{"id":2595,"date":"2024-10-09T10:00:27","date_gmt":"2024-10-09T08:00:27","guid":{"rendered":"https:\/\/clooma.ai\/?post_type=guide-dutilisateur&#038;p=2595"},"modified":"2024-10-23T16:21:54","modified_gmt":"2024-10-23T14:21:54","slug":"05-correlation","status":"publish","type":"guide-dutilisateur","link":"https:\/\/clooma.ai\/en\/users-guide\/05-correlation\/","title":{"rendered":"Correlation"},"content":{"rendered":"<p>Ellistat <a href=\"https:\/\/clooma.ai\/en\/data-analysis-solutions\/\">Data Analysis<\/a> offers the Correlation submenu, which contains several statistical tools. These tools can be used to perform<strong> correlation studies <\/strong>of multiple responses in a dataset. Or to reduce the size of a dataset or monitor processes with several variables simultaneously.<\/p>\n\n\n\n<p>In the examples below we present the tools:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Correlation matrix <\/li>\n\n\n\n<li>ACP<\/li>\n\n\n\n<li>T\u00b2 card<\/li>\n<\/ul>\n\n\n\n<p>The dataset used in these examples can be found on the following page.<\/p>\n\n\n\n<p><a href=\"https:\/\/www.notion.so\/Independent-Data-Donn-es-ind-pendantes-1ef260c96799456c8d41959236e2cf56?pvs=21\">Independent Data \ud83c\uddfa\ud83c\uddf8\/ Donn\u00e9es ind\u00e9pendantes\ud83c\uddeb\ud83c\uddf7&nbsp;<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example 1: Find the correlation between several Y responses, using the correlation matrix<\/h3>\n\n\n\n<p>Visit&nbsp;<strong>correlation matrix<\/strong>&nbsp;is an essential statistical tool used to understand the relationships between several variables in a data set.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-81-1024x522.png\" alt=\"\" class=\"wp-image-2598\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Place quantitative data from several Y columns in the grid. In the example, we want to find the correlation between responses Y1=\"Delta\", Y2=\"Force\" and Y3=\"Pressure\".<\/li>\n\n\n\n<li>Click on the \"<strong>Inferential statistics<\/strong>\".<\/li>\n\n\n\n<li>In the&nbsp;<strong>zone 1<\/strong>Select the Y columns Y1=\"Delta\", Y2=\"Force\" and Y3=\"Pressure\".<\/li>\n\n\n\n<li>In\u00a0<strong>zone 2,<\/strong>\u00a0select your data type. By default, if the selected columns contain quantitative values, Ellistat will plot the correlation curves between all the responses in pairs. In addition to the Correlation sub-menu, you can also choose the \"Proportion\" or \"Population\" sub-menus. \ud83d\udcdd: select \"Correlation matrix\".<\/li>\n\n\n\n<li>In\u00a0<strong>zone 3<\/strong>In the half above the diagonal, we obtain the correlation matrix containing all the correlation graphs of two answers in pairs. The diagonal of this matrix shows the names of the answers. And in the lower half we find the coefficients of determination R\u00b2 and the significance level (P-value).<\/li>\n<\/ul>\n\n\n\n<p>The diagram below shows the correlation graph, R\u00b2 and P-value for both Delta and Pressure responses.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-82-1024x512.png\" alt=\"\" class=\"wp-image-2599\"\/><\/figure>\n\n\n\n<p class=\"has-very-light-gray-background-color has-background\">\ud83d\udca1 When you click on a graph, you'll find a report of an XY Analysis of the two correlated responses:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-83-1024x1007.png\" alt=\"\" class=\"wp-image-2603\"\/><\/figure>\n\n\n\n<p class=\"has-very-light-gray-background-color has-background\">\ud83d\udca1 In the lower half of the correlation matrix there are two values :<\/p>\n\n\n\n<p>R\u00b2 (P-value).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-90.png\" alt=\"\" class=\"wp-image-2604\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Example 2: Find the correlation between several Y variables, using PCA.<\/h3>\n\n\n\n<p>Principal Component Analysis (PCA) is a statistical method used to reduce the dimensionality of a dataset while retaining as much information as possible. This technique is particularly useful when working with multivariate data (i.e. data containing several variables).<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-84-1-1024x549.png\" alt=\"\" class=\"wp-image-2605\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Place a set of quantitative data with several Y columns in the grid. In the example, we want to perform a PCA analysis on the data: Y1=\"Delta\", Y2=\"force\", Y3=\"Pressure\", Y4=\"Pressure 2\", Y5=\"Pressure 3\".<\/li>\n\n\n\n<li>Click on the \"<strong>Inferential statistics<\/strong>\".<\/li>\n\n\n\n<li>In the&nbsp;<strong>zone 1<\/strong>Select the Y columns Y1=\"Delta\", Y2=\"Force\" and Y3=\"Pressure\", Y4=\"Pressure 2\", Y5=\"Pressure 3\".<\/li>\n\n\n\n<li>In&nbsp;<strong>zone 2,<\/strong>&nbsp;select your data type. Press the \"correlation\" sub-menu and select \"correlation\".<strong>ACP<\/strong>\". In addition to this sub-menu, you can also select the \"Proportion\" or \"Population\" sub-menus. \ud83d\udcdd: select \"<strong>ACP<\/strong>\"<\/li>\n\n\n\n<li>In\u00a0<strong>zone 3<\/strong>we obtain the projection of the various responses in the plane composed of the principal vectors\u00a0<strong>C1 (x-axis)<\/strong>\u00a0and\u00a0<strong>C2 (ordinate).<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-very-light-gray-background-color has-background\">\ud83d\udca1 In the upper part of the&nbsp;<strong>zone 3<\/strong>There are two tools used to select one of the spreadsheet factors:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">With the \"Label\" tool :<\/h4>\n\n\n\n<p>It is possible to see the variation of individuals according to the chosen factor. This would make it possible to color-code individuals according to the chosen variable. The following case study shows the results obtained for the label = \"Delta\". We can see that individuals with a strong delta are in orange\/yellow. The individuals with a low delta are in blue.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-91.png\" alt=\"\" class=\"wp-image-2608\"\/><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-85-1.png\" alt=\"\" class=\"wp-image-2609\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">The \"other variable\" tool <\/h4>\n\n\n\n<p>It is used to plot a factor without taking it into account when determining the main vectors. Please note! For this feature to work, the factor must not be ticked in zones 1 and 3 at the same time. It must only be ticked in zone 3. Here, the example of the \"Delta\" factor (see figure below). This variable can be either a quantitative or a qualitative variable.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-86-1024x427.png\" alt=\"\" class=\"wp-image-2610\"\/><\/figure>\n\n\n\n<p>Whether you choose the \"Label\" option or the \"Other variable\" option, the variables selected can be quantitative or qualitative.<\/p>\n\n\n\n<p class=\"has-very-light-gray-background-color has-background\"> \ud83d\udca1 In the middle part of the&nbsp;<strong>zone 3<\/strong>you can select several tabs:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-87-1024x34.png\" alt=\"\" class=\"wp-image-2611\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">The \"Summary\" tab: <\/h4>\n\n\n\n<p>This tab contains the graph, menus for displaying individuals in the graph, classification settings and the table of main vectors.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Pareto tab: <\/h4>\n\n\n\n<p>This tab shows the Pareto diagram, which expresses the contribution of each main vector.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-88-1024x327.png\" alt=\"\" class=\"wp-image-2612\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">The \"variable\" tab: <\/h4>\n\n\n\n<p>This tab shows the degree of correlation significance between the variables and the various main axes (C1, C2,...). A P-value&lt;0.05 means that the correlation between the variable and the main vector is significant. (see table below)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-89-1024x176.png\" alt=\"\" class=\"wp-image-2613\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">Individual values\" tab: <\/h4>\n\n\n\n<p>This tab shows the coordinates of individuals in the space of principal vectors.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example 3: Hotelling's T\u00b2 card<\/h3>\n\n\n\n<p>Hotelling's T\u00b2 chart is a statistical tool used to calculate\u00a0<strong>multivariate quality control<\/strong>\u00a0and data analysis. They enable processes with several variables to be monitored simultaneously. It is a multivariate extension of Shewhart control charts, which focus on a single variable. Hotelling's T\u00b2 is often used in contexts where several quality characteristics need to be monitored at the same time. Examples include manufacturing, biology and engineering.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-92-1-1024x537.png\" alt=\"\" class=\"wp-image-2615\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Place quantitative data from several Y columns in the grid. In the example, we want to monitor the following data simultaneously: Y1=\"Delta\", Y2=\"Force\", Y3=\"Pressure\", Y4=\"Pressure 2\", Y5=\"Pressure 3\".<\/li>\n\n\n\n<li>Click on the \"<strong>Inferential statistics<\/strong>\".<\/li>\n\n\n\n<li>In the&nbsp;<strong>zone 1<\/strong>Select the Y columns Y1=\"Delta\", Y2=\"Force\" and Y3=\"Pressure\", Y4=\"Pressure 2\", Y5=\"Pressure 3\".<\/li>\n\n\n\n<li>In&nbsp;<strong>zone 2,<\/strong>&nbsp;select your data type. Press the \"correlation\" sub-menu and select \"correlation\".<strong>T\u00b2<\/strong>\". In addition to this sub-menu, you can also select the \"Proportion\" or \"Population\" sub-menus. \ud83d\udcdd: select \"<strong>T\u00b2<\/strong>\"<\/li>\n\n\n\n<li>In&nbsp;<strong>zone 3<\/strong>we obtain the control chart&nbsp;<strong>T\u00b2<\/strong>&nbsp;with individual values and control limits.<\/li>\n\n\n\n<li>In the&nbsp;<strong>zone 4<\/strong>Here you'll find options such as general map settings, display options and control limit calculation.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-very-light-gray-background-color has-background\"> \ud83d\udca1 In the middle part of the&nbsp;<strong>zone 4<\/strong>Several options can be set:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/Untitled-93-1024x216.png\" alt=\"\" class=\"wp-image-2616\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li> <strong>\"General<\/strong>With this option, you can choose the type of control chart calculation (classic, Sullivan and Chi-2). You can also choose the alpha risk level and determine the data for training.<\/li>\n\n\n\n<li><strong>\"Display<\/strong> : With this option, you can transform the ordinate into a logarithmic scale and apply a Label to the data.<\/li>\n\n\n\n<li><strong>\"Limits<\/strong> With this option, you can change the control limit by setting it manually.<\/li>\n<\/ul>","protected":false},"featured_media":0,"template":"","meta":{"_acf_changed":false},"menu-guide-dutilisateur":[23],"class_list":["post-2595","guide-dutilisateur","type-guide-dutilisateur","status-publish","hentry","menu-guide-dutilisateur-5-statistiques-inferentielles"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Corr\u00e9lation - Clooma<\/title>\n<meta name=\"description\" content=\"Comment r\u00e9aliser des \u00e9tudes de corr\u00e9lation de plusieurs r\u00e9ponses avec Ellistat ? 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