{"id":3707,"date":"2023-12-08T15:29:31","date_gmt":"2023-12-08T14:29:31","guid":{"rendered":"https:\/\/www.psyctc.org\/psyctc\/?post_type=docs&#038;p=3707"},"modified":"2024-05-06T09:19:13","modified_gmt":"2024-05-06T07:19:13","password":"","slug":"cumulative-distribution","status":"publish","type":"docs","link":"https:\/\/www.psyctc.org\/psyctc\/glossary2\/cumulative-distribution\/","title":{"rendered":"Cumulative distribution"},"content":{"rendered":"\n<p>It&#8217;s pretty much what it says: putting the data you have in order so that the counts mount up to the total number of observations you have.  It&#8217;s a fairly familiar way of tabulating things but a less familiar way of plotting them but it can be a very helpful way to plot as well as to tabulate and it underpins a lot of the ways that statisticians think about and model distributions.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Details<\/h4>\n\n\n\n<p>Suppose you have some data like this.<\/p>\n\n\n\n<div class=\"wpdt-c wdt-skin-light\">\n    \n    <input type=\"hidden\" id=\"table_1_desc\"\n           value='{\"tableId\":\"table_1\",\"tableType\":\"csv\",\"selector\":\"#table_1\",\"responsive\":true,\"responsiveAction\":\"icon\",\"editable\":false,\"inlineEditing\":false,\"infoBlock\":false,\"pagination_top\":0,\"pagination\":0,\"paginationAlign\":\"right\",\"paginationLayout\":\"full_numbers\",\"paginationLayoutMobile\":\"simple\",\"file_location\":\"wp_media_lib\",\"tableSkin\":\"light\",\"table_wcag\":0,\"simple_template_id\":0,\"scrollable\":false,\"fixedLayout\":false,\"globalSearch\":false,\"showRowsPerPage\":false,\"popoverTools\":false,\"loader\":\"1\",\"showCartInformation\":1,\"hideBeforeLoad\":false,\"number_format\":2,\"decimalPlaces\":2,\"spinnerSrc\":\"https:\\\/\\\/www.psyctc.org\\\/psyctc\\\/wp-content\\\/plugins\\\/wpdatatables\\\/assets\\\/\\\/img\\\/spinner.gif\",\"groupingEnabled\":false,\"tableWpId\":22,\"dataTableParams\":{\"sDom\":\"BT\\u003C\\u0027clear\\u0027\\u003Et\",\"bSortCellsTop\":false,\"bFilter\":true,\"aLengthMenu\":[[1,5,10,25,50,100,-1],[1,5,10,25,50,100,\"All\"]],\"iDisplayLength\":10,\"columnDefs\":[{\"sType\":\"formatted-num\",\"wdtType\":\"float\",\"bVisible\":true,\"orderable\":true,\"searchable\":true,\"InputType\":\"text\",\"name\":\"scores\",\"origHeader\":\"scores\",\"notNull\":false,\"conditionalFormattingRules\":[],\"transformValueRules\":\"\",\"className\":\"numdata float  column-scores\",\"aTargets\":[0]}],\"bAutoWidth\":false,\"order\":[[0,\"asc\"]],\"ordering\":false,\"fixedHeader\":{\"header\":false,\"headerOffset\":0},\"fixedColumns\":false,\"oLanguage\":{\"sSearchPlaceholder\":\"\"},\"buttons\":[],\"bProcessing\":false,\"oSearch\":{\"bSmart\":false,\"bRegex\":false,\"sSearch\":\"\"}},\"customRowDisplay\":\"\",\"tabletWidth\":\"1024\",\"mobileWidth\":\"480\",\"renderFilter\":\"footer\",\"advancedFilterEnabled\":false,\"serverSide\":false,\"columnsFixed\":0,\"sumFunctionsLabel\":\"\",\"avgFunctionsLabel\":\"\",\"minFunctionsLabel\":\"\",\"maxFunctionsLabel\":\"\",\"columnsDecimalPlaces\":{\"scores\":-1},\"columnsThousandsSeparator\":[],\"sumColumns\":[],\"avgColumns\":[],\"sumAvgColumns\":[],\"timeFormat\":\"h:i A\",\"datepickFormat\":\"dd\\\/mm\\\/yy\"}'\/>\n\n    <table id=\"table_1\"\n           class=\"  responsive display nowrap wdt-no-display data-t data-t wpDataTable wpDataTableID-22 \"\n           style=\"\"\n           data-described-by='table_1_desc'\n           data-wpdatatable_id=\"22\">\n        \n        <!-- Table header -->\n        \n<thead>\n<tr>\n                    <th\n        data-class=\"expand\"                class=\" wdtheader sort numdata float \"\n        style=\"\">        scores<\/th>    <\/tr>\n<\/thead>\n        <!-- \/Table header -->\n\n        <!-- Table body -->\n        \n<tbody>\n<!-- Table body -->\n<div data-id=\"22\"\n     class=\"wdt-timeline-item wdt-timeline-table_1\"\n     style=\"\">\n    <div class=\"wdt-table-loader\">\n        <div class=\"wdt-table-loader-row wdt-table-loader-header\">\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n        <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n            <\/div>\n<\/div><!-- \/Table body -->\n                    <tr id=\"table_22_row_0\"\n            data-row-index=\"0\">\n                            <td style=\"\">0.50<\/td>\n                    <\/tr>\n                            <tr id=\"table_22_row_1\"\n            data-row-index=\"1\">\n                            <td style=\"\">2.50<\/td>\n                    <\/tr>\n                            <tr id=\"table_22_row_2\"\n            data-row-index=\"2\">\n                            <td style=\"\">2.40<\/td>\n                    <\/tr>\n                            <tr id=\"table_22_row_3\"\n            data-row-index=\"3\">\n                            <td style=\"\">2.50<\/td>\n                    <\/tr>\n                            <tr id=\"table_22_row_4\"\n            data-row-index=\"4\">\n                            <td style=\"\">3.40<\/td>\n                    <\/tr>\n                            <tr id=\"table_22_row_5\"\n            data-row-index=\"5\">\n                            <td style=\"\">2.60<\/td>\n                    <\/tr>\n                            <tr id=\"table_22_row_6\"\n            data-row-index=\"6\">\n                            <td style=\"\">0.00<\/td>\n                    <\/tr>\n                            <tr id=\"table_22_row_7\"\n            data-row-index=\"7\">\n                            <td style=\"\">0.90<\/td>\n                    <\/tr>\n            <\/tbody>        <!-- \/Table body -->\n\n        <!-- Table footer -->\n        \n        <!-- \/Table footer -->\n    <\/table>\n\n<\/div><style>\n<\/style>\n<style>\n                    \n                                                                                        \/* table font color *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-family: Lucida Sans Unicode, Lucida Grande, sans-serif !important;\n    }\n\n            \/* table font size *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-size: 20px !important;\n    }\n\n            \n                <\/style>\n<style>\n<\/style>\n\n\n\n\n<p>Here&#8217;s a histogram of that dataset!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"684\" src=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/Glossary_cumulative_distribution_01-1024x684.png\" alt=\"\" class=\"wp-image-3710\" srcset=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/Glossary_cumulative_distribution_01-1024x684.png 1024w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/Glossary_cumulative_distribution_01-300x200.png 300w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/Glossary_cumulative_distribution_01-768x513.png 768w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/Glossary_cumulative_distribution_01-360x240.png 360w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/Glossary_cumulative_distribution_01.png 1092w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>Now here&#8217;s a very common way to tabulate that dataset: sorted, with percentages and cumulative percentages.<\/p>\n\n\n\n<div class=\"wpdt-c wdt-skin-light\">\n    \n    <input type=\"hidden\" id=\"table_2_desc\"\n           value='{\"tableId\":\"table_2\",\"tableType\":\"csv\",\"selector\":\"#table_2\",\"responsive\":true,\"responsiveAction\":\"icon\",\"editable\":false,\"inlineEditing\":false,\"infoBlock\":false,\"pagination_top\":0,\"pagination\":0,\"paginationAlign\":\"right\",\"paginationLayout\":\"full_numbers\",\"paginationLayoutMobile\":\"simple\",\"file_location\":\"wp_media_lib\",\"tableSkin\":\"light\",\"table_wcag\":0,\"simple_template_id\":0,\"scrollable\":false,\"fixedLayout\":false,\"globalSearch\":true,\"showRowsPerPage\":false,\"popoverTools\":false,\"loader\":\"1\",\"showCartInformation\":1,\"hideBeforeLoad\":false,\"number_format\":2,\"decimalPlaces\":2,\"spinnerSrc\":\"https:\\\/\\\/www.psyctc.org\\\/psyctc\\\/wp-content\\\/plugins\\\/wpdatatables\\\/assets\\\/\\\/img\\\/spinner.gif\",\"groupingEnabled\":false,\"tableWpId\":23,\"dataTableParams\":{\"sDom\":\"BT\\u003C\\u0027clear\\u0027\\u003Eft\",\"bSortCellsTop\":false,\"bFilter\":true,\"aLengthMenu\":[[1,5,10,25,50,100,-1],[1,5,10,25,50,100,\"All\"]],\"iDisplayLength\":10,\"columnDefs\":[{\"sType\":\"formatted-num\",\"wdtType\":\"float\",\"bVisible\":true,\"orderable\":true,\"searchable\":true,\"InputType\":\"text\",\"name\":\"scores\",\"origHeader\":\"scores\",\"notNull\":false,\"conditionalFormattingRules\":[],\"transformValueRules\":\"\",\"className\":\"numdata float  column-scores\",\"aTargets\":[0]},{\"sType\":\"formatted-num\",\"wdtType\":\"int\",\"bVisible\":true,\"orderable\":true,\"searchable\":true,\"InputType\":\"text\",\"name\":\"n\",\"origHeader\":\"n\",\"notNull\":false,\"conditionalFormattingRules\":[],\"transformValueRules\":\"\",\"className\":\"numdata integer  column-n\",\"aTargets\":[1]},{\"sType\":\"string\",\"wdtType\":\"string\",\"bVisible\":true,\"orderable\":true,\"searchable\":true,\"InputType\":\"text\",\"name\":\"percent\",\"origHeader\":\"percent\",\"notNull\":false,\"conditionalFormattingRules\":[],\"transformValueRules\":\"\",\"className\":\" column-percent\",\"aTargets\":[2]},{\"sType\":\"string\",\"wdtType\":\"string\",\"bVisible\":true,\"orderable\":true,\"searchable\":true,\"InputType\":\"text\",\"name\":\"cumPerc\",\"origHeader\":\"cumPerc\",\"notNull\":false,\"conditionalFormattingRules\":[],\"transformValueRules\":\"\",\"className\":\" column-cumperc\",\"aTargets\":[3]}],\"bAutoWidth\":false,\"order\":[[0,\"asc\"]],\"ordering\":false,\"fixedHeader\":{\"header\":false,\"headerOffset\":0},\"fixedColumns\":false,\"buttons\":[{\"extend\":\"print\",\"exportOptions\":{\"columns\":\":visible\",\"stripHtml\":true},\"className\":\"DTTT_button DTTT_button_print\",\"title\":\"New wpDataTable\",\"text\":\"Print\"},{\"extend\":\"excelHtml5\",\"exportOptions\":{\"columns\":\":visible\",\"stripHtml\":true},\"className\":\"DTTT_button DTTT_button_xls\",\"filename\":\"New wpDataTable\",\"title\":null,\"text\":\"Excel\"},{\"extend\":\"csvHtml5\",\"exportOptions\":{\"columns\":\":visible\",\"stripHtml\":true},\"className\":\"DTTT_button DTTT_button_csv\",\"title\":\"New wpDataTable\",\"text\":\"CSV\"},{\"extend\":\"copyHtml5\",\"exportOptions\":{\"columns\":\":visible\",\"stripHtml\":true},\"className\":\"DTTT_button DTTT_button_copy\",\"filename\":\"New wpDataTable\",\"title\":null,\"text\":\"Copy\"}],\"oLanguage\":{\"sSearchPlaceholder\":\"\"},\"bProcessing\":false,\"oSearch\":{\"bSmart\":false,\"bRegex\":false,\"sSearch\":\"\"}},\"customRowDisplay\":\"\",\"tabletWidth\":\"1024\",\"mobileWidth\":\"480\",\"renderFilter\":\"footer\",\"advancedFilterEnabled\":false,\"serverSide\":false,\"columnsFixed\":0,\"sumFunctionsLabel\":\"\",\"avgFunctionsLabel\":\"\",\"minFunctionsLabel\":\"\",\"maxFunctionsLabel\":\"\",\"columnsDecimalPlaces\":{\"scores\":-1,\"n\":-1,\"percent\":-1,\"cumPerc\":-1},\"columnsThousandsSeparator\":{\"n\":1},\"sumColumns\":[],\"avgColumns\":[],\"sumAvgColumns\":[],\"timeFormat\":\"h:i A\",\"datepickFormat\":\"dd\\\/mm\\\/yy\"}'\/>\n\n    <table id=\"table_2\"\n           class=\"  responsive display nowrap wdt-no-display data-t data-t wpDataTable wpDataTableID-23 \"\n           style=\"\"\n           data-described-by='table_2_desc'\n           data-wpdatatable_id=\"23\">\n        \n        <!-- Table header -->\n        \n<thead>\n<tr>\n                    <th\n        data-class=\"expand\"                class=\" wdtheader sort numdata float \"\n        style=\"\">        scores<\/th>        <th\n                        class=\" wdtheader sort numdata integer \"\n        style=\"\">        n<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        percent<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        cumPerc<\/th>    <\/tr>\n<\/thead>\n        <!-- \/Table header -->\n\n        <!-- Table body -->\n        \n<tbody>\n<!-- Table body -->\n<div data-id=\"23\"\n     class=\"wdt-timeline-item wdt-timeline-table_2\"\n     style=\"\">\n    <div class=\"wdt-table-loader\">\n        <div class=\"wdt-table-loader-row wdt-table-loader-header\">\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n        <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n            <\/div>\n<\/div><!-- \/Table body -->\n                    <tr id=\"table_23_row_0\"\n            data-row-index=\"0\">\n                            <td style=\"\">0.00<\/td>\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">12.5%<\/td>\n                            <td style=\"\">12.5%<\/td>\n                    <\/tr>\n                            <tr id=\"table_23_row_1\"\n            data-row-index=\"1\">\n                            <td style=\"\">0.50<\/td>\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">12.5%<\/td>\n                            <td style=\"\">25.0%<\/td>\n                    <\/tr>\n                            <tr id=\"table_23_row_2\"\n            data-row-index=\"2\">\n                            <td style=\"\">0.90<\/td>\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">12.5%<\/td>\n                            <td style=\"\">37.5%<\/td>\n                    <\/tr>\n                            <tr id=\"table_23_row_3\"\n            data-row-index=\"3\">\n                            <td style=\"\">2.40<\/td>\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">12.5%<\/td>\n                            <td style=\"\">50.0%<\/td>\n                    <\/tr>\n                            <tr id=\"table_23_row_4\"\n            data-row-index=\"4\">\n                            <td style=\"\">2.50<\/td>\n                            <td style=\"\">2<\/td>\n                            <td style=\"\">25.0%<\/td>\n                            <td style=\"\">75.0%<\/td>\n                    <\/tr>\n                            <tr id=\"table_23_row_5\"\n            data-row-index=\"5\">\n                            <td style=\"\">2.60<\/td>\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">12.5%<\/td>\n                            <td style=\"\">87.5%<\/td>\n                    <\/tr>\n                            <tr id=\"table_23_row_6\"\n            data-row-index=\"6\">\n                            <td style=\"\">3.40<\/td>\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">12.5%<\/td>\n                            <td style=\"\">100.0%<\/td>\n                    <\/tr>\n            <\/tbody>        <!-- \/Table body -->\n\n        <!-- Table footer -->\n        \n        <!-- \/Table footer -->\n    <\/table>\n\n<\/div><style>\n<\/style>\n<style>\n                    \n                                                                                        \/* table font color *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-family: Lucida Sans Unicode, Lucida Grande, sans-serif !important;\n    }\n\n            \/* table font size *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-size: 20px !important;\n    }\n\n            \n                <\/style>\n<style>\n<\/style>\n\n\n\n\n<p>That last column is a cumulative distribution.  Here it is mapping scores to their cumulative distribution as a cumulative percentage between zero and 100%, you may also see it between zero and 1 (cumulative proportion) and you might also see it terms of cumulative <em>n<\/em> which here would between zero and eight.  This distribution give us the cumulative distribution plot.<\/p>\n\n\n\n<p>That&#8217;s pretty uninteresting with a tiny dataset and only one variable but cumulative distributions come into their own with larger datasets and a second variable. For example exploring the relationship between gender and CORE-OM scores.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"684\" src=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/genderECDF-1024x684.png\" alt=\"\" class=\"wp-image-3714\" srcset=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/genderECDF-1024x684.png 1024w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/genderECDF-300x200.png 300w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/genderECDF-768x513.png 768w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/genderECDF-1536x1026.png 1536w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/genderECDF-2048x1367.png 2048w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2023\/12\/genderECDF-360x240.png 360w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>I always have to remind myself that the fact that ECDF line for the women is <em>under<\/em> that for the men is because the women are tending to score higher generally than the men so the quantiles for the women tend to be higher (to the right of) those for the men. A non-parametric test with the glorious name of the Kolmogorov-Smirnov test is a formal test of whether the largest absolute vertical distance between the lines is larger than you would expect to have happened had Gender had no relationship with score in the population and this just a chance sampling vagary.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Try also<\/h4>\n\n\n\n<p><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/distribution\/\" title=\"\">Distribution<\/a><br><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/empirical-cumulative-distribution-function-ecdf\/\" title=\"\">Empirical Cumulative Distribution Function (ECDF)<\/a><br><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/histograms-and-barplots\/\" title=\"\">Histograms and boxplots<\/a><br><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/kolmogorov-smirnov-test\/\" title=\"\">Kolmogorov-Smirnov test<\/a><br><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/violin-plot-or-violinplot\/\" title=\"\">Violin plots<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Chapters<\/h4>\n\n\n\n<p>Not in the book.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Online resources<\/h4>\n\n\n\n<p><a href=\"https:\/\/www.psyctc.org\/Rblog\/\" title=\"\">Rblog<\/a> posts:<br>* <a href=\"https:\/\/www.psyctc.org\/Rblog\/posts\/2023-08-07-ecdfs\/\" title=\"\">What is an empirical cumulative distribution function?<\/a><br>* <a href=\"https:\/\/www.psyctc.org\/Rblog\/posts\/2023-08-09-confidence-intervals-for-quantiles\/\" title=\"\">Confidence intervals for quantiles<\/a><br>* <a href=\"https:\/\/www.psyctc.org\/Rblog\/posts\/2023-08-11-mapping-individual-scores-to-referential-data-using-quantiles\/\" title=\"\">Mapping individual scores to referential data using quantiles<\/a><br><a href=\"https:\/\/shiny.psyctc.org\/\" title=\"\">My interactive shiny apps<\/a>:<br>* <a href=\"https:\/\/shiny.psyctc.org\/apps\/ECDFplot\/\" title=\"\">Plot ECDF with CIs for arbitrary quantiles<\/a><br>* <a href=\"https:\/\/shiny.psyctc.org\/apps\/Gaussian1\/\" target=\"_blank\" rel=\"noopener\" title=\"\">App creating samples from Gaussian distribution<\/a> showing histogram, ecdf and qqplot <br>* <a href=\"https:\/\/shiny.psyctc.org\/apps\/ECDFplot\/\" target=\"_blank\" rel=\"noopener\" title=\"\">App that takes data<\/a>, pasted in or uploaded in various formats, and plots the ecdf with confidence intervals for quantiles of your choosing!<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Dates<\/h4>\n\n\n\n<p>First created 8.xii.23, tweaked links 6.v.24.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It&#8217;s pretty much what it says: putting the data you have in order so that the counts mount up to the total number of observations you have. It&#8217;s a fairly familiar way of tabulating things but a less familiar way of plotting them but it can be a very helpful way to plot as well &hellip; <a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/cumulative-distribution\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Cumulative distribution<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"doc_category":[18],"glossaries":[],"doc_tag":[],"knowledge_base":[],"class_list":["post-3707","docs","type-docs","status-publish","hentry","doc_category-om-book"],"year_month":"2026-04","word_count":394,"total_views":"676","reactions":{"happy":"0","normal":"0","sad":"0"},"author_info":{"name":"chris","author_nicename":"chris","author_url":"https:\/\/www.psyctc.org\/psyctc\/author\/chris\/"},"doc_category_info":[{"term_name":"All OM book glossary entries","term_url":"https:\/\/www.psyctc.org\/psyctc\/glossary\/non-knowledgebase\/om-book\/"}],"doc_tag_info":[],"knowledge_base_info":[],"knowledge_base_slug":[],"_links":{"self":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3707","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs"}],"about":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/types\/docs"}],"author":[{"embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/comments?post=3707"}],"version-history":[{"count":8,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3707\/revisions"}],"predecessor-version":[{"id":4238,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3707\/revisions\/4238"}],"wp:attachment":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/media?parent=3707"}],"wp:term":[{"taxonomy":"doc_category","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_category?post=3707"},{"taxonomy":"glossaries","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/glossaries?post=3707"},{"taxonomy":"doc_tag","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_tag?post=3707"},{"taxonomy":"knowledge_base","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/knowledge_base?post=3707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}