{"id":853,"date":"2015-08-10T15:38:04","date_gmt":"2015-08-10T14:38:04","guid":{"rendered":"http:\/\/pcool.dyndns.org:8080\/statsbook\/?page_id=853"},"modified":"2025-07-04T13:53:23","modified_gmt":"2025-07-04T12:53:23","slug":"interclass-correlation-coefficient","status":"publish","type":"page","link":"https:\/\/pcool.dyndns.org\/index.php\/interclass-correlation-coefficient\/","title":{"rendered":"Interclass Correlation Coefficient"},"content":{"rendered":"\n<p>An alternative correlation statistic is the Intraclass Correlation Coefficient (ICC). This is commonly used to compare observers (for inter-observer correlation\/reliability) or sets of measurements for one observer (for intra-observer correlation\/reliability). Suppose that an observer makes a series of measurements on MRI scans. He or she then repeats the measurement after a period of time and we want to quantify the intra-observer reliability. The data set <a href=\"https:\/\/pcool.dyndns.org:\/wp-content\/data_files\/MRI.rda\" target=\"_blank\" rel=\"noreferrer noopener\">MRI.rda<\/a> contains 62 measurement pairs. Load it into the Data Viewer to proceed.<\/p>\n\n\n\n<p>A Pearson&#8217;s correlation coefficient can be calculated <a href=\"https:\/\/pcool.dyndns.org\/index.php\/correlation-coefficient\/\" data-type=\"page\" data-id=\"823\">as described<\/a>:<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><span style=\"color: #ff0000;\"><em>cor(MRI$FirstMeasurement,MRI$SecondMeasurement,method='pearson')<\/em><\/span>\n<span style=\"color: #ff0000;\"><em><span style=\"color: #0000ff;\">&#091;1] 0.9962104<\/span><\/em><\/span><\/code><\/pre>\n\n\n\n<p>For the ICC, the package &#8220;irr&#8221;<sup class='sup-ref-note' id='note-zotero-ref-p853-r1-o1'><a class='sup-ref-note' href='#zotero-ref-p853-r1'>1<\/a><\/sup> should be <a href=\"https:\/\/pcool.dyndns.org\/index.php\/packages\/\" data-type=\"page\" data-id=\"22\">installed<\/a>:<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><span style=\"color: #ff0000;\"><em>library(irr)<\/em><\/span><\/code><\/pre>\n\n\n\n<p>And call the icc funtion to calculate the ICC:<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><span style=\"color: #ff0000;\"><em>icc(MRI,model=\"twoway\",type=\"agreement\")<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0Single Score Intraclass Correlation<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0 Model: twoway <\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0 Type : agreement <\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0 Subjects = 60 <\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0\u00a0\u00a0 Raters = 2 <\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0<strong>\u00a0 ICC(A,1) = 0.996<\/strong><\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0F-Test, H0: r0 = 0 ; H1: r0 > 0 <\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0F(59,54.9) = 525 ,<strong> p = 1.93e-60<\/strong> <\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a095%-Confidence Interval for ICC Population Values:<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0 0.993 &lt; ICC &lt; 0.998<\/em><\/span><\/code><\/pre>\n\n\n\n<p>The interclass correlation coefficient is 99.6% and the p-value for the test of no association is significant, confirming there is an association.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An alternative correlation statistic is the Intraclass Correlation Coefficient (ICC). This is commonly used to compare observers (for inter-observer correlation\/reliability) or sets of measurements for one observer (for intra-observer correlation\/reliability). Suppose that an observer makes a series of measurements on MRI scans. He or she then repeats the measurement after a period of time and [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-853","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/853","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/comments?post=853"}],"version-history":[{"count":3,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/853\/revisions"}],"predecessor-version":[{"id":4903,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/853\/revisions\/4903"}],"wp:attachment":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/media?parent=853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}