\"article:modified_time\" content=\"2019-07-29T15:21:52+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/\",\"url\":\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/\",\"name\":\"Introduction to sensitivity coefficients - Fiduceo\",\"isPartOf\":{\"@id\":\"https:\/\/research.reading.ac.uk\/fiduceo\/#website\"},\"datePublished\":\"2019-07-11T16:03:07+00:00\",\"dateModified\":\"2019-07-29T15:21:52+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/#breadcrumb\"},\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/research.reading.ac.uk\/fiduceo\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Archive\",\"item\":\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Tutorials\",\"item\":\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Sensitivity coefficients, errors and uncertainty\",\"item\":\"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/\"},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"Introduction to sensitivity coefficients\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/research.reading.ac.uk\/fiduceo\/#website\",\"url\":\"https:\/\/research.reading.ac.uk\/fiduceo\/\",\"name\":\"Fiduceo\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/research.reading.ac.uk\/fiduceo\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-GB\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Introduction to sensitivity coefficients - Fiduceo","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/","og_locale":"en_GB","og_type":"article","og_title":"Introduction to sensitivity coefficients - Fiduceo","og_description":"Introduction to sensitivity coefficients Sensitivity coefficients provide a measure of how sensitive the measurand () is to a change in given input quantity . Simply put, a sensitivity coefficient answers...Read More >","og_url":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/","og_site_name":"Fiduceo","article_modified_time":"2019-07-29T15:21:52+00:00","twitter_card":"summary_large_image","twitter_misc":{"Estimated reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/","url":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/","name":"Introduction to sensitivity coefficients - Fiduceo","isPartOf":{"@id":"https:\/\/research.reading.ac.uk\/fiduceo\/#website"},"datePublished":"2019-07-11T16:03:07+00:00","dateModified":"2019-07-29T15:21:52+00:00","breadcrumb":{"@id":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/introduction-to-sensitivity-coefficients\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/research.reading.ac.uk\/fiduceo\/"},{"@type":"ListItem","position":2,"name":"Archive","item":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/"},{"@type":"ListItem","position":3,"name":"Tutorials","item":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/"},{"@type":"ListItem","position":4,"name":"Sensitivity coefficients, errors and uncertainty","item":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/"},{"@type":"ListItem","position":5,"name":"Introduction to sensitivity coefficients"}]},{"@type":"WebSite","@id":"https:\/\/research.reading.ac.uk\/fiduceo\/#website","url":"https:\/\/research.reading.ac.uk\/fiduceo\/","name":"Fiduceo","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/research.reading.ac.uk\/fiduceo\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-GB"}]}},"_links":{"self":[{"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/pages\/697","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/users\/219"}],"replies":[{"embeddable":true,"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/comments?post=697"}],"version-history":[{"count":1,"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/pages\/697\/revisions"}],"predecessor-version":[{"id":1358,"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/pages\/697\/revisions\/1358"}],"up":[{"embeddable":true,"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/pages\/689"}],"wp:attachment":[{"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/media?parent=697"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/research.reading.ac.uk\/fiduceo\/wp-json\/wp\/v2\/coauthors?post=697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}