{"id":325,"date":"2014-05-01T21:33:47","date_gmt":"2014-05-01T21:33:47","guid":{"rendered":"http:\/\/kourentzes.com\/forecasting\/?p=325"},"modified":"2014-05-01T21:57:44","modified_gmt":"2014-05-01T21:57:44","slug":"critical-values-for-the-nemenyi-test","status":"publish","type":"post","link":"https:\/\/kourentzes.com\/forecasting\/2014\/05\/01\/critical-values-for-the-nemenyi-test\/","title":{"rendered":"Critical values for the Nemenyi test"},"content":{"rendered":"<p>The critical distance for the Nemenyi test is calculated as:<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=r_%7B%5Calpha%2CK%2CN%7D+%5Capprox+q_%7B%5Calpha%2CK%7D%5Csqrt%7B%5Cfrac%7BK%28K%2B1%29%7D%7B6N%7D%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='r_{\\alpha,K,N} \\approx q_{\\alpha,K}\\sqrt{\\frac{K(K+1)}{6N}}' title='r_{\\alpha,K,N} \\approx q_{\\alpha,K}\\sqrt{\\frac{K(K+1)}{6N}}' class='latex' \/>,<\/p>\n<p style=\"text-align: justify;\">where <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Calpha&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\alpha' title='\\alpha' class='latex' \/> is the confidence level, <img src='https:\/\/s0.wp.com\/latex.php?latex=K&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='K' title='K' class='latex' \/> is the number of models and <img src='https:\/\/s0.wp.com\/latex.php?latex=N&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='N' title='N' class='latex' \/> is the number of measurements. To calculate <img src='https:\/\/s0.wp.com\/latex.php?latex=q_%7B%5Calpha%2CK%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='q_{\\alpha,K}' title='q_{\\alpha,K}' class='latex' \/> the Studentised range statistic for infinite degrees of freedom divided by <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Csqrt%7B2%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\sqrt{2}' title='\\sqrt{2}' class='latex' \/> is used. The values of <img src='https:\/\/s0.wp.com\/latex.php?latex=q_%7B%5Calpha%2CK%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='q_{\\alpha,K}' title='q_{\\alpha,K}' class='latex' \/> for up to <img src='https:\/\/s0.wp.com\/latex.php?latex=K%3D100&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='K=100' title='K=100' class='latex' \/> can be download <a href=\"http:\/\/kourentzes.com\/forecasting\/wp-content\/uploads\/2014\/05\/nemenyi.csv\">here as csv<\/a>.<\/p>\n<p style=\"text-align: justify;\">You may also be interested in the implementations of the Nemenyi test in <a title=\"ANOM and Nemenyi tests\" href=\"http:\/\/kourentzes.com\/forecasting\/2013\/04\/19\/nemenyi-test\/\">MatLab<\/a> and <a title=\"TStools for R\" href=\"http:\/\/kourentzes.com\/forecasting\/2014\/04\/19\/tstools-for-r\/\">R<\/a>, or a <a title=\"Statistical Significance of Forecasting Methods \u2013 an empirical evaluation of the robustness and interpretability of the MCB, ANOM and Friedman-Nemenyi Test\" href=\"http:\/\/kourentzes.com\/forecasting\/2012\/04\/19\/statistical-significance-of-forecasting-methods-an-empirical-evaluation-of-the-robustness-and-interpretability-of-the-mcb-anom-and-friedman-nemenyi-test\/\">discussion<\/a> on how to best visualise its results and its connection with the MCB test.<\/p>\n<div class=\"SPOSTARBUST-Related-Posts\"><H3>Related Posts<\/H3><ul class=\"entry-meta\"><li class=\"SPOSTARBUST-Related-Post\"><a title=\"Tutorial for the nnfor R package\" href=\"https:\/\/kourentzes.com\/forecasting\/2019\/01\/16\/tutorial-for-the-nnfor-r-package\/\" rel=\"bookmark\">Tutorial for the nnfor R package<\/a><\/li>\n<li class=\"SPOSTARBUST-Related-Post\"><a title=\"Update for nnfor: reuse and retrain models\" href=\"https:\/\/kourentzes.com\/forecasting\/2017\/12\/11\/update-for-nnfor-reuse-and-retrain-models\/\" rel=\"bookmark\">Update for nnfor: reuse and retrain models<\/a><\/li>\n<li class=\"SPOSTARBUST-Related-Post\"><a title=\"MAPAx example for R\" href=\"https:\/\/kourentzes.com\/forecasting\/2017\/11\/09\/mapax-example-for-r\/\" rel=\"bookmark\">MAPAx example for R<\/a><\/li>\n<\/ul><\/div><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>The critical distance for the Nemenyi test is calculated as: , where is the confidence level, is the number of models and is the number of measurements. To calculate the Studentised range statistic for infinite degrees of freedom divided by is used. The values of for up to can be download here as csv. You\u2026 <span class=\"read-more\"><a href=\"https:\/\/kourentzes.com\/forecasting\/2014\/05\/01\/critical-values-for-the-nemenyi-test\/\">Read More &raquo;<\/a><\/span><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[50],"tags":[45,24,25],"_links":{"self":[{"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/posts\/325"}],"collection":[{"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/comments?post=325"}],"version-history":[{"count":0,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/posts\/325\/revisions"}],"wp:attachment":[{"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/media?parent=325"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/categories?post=325"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/tags?post=325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<!-- WP Super Cache is installed but broken. 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