{"id":15694,"date":"2022-04-22T11:50:15","date_gmt":"2022-04-22T10:50:15","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=15694"},"modified":"2024-02-13T14:09:56","modified_gmt":"2024-02-13T13:09:56","slug":"ex-analyse-exploratoire","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/ejercicios-corregidos-analisis-exploratorio-de-datos\/","title":{"rendered":"2 Ejercicios corregidos de an\u00e1lisis exploratorio de datos."},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"15694\" class=\"elementor elementor-15694\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7437700 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7437700\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div 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rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bbf1d73 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bbf1d73\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ec2fbd9\" data-id=\"ec2fbd9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bede89d elementor-widget elementor-widget-heading\" data-id=\"bede89d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenus<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Alternar tabla de contenidos\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/ejercicios-corregidos-analisis-exploratorio-de-datos\/#Exercices-Corriges-sur-Analyse-exploratoire-des-donnees\" >Exercices Corrig\u00e9s sur Analyse exploratoire des donn\u00e9es<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/ejercicios-corregidos-analisis-exploratorio-de-datos\/#Exercice-1\" >Exercice 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/ejercicios-corregidos-analisis-exploratorio-de-datos\/#Considerons-un-echantillon-aleatoire-de-finisseurs-du-marathon-de-New-York-en-2002-Cet-ensemble-de-donnees-se-trouve-dans-le-package-UsingR-Chargez-la-bibliotheque-puis-chargez-lensemble-de-donnees-nym2002\" >Consid\u00e9rons un \u00e9chantillon al\u00e9atoire de finisseurs du marathon de New York en 2002. Cet ensemble de donn\u00e9es se trouve dans le package UsingR. Chargez la biblioth\u00e8que, puis chargez l&rsquo;ensemble de donn\u00e9es nym.2002.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/ejercicios-corregidos-analisis-exploratorio-de-datos\/#Exercice-2\" >Exercice 2<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercices-Corriges-sur-Analyse-exploratoire-des-donnees\"><\/span>Exercices Corrig\u00e9s sur Analyse exploratoire des donn\u00e9es<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2b7c26f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b7c26f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ea3e7c5\" data-id=\"ea3e7c5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-110ad5a elementor-widget elementor-widget-text-editor\" data-id=\"110ad5a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Cette page pr\u00e9sente deux exercices corrig\u00e9s et d\u00e9taill\u00e9s avec le code python sur l&rsquo;analyse exploratoire des donn\u00e9es.<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"analyse exploratoire des donn\u00e9es\" width=\"97\" height=\"97\" title=\"\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ae04e46 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ae04e46\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-065a3b8\" data-id=\"065a3b8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0c00321 elementor-widget elementor-widget-heading\" data-id=\"0c00321\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-1\"><\/span>Exercice 1<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2c24d91 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2c24d91\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e12ec5a\" data-id=\"e12ec5a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4510e71 elementor-widget elementor-widget-text-editor\" data-id=\"4510e71\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span class=\"ez-toc-section\" id=\"Considerons-un-echantillon-aleatoire-de-finisseurs-du-marathon-de-New-York-en-2002-Cet-ensemble-de-donnees-se-trouve-dans-le-package-UsingR-Chargez-la-bibliotheque-puis-chargez-lensemble-de-donnees-nym2002\"><\/span><span style=\"font-family: 'Source Sans Pro', Graphik, -apple-system, BlinkMacSystemFont, 'Segoe UI', Helvetica, Arial, sans-serif; font-size: 1.125rem;\">Consid\u00e9rons un \u00e9chantillon al\u00e9atoire de finisseurs du marathon de New York en 2002. Cet ensemble de donn\u00e9es se trouve dans le package UsingR. Chargez la biblioth\u00e8que, puis chargez l&rsquo;ensemble de donn\u00e9es nym.2002.<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2><div class=\"question\"><div id=\"cb168\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb168-1\"><span class=\"fu\">library<\/span>(dplyr)<\/span>\n<span id=\"cb168-2\"><span class=\"fu\">data<\/span>(nym<span class=\"fl\">.2002<\/span>, <span class=\"at\">package=<\/span><span class=\"st\">\"UsingR\"<\/span>)<\/span><\/code><\/pre><\/div><p>Utilisez des bo\u00eetes \u00e0 moustaches et des histogrammes pour comparer les temps d&rsquo;arriv\u00e9e des hommes et des femmes. Lequel des r\u00e9sum\u00e9s\u00a0 d\u00e9crit le mieux la diff\u00e9rence ?<\/p><\/div><div class=\"answer\"><div id=\"cb169\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb169-1\"><span class=\"fu\">data<\/span>(nym<span class=\"fl\">.2002<\/span>, <span class=\"at\">package=<\/span><span class=\"st\">\"UsingR\"<\/span>)<\/span>\n<span id=\"cb169-2\">male <span class=\"ot\">&lt;-<\/span> nym<span class=\"fl\">.2002<\/span> <span class=\"sc\">%&gt;%<\/span> <span class=\"fu\">filter<\/span>(gender <span class=\"sc\">==<\/span> <span class=\"st\">'Male'<\/span>)<\/span>\n<span id=\"cb169-3\">female <span class=\"ot\">&lt;-<\/span> nym<span class=\"fl\">.2002<\/span> <span class=\"sc\">%&gt;%<\/span> <span class=\"fu\">filter<\/span>(gender <span class=\"sc\">==<\/span> <span class=\"st\">'Female'<\/span>)<\/span>\n<span id=\"cb169-4\"><span class=\"fu\">mypar<\/span>(<span class=\"dv\">1<\/span>,<span class=\"dv\">2<\/span>)<\/span>\n<span id=\"cb169-5\"><span class=\"fu\">hist<\/span>(female<span class=\"sc\">$<\/span>time, <span class=\"at\">xlim =<\/span> <span class=\"fu\">c<\/span>(<span class=\"dv\">100<\/span>,<span class=\"dv\">600<\/span>))<\/span>\n<span id=\"cb169-6\"><span class=\"fu\">hist<\/span>(male<span class=\"sc\">$<\/span>time, <span class=\"at\">xlim =<\/span> <span class=\"fu\">c<\/span>(<span class=\"dv\">100<\/span>,<span class=\"dv\">600<\/span>))<\/span><\/code><\/pre><\/div><p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-15699 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-137-1-1024x731.png\" alt=\"\" width=\"1024\" height=\"731\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-137-1-1024x731.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-137-1-300x214.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-137-1-768x549.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-137-1-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-137-1-120x85.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-137-1-600x429.png 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-137-1.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><p>Les deux histogrammes ont une distribution similaire (inclin\u00e9e vers la droite). Mais le centre de l&rsquo;histogramme semble \u00eatre diff\u00e9rent. Nous pouvons le v\u00e9rifier en calculant la diff\u00e9rence absolue entre la moyenne et la m\u00e9diane.<\/p><div id=\"cb170\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb170-1\"><span class=\"fu\">abs<\/span>(<span class=\"fu\">mean<\/span>(male<span class=\"sc\">$<\/span>time) <span class=\"sc\">-<\/span> <span class=\"fu\">mean<\/span>(female<span class=\"sc\">$<\/span>time))<\/span><\/code><\/pre><\/div><pre><code>## [1] 23.11574<\/code><\/pre><div id=\"cb172\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb172-1\"><span class=\"fu\">abs<\/span>(<span class=\"fu\">median<\/span>(male<span class=\"sc\">$<\/span>time) <span class=\"sc\">-<\/span> <span class=\"fu\">median<\/span>(female<span class=\"sc\">$<\/span>time))<\/span><\/code><\/pre><\/div><pre><code>## [1] 21.70833<\/code><\/pre><p>Il y a une diff\u00e9rence d&rsquo;environ 21-23 minutes entre les hommes et les femmes. Les hommes et les femmes ont des distributions similaires asym\u00e9triques vers la droite, les premi\u00e8res 20 minutes \u00e9tant d\u00e9cal\u00e9es vers la gauche.<\/p><\/div><div id=\"question-6-6\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Utilisez dplyr pour cr\u00e9er deux nouvelles trames de donn\u00e9es : hommes et femmes, avec les donn\u00e9es pour chaque sexe. Pour les hommes, quelle est la corr\u00e9lation de Pearson entre l&rsquo;\u00e2ge et le temps pour terminer ?<\/p><\/div><div class=\"answer\"><div id=\"cb174\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb174-1\"><span class=\"fu\">plot<\/span>(male<span class=\"sc\">$<\/span>age, male<span class=\"sc\">$<\/span>time, <span class=\"at\">main =<\/span> <span class=\"st\">'male'<\/span>)<\/span><\/code><\/pre><\/div><p><img decoding=\"async\" class=\"aligncenter wp-image-15700 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-139-1-1024x731.png\" alt=\"\" width=\"1024\" height=\"731\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-139-1-1024x731.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-139-1-300x214.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-139-1-768x549.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-139-1-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-139-1-120x85.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-139-1-600x429.png 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-139-1.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><div id=\"cb175\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb175-1\"><span class=\"fu\">cor<\/span>(male<span class=\"sc\">$<\/span>age, male<span class=\"sc\">$<\/span>time)<\/span><\/code><\/pre><\/div><pre><code>## [1] 0.2432273<\/code><\/pre><\/div><div id=\"question-7-6\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Pour les femmes, quelle est la corr\u00e9lation de Pearson entre l&rsquo;\u00e2ge et le temps pour terminer ?<\/p><\/div><div class=\"answer\"><div id=\"cb177\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb177-1\"><span class=\"fu\">plot<\/span>(female<span class=\"sc\">$<\/span>age, female<span class=\"sc\">$<\/span>time, <span class=\"at\">main =<\/span> <span class=\"st\">'female'<\/span>)<\/span><\/code><\/pre><\/div><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15701 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-140-1-1024x731.png\" alt=\"\" width=\"1024\" height=\"731\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-140-1-1024x731.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-140-1-300x214.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-140-1-768x549.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-140-1-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-140-1-120x85.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-140-1-600x429.png 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-140-1.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><div id=\"cb178\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb178-1\"><span class=\"fu\">cor<\/span>(female<span class=\"sc\">$<\/span>age, female<span class=\"sc\">$<\/span>time)<\/span><\/code><\/pre><\/div><pre><code>## [1] 0.2443156<\/code><\/pre><\/div><div id=\"question-8-5\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Si nous interpr\u00e9tons ces corr\u00e9lations sans visualiser les donn\u00e9es, nous conclurions que plus nous vieillissons, plus nous courons des marathons lentement, quel que soit le sexe. Examinez les diagrammes de dispersion et les bo\u00eetes \u00e0 moustaches des heures stratifi\u00e9es par tranches d&rsquo;\u00e2ge (20-24, 25-30, etc.). Apr\u00e8s avoir examin\u00e9 les donn\u00e9es, quelle est la conclusion la plus raisonnable ?<\/p><\/div><div class=\"answer\"><div id=\"cb180\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb180-1\">groups_m <span class=\"ot\">&lt;-<\/span> <span class=\"fu\">split<\/span>(male<span class=\"sc\">$<\/span>time, <span class=\"fu\">floor<\/span>(male<span class=\"sc\">$<\/span>age<span class=\"sc\">\/<\/span><span class=\"dv\">5<\/span>)<span class=\"sc\">*<\/span><span class=\"dv\">5<\/span>) <span class=\"co\"># 10-14, 15-19, etc<\/span><\/span>\n<span id=\"cb180-2\">groups_f <span class=\"ot\">&lt;-<\/span> <span class=\"fu\">split<\/span>(female<span class=\"sc\">$<\/span>time, <span class=\"fu\">floor<\/span>(female<span class=\"sc\">$<\/span>age<span class=\"sc\">\/<\/span><span class=\"dv\">5<\/span>)<span class=\"sc\">*<\/span><span class=\"dv\">5<\/span>) <span class=\"co\"># 10-14, 15-19, etc<\/span><\/span>\n<span id=\"cb180-3\"><span class=\"fu\">mypar<\/span>(<span class=\"dv\">1<\/span>,<span class=\"dv\">2<\/span>)<\/span>\n<span id=\"cb180-4\"><span class=\"fu\">boxplot<\/span>(groups_m)<\/span>\n<span id=\"cb180-5\"><span class=\"fu\">boxplot<\/span>(groups_f)<\/span><\/code><\/pre><\/div><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15702 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-141-1-1024x731.png\" alt=\"\" width=\"1024\" height=\"731\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-141-1-1024x731.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-141-1-300x214.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-141-1-768x549.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-141-1-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-141-1-120x85.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-141-1-600x429.png 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-141-1.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><p>C&rsquo;est une question d\u00e9licate car la question vous demande de stratifier les donn\u00e9es en groupes. La stratification peut \u00eatre r\u00e9alis\u00e9e via\u00a0la\u00a0fonction\u00a0de\u00a0split. Pour que chaque groupe ait une plage de 5 (ex. 25-30), tous les nombres d&rsquo;\u00e2ge devront \u00eatre arrondis vers le haut ou vers le bas afin que les nombres r\u00e9sultants soient divisibles par 5. J&rsquo;ai arrondi les nombres vers le bas en utilisant la fonction plancher.<\/p><p>Par cons\u00e9quent,\u00a040\u00a0repr\u00e9sente la tranche d&rsquo;\u00e2ge\u00a040-44\u00a0. Vous pouvez \u00e9galement utiliser la fonction de plafond pour stratifier les donn\u00e9es, qui seront ensuite arrondies. Ainsi, 45\u00a0repr\u00e9sente\u00a041-45\u00a0groupe d&rsquo;\u00e2ge. Dans l&rsquo;exemple ci-dessous, l&rsquo;\u00e2ge de 42\u00a0ans est class\u00e9 \u00e0 l&rsquo;aide des fonctions de plancher et de plafond.<\/p><div id=\"cb181\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb181-1\"><span class=\"fu\">floor<\/span>(<span class=\"dv\">42<\/span><span class=\"sc\">\/<\/span><span class=\"dv\">5<\/span>)<span class=\"sc\">*<\/span><span class=\"dv\">5<\/span> <\/span><\/code><\/pre><\/div><pre><code>## [1] 40<\/code><\/pre><div id=\"cb183\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb183-1\"><span class=\"fu\">ceiling<\/span>(<span class=\"dv\">42<\/span><span class=\"sc\">\/<\/span><span class=\"dv\">5<\/span>)<span class=\"sc\">*<\/span><span class=\"dv\">5<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 45<\/code><\/pre><p>Les temps d&rsquo;arriv\u00e9e sont constants jusqu&rsquo;\u00e0 environ nos 40 ans, puis nous devenons plus lents.<\/p><\/div><\/div><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f249879 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f249879\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-eb2a29d\" data-id=\"eb2a29d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-919c212 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"919c212\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1947749 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1947749\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-af90601\" data-id=\"af90601\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9c2d6ca elementor-widget elementor-widget-heading\" data-id=\"9c2d6ca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-2\"><\/span>Exercice 2<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bab8816 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bab8816\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0570310\" data-id=\"0570310\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4db125e elementor-widget elementor-widget-text-editor\" data-id=\"4db125e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Chargeons les donn\u00e9es :<\/p><div id=\"cb185\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb185-1\"><span class=\"fu\">data<\/span>(ChickWeight)<\/span>\n<span id=\"cb185-2\"><span class=\"fu\">mypar<\/span>()<\/span>\n<span id=\"cb185-3\"><span class=\"fu\">plot<\/span>(ChickWeight<span class=\"sc\">$<\/span>Time, ChickWeight<span class=\"sc\">$<\/span>weight, <span class=\"at\">col=<\/span>ChickWeight<span class=\"sc\">$<\/span>Diet)<\/span><\/code><\/pre><\/div><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15703 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-143-1-1024x731.png\" alt=\"\" width=\"1024\" height=\"731\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-143-1-1024x731.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-143-1-300x214.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-143-1-768x549.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-143-1-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-143-1-120x85.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-143-1-600x429.png 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-143-1.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><div id=\"cb186\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb186-1\">chick <span class=\"ot\">=<\/span> <span class=\"fu\">reshape<\/span>(ChickWeight, <span class=\"at\">idvar=<\/span><span class=\"fu\">c<\/span>(<span class=\"st\">\"Chick\"<\/span>,<span class=\"st\">\"Diet\"<\/span>), <span class=\"at\">timevar=<\/span><span class=\"st\">\"Time\"<\/span>,<\/span>\n<span id=\"cb186-2\">                <span class=\"at\">direction=<\/span><span class=\"st\">\"wide\"<\/span>)<\/span>\n<span id=\"cb186-3\">chick <span class=\"ot\">=<\/span> <span class=\"fu\">na.omit<\/span>(chick)<\/span><\/code><\/pre><\/div><div id=\"question-1-9\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Concentrez-vous sur les poids des poussins le jour 4 (v\u00e9rifiez les noms de colonne du poussin et notez les chiffres). De combien la moyenne des poids des poussins au jour 4 augmente-t-elle si nous ajoutons une mesure aberrante de 3000 grammes ? Plus pr\u00e9cis\u00e9ment, quel est le poids moyen des poussins du jour 4, y compris le poussin aberrant, divis\u00e9 par la moyenne du poids des poussins du jour 4 sans la valeur aberrante. Astuce : utilisez c pour ajouter un nombre \u00e0 un vecteur.<\/p><\/div><div class=\"answer\"><div id=\"cb187\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb187-1\">chick_w4 <span class=\"ot\">&lt;-<\/span> chick[,<span class=\"st\">'weight.4'<\/span>]<\/span>\n<span id=\"cb187-2\">chick_w4_add <span class=\"ot\">&lt;-<\/span> <span class=\"fu\">append<\/span>(chick_w4, <span class=\"dv\">3000<\/span>)<\/span>\n<span id=\"cb187-3\"><span class=\"co\"># or use function c<\/span><\/span>\n<span id=\"cb187-4\"><span class=\"co\"># chick_w4_add &lt;- c(chick_w4, 3000) <\/span><\/span>\n<span id=\"cb187-5\">chick_w4_add <\/span><\/code><\/pre><\/div><pre><code>##  [1]   59   58   55   56   48   59   57   59   52   63   56   53   62\n## [14]   61   55   54   62   64   61   58   62   57   58   58   59   59\n## [27]   62   65   63   63   64   61   56   61   61   66   66   63   69\n## [40]   61   62   66   62   64   67 3000<\/code><\/pre><div id=\"cb189\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb189-1\"><span class=\"fu\">mean<\/span>(chick_w4_add) <span class=\"sc\">-<\/span> <span class=\"fu\">mean<\/span>(chick_w4) <span class=\"co\"># Difference between with and without outlier<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 63.90966<\/code><\/pre><div id=\"cb191\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb191-1\"><span class=\"fu\">mean<\/span>(chick_w4_add)<span class=\"sc\">\/<\/span><span class=\"fu\">mean<\/span>(chick_w4) <span class=\"co\"># Ratio between with and without outlier<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 2.062407<\/code><\/pre><\/div><div id=\"question-2-9\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Dans la premi\u00e8re partie, nous avons vu \u00e0 quel point la moyenne est sensible aux valeurs aberrantes. Voyons maintenant ce qui se passe lorsque nous utilisons la m\u00e9diane au lieu de la moyenne. Calculez le m\u00eame rapport, mais en utilisant maintenant la m\u00e9diane au lieu de la moyenne. Plus pr\u00e9cis\u00e9ment, quel est le poids m\u00e9dian des poussins du jour 4, y compris le poussin aberrant, divis\u00e9 par la m\u00e9diane du poids des poussins du jour 4 sans la valeur aberrante.<\/p><\/div><div class=\"answer\"><div id=\"cb193\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb193-1\"><span class=\"fu\">median<\/span>(chick_w4_add) <span class=\"sc\">-<\/span> <span class=\"fu\">median<\/span>(chick_w4) <span class=\"co\"># difference<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 0<\/code><\/pre><div id=\"cb195\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb195-1\"><span class=\"fu\">median<\/span>(chick_w4_add)<span class=\"sc\">\/<\/span><span class=\"fu\">median<\/span>(chick_w4) <span class=\"co\"># ratio<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 1<\/code><\/pre><\/div><div id=\"question-3-7\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Essayez maintenant la m\u00eame chose avec l&rsquo;exemple d&rsquo;\u00e9cart type (la fonction sd dans R). Ajoutez un poussin pesant 3000 grammes aux poids des poussins du jour 4. De combien l&rsquo;\u00e9cart type change-t-il ? Quel est l&rsquo;\u00e9cart type avec le poussin aberrant divis\u00e9 par l&rsquo;\u00e9cart type sans le poussin aberrant ?<\/p><\/div><div class=\"answer\"><div id=\"cb197\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb197-1\"><span class=\"fu\">sd<\/span>(chick_w4_add) <span class=\"sc\">-<\/span> <span class=\"fu\">sd<\/span>(chick_w4) <span class=\"co\"># difference<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 429.1973<\/code><\/pre><div id=\"cb199\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb199-1\"><span class=\"fu\">sd<\/span>(chick_w4_add)<span class=\"sc\">\/<\/span> <span class=\"fu\">sd<\/span>(chick_w4) <span class=\"co\"># ratio<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 101.2859<\/code><\/pre><\/div><div id=\"question-4-7\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Comparez le r\u00e9sultat ci-dessus \u00e0 l&rsquo;\u00e9cart absolu m\u00e9dian de R, qui est calcul\u00e9 avec la fonction mad. Notez que le mad n&rsquo;est pas affect\u00e9 par l&rsquo;ajout d&rsquo;une seule valeur aberrante. La fonction mad dans R inclut le facteur d&rsquo;\u00e9chelle 1,4826, de sorte que mad et sd sont tr\u00e8s similaires pour un \u00e9chantillon d&rsquo;une distribution normale. Quel est le MAD avec le poussin aberrant divis\u00e9 par le MAD sans le poussin aberrant ?<\/p><\/div><div class=\"answer\"><div id=\"cb201\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb201-1\"><span class=\"fu\">mad<\/span>(chick_w4_add) <span class=\"sc\">-<\/span> <span class=\"fu\">mad<\/span>(chick_w4) <span class=\"co\"># difference<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 0<\/code><\/pre><div id=\"cb203\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb203-1\"><span class=\"fu\">mad<\/span>(chick_w4_add)<span class=\"sc\">\/<\/span> <span class=\"fu\">mad<\/span>(chick_w4) <span class=\"co\"># ratio<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 1<\/code><\/pre><\/div><div id=\"question-5-7\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Notre derni\u00e8re question porte sur la fa\u00e7on dont la corr\u00e9lation de Pearson est affect\u00e9e par une valeur aberrante par rapport \u00e0 la corr\u00e9lation de Spearman. La corr\u00e9lation de Pearson entre x et y est donn\u00e9e dans R par cor(x,y). La corr\u00e9lation de Spearman est donn\u00e9e par\u00a0cor(x,y,method=\u00a0\u00bbspearman\u00a0\u00bb).<\/p><p>Tracez les poids des poussins du jour 4 et du jour 21. Nous pouvons voir qu&rsquo;il existe une tendance g\u00e9n\u00e9rale, les poussins de poids inf\u00e9rieur le jour 4 ayant \u00e0 nouveau un poids faible le jour 21, et de m\u00eame pour les poussins de poids \u00e9lev\u00e9.<\/p><p>Calculez la corr\u00e9lation de Pearson des poids des poussins du jour 4 et du jour 21. Calculez maintenant de combien la corr\u00e9lation de Pearson change si nous ajoutons un poussin qui p\u00e8se 3000 le jour 4 et 3000 le jour 21. Encore une fois, divisez la corr\u00e9lation de Pearson avec la valeur aberrante chick sur la corr\u00e9lation de Pearson calcul\u00e9e sans les valeurs aberrantes.<\/p><\/div><div class=\"answer\"><div id=\"cb205\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb205-1\">chick_w21 <span class=\"ot\">&lt;-<\/span> chick[, <span class=\"st\">'weight.21'<\/span>]<\/span>\n<span id=\"cb205-2\">chick_w21<\/span><\/code><\/pre><\/div><pre><code>##  [1] 205 215 202 157 223 157 305  98 124 175 205  96 266 142 157 117\n## [17] 331 167 175  74 265 251 192 233 309 150 256 305 147 341 373 220\n## [33] 178 290 272 321 204 281 200 196 238 205 322 237 264<\/code><\/pre><div id=\"cb207\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb207-1\"><span class=\"fu\">plot<\/span>(chick_w4, chick_w21)<\/span><\/code><\/pre><\/div><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15704 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-148-1-1024x731.png\" alt=\"\" width=\"1024\" height=\"731\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-148-1-1024x731.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-148-1-300x214.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-148-1-768x549.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-148-1-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-148-1-120x85.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-148-1-600x429.png 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-148-1.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><div id=\"cb208\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb208-1\"><span class=\"fu\">cor<\/span>(chick_w4,chick_w21) <span class=\"co\"># correlation before<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 0.4159499<\/code><\/pre><div id=\"cb210\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb210-1\">chick_w21_add <span class=\"ot\">&lt;-<\/span> <span class=\"fu\">append<\/span>(chick_w21, <span class=\"dv\">3000<\/span>)<\/span>\n<span id=\"cb210-2\"><span class=\"fu\">cor<\/span>(chick_w4_add, chick_w21_add) <span class=\"co\"># correlation after outlier<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 0.9861002<\/code><\/pre><div id=\"cb212\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb212-1\"><span class=\"fu\">cor<\/span>(chick_w4_add, chick_w21_add)<span class=\"sc\">\/<\/span><span class=\"fu\">cor<\/span>(chick_w4,chick_w21) <span class=\"co\"># ratio between after and before<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 2.370719<\/code><\/pre><\/div><div id=\"question-6-7\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Enregistrez les poids des poussins au jour 4 du r\u00e9gime 1 en tant que vecteur x. Enregistrez les poids des poussins au jour 4 du r\u00e9gime 4 en tant que vecteur y. Effectuez un test\u00a0t comparant\u00a0x\u00a0et\u00a0y (dans R, la fonction\u00a0t.test(x,y)\u00a0effectuera le test). Effectuez ensuite un test de Wilcoxon de\u00a0x\u00a0et\u00a0y\u00a0(dans R, la fonction\u00a0wilcox.test(x,y)\u00a0effectuera le test). Un avertissement appara\u00eetra indiquant qu&rsquo;une valeur p exacte ne peut pas \u00eatre calcul\u00e9e avec des liens, donc une approximation est utilis\u00e9e, ce qui est bien pour nos besoins.<\/p><\/div><div class=\"answer\"><div id=\"cb214\" class=\"sourceCode\"><p>Effectuez un test\u00a0t de\u00a0x\u00a0et\u00a0y, apr\u00e8s avoir ajout\u00e9 un seul poussin de 200\u00a0grammes \u00e0\u00a0x\u00a0(les poussins du r\u00e9gime 1). Quelle est la valeur p de ce test\u00a0? La valeur de p d&rsquo;un test est disponible avec le code suivant\u00a0:\u00a0t.test(x,y)$p.value<\/p><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb214-1\">x <span class=\"ot\">&lt;-<\/span> chick <span class=\"sc\">%&gt;%<\/span> <span class=\"fu\">filter<\/span>(Diet <span class=\"sc\">==<\/span> <span class=\"dv\">1<\/span>) <\/span>\n<span id=\"cb214-2\">x <span class=\"ot\">&lt;-<\/span> x[,<span class=\"st\">'weight.4'<\/span>]<\/span>\n<span id=\"cb214-3\"><\/span>\n<span id=\"cb214-4\">y <span class=\"ot\">&lt;-<\/span> chick <span class=\"sc\">%&gt;%<\/span> <span class=\"fu\">filter<\/span>(Diet <span class=\"sc\">==<\/span> <span class=\"dv\">4<\/span>) <\/span>\n<span id=\"cb214-5\">y <span class=\"ot\">&lt;-<\/span> y[,<span class=\"st\">'weight.4'<\/span>]<\/span>\n<span id=\"cb214-6\"><span class=\"fu\">t.test<\/span>(x,y)<span class=\"sc\">$<\/span>p.value <span class=\"co\"># t.test result with no outlier<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 7.320259e-06<\/code><\/pre><div id=\"cb216\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb216-1\"><span class=\"fu\">wilcox.test<\/span>(x,y)<span class=\"sc\">$<\/span>p.value <span class=\"co\"># wilcox result with no outlier<\/span><\/span><\/code><\/pre><\/div><pre><code>## Warning in wilcox.test.default(x, y): cannot compute exact p-value\n## with ties<\/code><\/pre><pre><code>## [1] 0.0002011939<\/code><\/pre><div id=\"cb219\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb219-1\">x_add <span class=\"ot\">&lt;-<\/span> <span class=\"fu\">c<\/span>(x,<span class=\"dv\">200<\/span>) <span class=\"co\"># outlier added<\/span><\/span>\n<span id=\"cb219-2\"><span class=\"fu\">t.test<\/span>(x_add,y)<span class=\"sc\">$<\/span>p.value <span class=\"co\"># t-test after outlier<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 0.9380347<\/code><\/pre><\/div><div id=\"question-7-7\" class=\"section level3 unnumbered\"><p class=\"hasAnchor\">Faites de m\u00eame pour le test de Wilcoxon. Le test de Wilcoxon est robuste \u00e0 la valeur aberrante. De plus, il comporte moins d&rsquo;hypoth\u00e8ses que le test t sur la distribution des donn\u00e9es sous-jacentes.<\/p><div class=\"answer\"><div id=\"cb221\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb221-1\"><span class=\"fu\">wilcox.test<\/span>(x_add,y)<span class=\"sc\">$<\/span>p.value <span class=\"co\"># even with outlier, p-value is not perturbed<\/span><\/span><\/code><\/pre><\/div><pre><code>## Warning in wilcox.test.default(x_add, y): cannot compute exact p-\n## value with ties<\/code><\/pre><pre><code>## [1] 0.0009840921<\/code><\/pre><\/div><div id=\"question-8-6\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Nous allons maintenant \u00e9tudier un \u00e9ventuel inconv\u00e9nient de la statistique du test de Wilcoxon-Mann-Whitney. En utilisant le code suivant pour cr\u00e9er trois bo\u00eetes \u00e0 moustaches, montrant les vrais poids du r\u00e9gime 1 contre 4, puis deux versions modifi\u00e9es : une avec une diff\u00e9rence suppl\u00e9mentaire de 10 grammes et une avec une diff\u00e9rence suppl\u00e9mentaire de 100 grammes. Utilisez les x et y tels que d\u00e9finis ci-dessus, PAS ceux avec la valeur aberrante ajout\u00e9e.<\/p><div id=\"cb224\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb224-1\"><span class=\"fu\">library<\/span>(rafalib)<\/span>\n<span id=\"cb224-2\"><span class=\"fu\">mypar<\/span>(<span class=\"dv\">1<\/span>,<span class=\"dv\">3<\/span>)<\/span>\n<span id=\"cb224-3\"><span class=\"fu\">boxplot<\/span>(x,y)<\/span>\n<span id=\"cb224-4\"><span class=\"fu\">boxplot<\/span>(x,y<span class=\"sc\">+<\/span><span class=\"dv\">10<\/span>)<\/span>\n<span id=\"cb224-5\"><span class=\"fu\">boxplot<\/span>(x,y<span class=\"sc\">+<\/span><span class=\"dv\">100<\/span>)<\/span><\/code><\/pre><\/div><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15705 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-151-1-1024x731.png\" alt=\"\" width=\"1024\" height=\"731\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-151-1-1024x731.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-151-1-300x214.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-151-1-768x549.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-151-1-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-151-1-120x85.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-151-1-600x429.png 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/unnamed-chunk-151-1.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><p>Quelle est la diff\u00e9rence dans la statistique du test\u00a0t (obtenue par t.test(x,y)$statistic) entre l&rsquo;ajout de 10 et l&rsquo;ajout de 100 \u00e0 toutes les valeurs du groupe\u00a0y\u00a0? Prenez la statistique du test\u00a0t avec\u00a0x\u00a0et\u00a0y\u00a0+\u00a010\u00a0et soustrayez la statistique du test\u00a0t avec\u00a0x\u00a0et\u00a0y\u00a0+100. La valeur doit \u00eatre positive.<\/p><\/div><div class=\"answer\"><div id=\"cb225\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb225-1\"><span class=\"fu\">t.test<\/span>(x,y<span class=\"sc\">+<\/span><span class=\"dv\">10<\/span>)<span class=\"sc\">$<\/span>statistic <span class=\"sc\">-<\/span> <span class=\"fu\">t.test<\/span>(x,y<span class=\"sc\">+<\/span><span class=\"dv\">100<\/span>)<span class=\"sc\">$<\/span>statistic <\/span><\/code><\/pre><\/div><pre><code>##        t \n## 67.75097<\/code><\/pre><\/div><div id=\"question-9-6\" class=\"section level3 unnumbered\"><p class=\"hasAnchor\">Examinez la statistique du test de Wilcoxon pour x\u00a0et\u00a0y+10\u00a0et pour\u00a0x\u00a0et\u00a0y+100. \u00c9tant donn\u00e9 que le Wilcoxon fonctionne sur les rangs, une fois que les deux groupes montrent une s\u00e9paration compl\u00e8te, c&rsquo;est-\u00e0-dire que tous les points du groupe\u00a0y\u00a0sont sup\u00e9rieurs \u00e0 tous les points du groupe\u00a0x, la statistique ne changera pas, quelle que soit l&rsquo;ampleur de la diff\u00e9rence. De m\u00eame, la valeur p a une valeur minimale, quelle que soit la distance entre les groupes.<\/p><p class=\"hasAnchor\">Cela signifie que le test de Wilcoxon peut \u00eatre consid\u00e9r\u00e9 comme moins puissant que le test t dans certains contextes. En fait, pour les petits \u00e9chantillons, la valeur de p ne peut pas \u00eatre tr\u00e8s petite, m\u00eame lorsque la diff\u00e9rence est tr\u00e8s grande. Quelle est la valeur de p si nous comparons\u00a0c(1,2,3)\u00a0\u00e0\u00a0c(4,5,6) \u00e0 l&rsquo;aide d&rsquo;un test de Wilcoxon\u00a0?<\/p><div class=\"answer\"><div id=\"cb227\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb227-1\"><span class=\"fu\">wilcox.test<\/span>(x,y<span class=\"sc\">+<\/span><span class=\"dv\">10<\/span>)<span class=\"sc\">$<\/span>p.value<\/span><\/code><\/pre><\/div><pre><code>## Warning in wilcox.test.default(x, y + 10): cannot compute exact p-\n## value with ties<\/code><\/pre><pre><code>## [1] 5.032073e-05<\/code><\/pre><div id=\"cb230\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb230-1\"><span class=\"fu\">wilcox.test<\/span>(x,y<span class=\"sc\">+<\/span><span class=\"dv\">100<\/span>)<span class=\"sc\">$<\/span>p.value<\/span><\/code><\/pre><\/div><pre><code>## Warning in wilcox.test.default(x, y + 100): cannot compute exact p-\n## value with ties<\/code><\/pre><pre><code>## [1] 5.032073e-05<\/code><\/pre><div id=\"cb233\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb233-1\"><span class=\"fu\">wilcox.test<\/span>(<span class=\"fu\">c<\/span>(<span class=\"dv\">1<\/span>,<span class=\"dv\">2<\/span>,<span class=\"dv\">3<\/span>),<span class=\"fu\">c<\/span>(<span class=\"dv\">4<\/span>,<span class=\"dv\">5<\/span>,<span class=\"dv\">6<\/span>))<span class=\"sc\">$<\/span>p.value <span class=\"co\"># Answer<\/span><\/span><\/code><\/pre><\/div><pre><code>## [1] 0.1<\/code><\/pre><\/div><div id=\"question-10-5\" class=\"section level3 unnumbered\"><div class=\"question\"><p>Quelle est la valeur de p si nous comparons\u00a0c(1,2,3)\u00a0\u00e0\u00a0c(400\u00a0500\u00a0600) \u00e0 l&rsquo;aide d&rsquo;un test de Wilcoxon\u00a0?<\/p><\/div><div class=\"answer\"><div id=\"cb235\" class=\"sourceCode\"><pre class=\"sourceCode r\"><code class=\"sourceCode r\"><span id=\"cb235-1\"><span class=\"fu\">wilcox.test<\/span>(<span class=\"fu\">c<\/span>(<span class=\"dv\">1<\/span>,<span class=\"dv\">2<\/span>,<span class=\"dv\">3<\/span>),<span class=\"fu\">c<\/span>(<span class=\"dv\">400<\/span>,<span class=\"dv\">500<\/span>,<span class=\"dv\">600<\/span>))<span class=\"sc\">$<\/span>p.value<\/span><\/code><\/pre><\/div><pre><code>## [1] 0.1<\/code><\/pre><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>An\u00e1lisis descriptivo P\u00e1gina de inicio Wiki Ejercicios respondidos sobre An\u00e1lisis exploratorio de datos Esta p\u00e1gina presenta dos ejercicios corregidos y detallados con el c\u00f3digo Python sobre\u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":15506,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-15694","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15694","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=15694"}],"version-history":[{"count":9,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15694\/revisions"}],"predecessor-version":[{"id":20687,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15694\/revisions\/20687"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15506"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=15694"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}