{"id":915,"date":"2023-07-28T07:59:26","date_gmt":"2023-07-28T07:59:26","guid":{"rendered":"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/"},"modified":"2023-07-28T07:59:26","modified_gmt":"2023-07-28T07:59:26","slug":"odleglosc-mahalanobisa-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/","title":{"rendered":"Jak obliczy\u0107 odleg\u0142o\u015b\u0107 mahalanobisa w r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Odleg\u0142o\u015b\u0107 Mahalanobisa<\/strong> to odleg\u0142o\u015b\u0107 mi\u0119dzy dwoma punktami w przestrzeni wielowymiarowej.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Jest cz\u0119sto u\u017cywany do wykrywania warto\u015bci odstaj\u0105cych w analizach statystycznych obejmuj\u0105cych wiele zmiennych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym samouczku wyja\u015bniono, jak obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa w R.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Przyk\u0142ad: odleg\u0142o\u015b\u0107 Mahalanobisa w R<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Wykonaj poni\u017csze kroki, aby obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa dla ka\u017cdej <a href=\"https:\/\/statorials.org\/pl\/obserwacja-w-statystyce\/\" target=\"_blank\" rel=\"noopener\">obserwacji<\/a> w zbiorze danych w R.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 1: Utw\u00f3rz zbi\u00f3r danych.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Najpierw utworzymy zbi\u00f3r danych, kt\u00f3ry wy\u015bwietli wyniki egzamin\u00f3w 20 uczni\u00f3w, liczb\u0119 godzin sp\u0119dzonych na nauce, liczb\u0119 zdanych egzamin\u00f3w pr\u00f3bnych i ich obecn\u0105 ocen\u0119 z kursu:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data<\/span>\ndf = data.frame(score = c(91, 93, 72, 87, 86, 73, 68, 87, 78, 99, 95, 76, 84, 96, 76, 80, 83, 84, 73, 74) ,\n        hours = c(16, 6, 3, 1, 2, 3, 2, 5, 2, 5, 2, 3, 4, 3, 3, 3, 4, 3, 4, 4),\n        prep = c(3, 4, 0, 3, 4, 0, 1, 2, 1, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2),\n        grade = c(70, 88, 80, 83, 88, 84, 78, 94, 90, 93, 89, 82, 95, 94, 81, 93, 93, 90, 89, 89))\n\n<span style=\"color: #008080;\">#view first six rows of data\n<\/span>head(df)\n\n  score hours prep grade\n1 91 16 3 70\n2 93 6 4 88\n3 72 3 0 80\n4 87 1 3 83\n5 86 2 4 88\n6 73 3 0 84\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Krok 2: Oblicz odleg\u0142o\u015b\u0107 Mahalanobisa dla ka\u017cdej obserwacji.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie u\u017cyjemy wbudowanej w R funkcji <a href=\"https:\/\/stat.ethz.ch\/R-manual\/R-devel\/library\/stats\/html\/mahalanobis.html\" target=\"_blank\" rel=\"noopener noreferrer\">mahalanobis()<\/a> do obliczenia odleg\u0142o\u015bci Mahalanobisa dla ka\u017cdej obserwacji, stosuj\u0105c nast\u0119puj\u0105c\u0105 sk\u0142adni\u0119:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">mahalanobis (x, \u015brodek, cov)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x:<\/strong> macierz danych<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u015brodek:<\/strong> \u015bredni wektor rozk\u0142adu<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>cov:<\/strong> macierz kowariancji rozk\u0142adu<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak zaimplementowa\u0107 t\u0119 funkcj\u0119 dla naszego zbioru danych:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate Mahalanobis distance for each observation<\/span>\nmahalanobis(df, colMeans(df), cov(df))\n\n [1] 16.5019630 2.6392864 4.8507973 5.2012612 3.8287341 4.0905633\n [7] 4.2836303 2.4198736 1.6519576 5.6578253 3.9658770 2.9350178\n[13] 2.8102109 4.3682945 1.5610165 1.4595069 2.0245748 0.7502536\n[19] 2.7351292 2.2642268\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Krok 3: Oblicz warto\u015b\u0107 p dla ka\u017cdej odleg\u0142o\u015bci Mahalanobisa.<\/strong><\/span> <\/p>\n<div id=\"mv-first-video\" class=\"mv-video-target mv-video__featured mv-video__optimized mv-video__embedded\" data-video-id=\"tmdycgxksxqpmqpu0vbx\" data-autoplay=\"true\" data-automobile=\"true\" data-muted=\"true\" data-sticky=\"true\" data-autoinsert=\"true\" data-disable-jsonld=\"true\" data-video-placement-inited=\"true\">\n<div id=\"mediavine-video__target-div__8330b88d-7ed9-463c-85d3-dc370a4c9ab3\" class=\"mediavine-video__target-div\">\n<div class=\"mediavine-video__root-container\">\n<div class=\"mediavine-video__placement-container mediavine-video__bottom mediavine-video__right mediavine-video__dark-theme\">\n<div class=\"mediavine-video__title-bar\">\n<p> <span style=\"color: #000000;\">Widzimy, \u017ce niekt\u00f3re odleg\u0142o\u015bci Mahalanobisa s\u0105 znacznie wi\u0119ksze ni\u017c inne.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby okre\u015bli\u0107, czy kt\u00f3rakolwiek z odleg\u0142o\u015bci jest istotna statystycznie, musimy obliczy\u0107 ich <a href=\"https:\/\/statorials.org\/pl\/p-oznacza-istotnosc-statystyczna\/\" target=\"_blank\" rel=\"noopener\">warto\u015bci p<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 p dla ka\u017cdej odleg\u0142o\u015bci oblicza si\u0119 jako warto\u015b\u0107 p odpowiadaj\u0105c\u0105 statystyce chi-kwadrat odleg\u0142o\u015bci Mahalanobisa z k-1 stopniami swobody, gdzie k = liczba zmiennych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zatem w tym przypadku u\u017cyjemy stopni swobody 4-1 = 3.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create new column in data frame to hold Mahalanobis distances<\/span>\ndf$mahal &lt;- mahalanobis(df, colMeans(df), cov(df))\n\n<span style=\"color: #008080;\">#create new column in data frame to hold p-value for each Mahalanobis distance\n<\/span>df$p &lt;- <span style=\"color: #3366ff;\">pchisq<\/span> (df$mahal, df= <span style=\"color: #339966;\">3<\/span> , lower.tail=FALSE)\n\n<span style=\"color: #008080;\">#view data frame\n<\/span>df\n\n   score hours prep grade mahal p\n1 91 16 3 70 16.5019630 0.0008945642\n2 93 6 4 88 2.6392864 0.4506437265\n3 72 3 0 80 4.8507973 0.1830542407\n4 87 1 3 83 5.2012612 0.1576392526\n5 86 2 4 88 3.8287341 0.2805615121\n6 73 3 0 84 4.0905633 0.2518495222\n7 68 2 1 78 4.2836303 0.2324211504\n8 87 5 2 94 2.4198736 0.4899458807\n9 78 2 1 90 1.6519576 0.6476670033\n10 99 5 2 93 5.6578253 0.1294978092\n11 95 2 3 89 3.9658770 0.2651724541\n12 76 3 3 82 2.9350178 0.4017530495\n13 84 4 3 95 2.8102109 0.4218217836\n14 96 3 2 94 4.3682945 0.2243432904\n15 76 3 2 81 1.5610165 0.6682610031\n16 80 3 2 93 1.4595069 0.6916471506\n17 83 4 3 93 2.0245748 0.5673218169\n18 84 3 3 90 0.7502536 0.8613248635\n19 73 4 2 89 2.7351292 0.4342904353\n20 74 4 2 89 2.2642268 0.5194087143\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Og\u00f3lnie rzecz bior\u0105c, warto\u015b\u0107 p <strong>mniejsza ni\u017c 0,001<\/strong> jest uwa\u017cana za warto\u015b\u0107 odstaj\u0105c\u0105.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Widzimy, \u017ce pierwsza obserwacja jest warto\u015bci\u0105 odstaj\u0105c\u0105 w zbiorze danych, poniewa\u017c ma warto\u015b\u0107 p mniejsz\u0105 ni\u017c 0,001.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W zale\u017cno\u015bci od kontekstu problemu mo\u017cesz podj\u0105\u0107 decyzj\u0119 o usuni\u0119ciu tej obserwacji ze zbioru danych, poniewa\u017c jest to warto\u015b\u0107 odstaj\u0105ca i mo\u017ce mie\u0107 wp\u0142yw na wyniki analizy.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\"><b>Powi\u0105zane:<\/b><\/span> <a href=\"https:\/\/statorials.org\/pl\/wielowymiarowy-test-normalnosci-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak wykonywa\u0107 wielowymiarowe testy normalno\u015bci w R<\/a><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Odleg\u0142o\u015b\u0107 Mahalanobisa to odleg\u0142o\u015b\u0107 mi\u0119dzy dwoma punktami w przestrzeni wielowymiarowej. Jest cz\u0119sto u\u017cywany do wykrywania warto\u015bci odstaj\u0105cych w analizach statystycznych obejmuj\u0105cych wiele zmiennych. W tym samouczku wyja\u015bniono, jak obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa w R. Przyk\u0142ad: odleg\u0142o\u015b\u0107 Mahalanobisa w R Wykonaj poni\u017csze kroki, aby obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa dla ka\u017cdej obserwacji w zbiorze danych w R. Krok 1: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-915","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa w R - Statologia<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie, jak obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa w R, z przyk\u0142adem.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa w R - Statologia\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie, jak obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa w R, z przyk\u0142adem.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T07:59:26+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/\",\"url\":\"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/\",\"name\":\"Jak obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa w R - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-28T07:59:26+00:00\",\"dateModified\":\"2023-07-28T07:59:26+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie, jak obliczy\u0107 odleg\u0142o\u015b\u0107 Mahalanobisa w R, z przyk\u0142adem.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/odleglosc-mahalanobisa-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 odleg\u0142o\u015b\u0107 mahalanobisa w r\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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