{"id":1145,"date":"2023-07-27T12:35:01","date_gmt":"2023-07-27T12:35:01","guid":{"rendered":"https:\/\/statorials.org\/tr\/rde-asimetri-basikligi\/"},"modified":"2023-07-27T12:35:01","modified_gmt":"2023-07-27T12:35:01","slug":"rde-asimetri-basikligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rde-asimetri-basikligi\/","title":{"rendered":"R&#39;de \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131k nas\u0131l hesaplan\u0131r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistikte <strong>\u00e7arp\u0131kl\u0131k<\/strong> ve <strong>bas\u0131kl\u0131k<\/strong> bir da\u011f\u0131l\u0131m\u0131n \u015feklini \u00f6l\u00e7menin iki yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7arp\u0131kl\u0131k<\/strong> , bir da\u011f\u0131l\u0131m\u0131n \u00e7arp\u0131kl\u0131\u011f\u0131n\u0131n bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Bu de\u011fer pozitif ya da negatif olabilir.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Negatif \u00e7arp\u0131kl\u0131k, kuyru\u011fun da\u011f\u0131l\u0131m\u0131n sol taraf\u0131nda oldu\u011funu ve daha negatif de\u011ferlere do\u011fru uzand\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Pozitif bir \u00e7arp\u0131kl\u0131k, kuyru\u011fun da\u011f\u0131l\u0131m\u0131n sa\u011f taraf\u0131nda oldu\u011funu ve daha pozitif de\u011ferlere do\u011fru uzand\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">S\u0131f\u0131r de\u011feri, da\u011f\u0131l\u0131mda asimetri olmad\u0131\u011f\u0131n\u0131, yani da\u011f\u0131l\u0131m\u0131n tamamen simetrik oldu\u011funu g\u00f6sterir.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Bas\u0131kl\u0131k,<\/strong> bir da\u011f\u0131l\u0131m\u0131n normal da\u011f\u0131l\u0131ma g\u00f6re a\u011f\u0131r m\u0131 yoksa hafif kuyruklu mu oldu\u011funun \u00f6l\u00e7\u00fcs\u00fcd\u00fcr.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Normal da\u011f\u0131l\u0131m\u0131n bas\u0131kl\u0131\u011f\u0131 3&#8217;t\u00fcr.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Belirli bir da\u011f\u0131l\u0131m\u0131n bas\u0131kl\u0131\u011f\u0131 3&#8217;ten k\u00fc\u00e7\u00fckse buna <em>playkurtic<\/em> denir, bu da normal da\u011f\u0131l\u0131ma g\u00f6re giderek daha az u\u00e7 de\u011ferler \u00fcretme e\u011filiminde oldu\u011fu anlam\u0131na gelir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Belirli bir da\u011f\u0131l\u0131m\u0131n bas\u0131kl\u0131\u011f\u0131 3&#8217;ten b\u00fcy\u00fckse buna <em>leptokurtik<\/em> denir, bu da normal da\u011f\u0131l\u0131mdan daha fazla ayk\u0131r\u0131 de\u011fer \u00fcretme e\u011filiminde oldu\u011fu anlam\u0131na gelir.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Not:<\/strong> Baz\u0131 form\u00fcller (Fisher tan\u0131m\u0131), normal da\u011f\u0131l\u0131mla kar\u015f\u0131la\u015ft\u0131rmay\u0131 kolayla\u015ft\u0131rmak i\u00e7in bas\u0131kl\u0131ktan 3 \u00e7\u0131kar\u0131r. Bu tan\u0131m\u0131 kullanarak, bas\u0131kl\u0131k de\u011feri 0&#8217;dan b\u00fcy\u00fck olan bir da\u011f\u0131l\u0131m normal da\u011f\u0131l\u0131ma g\u00f6re daha b\u00fcy\u00fck bas\u0131kl\u0131\u011fa sahip olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde, R&#8217;de belirli bir veri k\u00fcmesinin hem \u00e7arp\u0131kl\u0131\u011f\u0131n\u0131n hem de bas\u0131kl\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: R&#8217;de \u00c7arp\u0131kl\u0131k ve D\u00fczle\u015fme<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>data = c(88, 95, 92, 97, 96, 97, 94, 86, 91, 95, 97, 88, 85, 76, 68)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Bu veri k\u00fcmesindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 bir histogram olu\u015fturarak h\u0131zl\u0131 bir \u015fekilde g\u00f6rselle\u015ftirebiliriz:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>hist(data, col=' <span style=\"color: #008000;\">steelblue<\/span> ')<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11471 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/biaisr1.png\" alt=\"R'de \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131k\" width=\"440\" height=\"440\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Histogram bize da\u011f\u0131l\u0131m\u0131n sola \u00e7arp\u0131k g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc g\u00f6steriyor. Yani de\u011ferlerin daha b\u00fcy\u00fck bir k\u0131sm\u0131 da\u011f\u0131l\u0131m\u0131n sa\u011f taraf\u0131nda yo\u011funla\u015fm\u0131\u015ft\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu veri k\u00fcmesinin \u00e7arp\u0131kl\u0131\u011f\u0131n\u0131 ve bas\u0131kl\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in R&#8217;deki <strong>moment<\/strong> k\u00fct\u00fcphanesindeki <strong>skewness()<\/strong> ve <strong>bas\u0131kl\u0131k()<\/strong> i\u015flevlerini kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #993300;\">library<\/span> (moments)\n<\/span><\/span><span style=\"color: #008080;\">\n#calculate skewness<\/span>\nskewness(data)\n\n[1] -1.391777\n\n<span style=\"color: #008080;\">#calculate kurtosis<\/span>\nkurtosis(data)\n\n[1] 4.177865\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u00c7arp\u0131kl\u0131k <strong>-1,391777<\/strong> ve bas\u0131kl\u0131k <b>4,177865<\/b> olarak ortaya \u00e7\u0131k\u0131yor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c7arp\u0131kl\u0131\u011f\u0131n negatif olmas\u0131 da\u011f\u0131l\u0131m\u0131n \u00e7arp\u0131k kald\u0131\u011f\u0131n\u0131 g\u00f6sterir. Bu histogramda g\u00f6rd\u00fcklerimizi do\u011fruluyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bas\u0131kl\u0131\u011f\u0131n 3&#8217;ten b\u00fcy\u00fck olmas\u0131, da\u011f\u0131l\u0131m\u0131n normal da\u011f\u0131l\u0131ma g\u00f6re kuyruklarda daha fazla de\u011fere sahip oldu\u011funu g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Momentler<\/strong> kitapl\u0131\u011f\u0131 ayr\u0131ca, \u00f6rnek verilerin normal da\u011f\u0131l\u0131mla tutarl\u0131 \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131k g\u00f6sterip g\u00f6stermedi\u011fini belirleyen bir uyum iyili\u011fi testi ger\u00e7ekle\u015ftiren <strong>jarque.test()<\/strong> i\u015flevini de sunar. Bu testin s\u0131f\u0131r ve alternatif hipotezleri a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bo\u015f hipotez<\/strong> : Veri seti normal da\u011f\u0131l\u0131ma kar\u015f\u0131l\u0131k gelen \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131\u011fa sahiptir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Alternatif hipotez<\/strong> : Veri k\u00fcmesinde normal da\u011f\u0131l\u0131ma <em>uymayan<\/em> \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131k var.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod bu testin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong>jarque.test(data)\n\n\tJarque-Bera Normality Test\n\ndata:data\nJB = 5.7097, p-value = 0.05756\nalternative hypothesis: greater\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Testin p de\u011feri <strong>0,05756<\/strong> olarak \u00e7\u0131k\u0131yor. Bu de\u011fer \u03b1 = 0,05&#8217;ten k\u00fc\u00e7\u00fck olmad\u0131\u011f\u0131 i\u00e7in s\u0131f\u0131r hipotezini reddedemiyoruz. Bu veri setinin normal da\u011f\u0131l\u0131mdan farkl\u0131 \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131\u011fa sahip oldu\u011funu s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z yok.<\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>Moments<\/strong> Library belgelerinin tamam\u0131n\u0131 <a href=\"https:\/\/cran.r-project.org\/web\/packages\/moments\/moments.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">burada<\/a> bulabilirsiniz.<\/span><\/em><\/p>\n<h3> <strong>Bonus: \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131k hesaplay\u0131c\u0131s\u0131<\/strong><\/h3>\n<p> Ayr\u0131ca belirli bir veri k\u00fcmesi i\u00e7in \u00e7arp\u0131kl\u0131\u011f\u0131 ve bas\u0131kl\u0131\u011f\u0131 otomatik olarak hesaplayan <a href=\"https:\/\/statorials.org\/tr\" target=\"_blank\" rel=\"noopener noreferrer\">\u0130statistiksel \u00c7arp\u0131kl\u0131k ve Bas\u0131kl\u0131k Hesaplay\u0131c\u0131&#8217;y\u0131<\/a> <span style=\"color: #000000;\">kullanarak belirli bir veri k\u00fcmesi i\u00e7in \u00e7arp\u0131kl\u0131\u011f\u0131 hesaplayabilirsiniz<\/span> <span style=\"color: #000000;\">.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistikte \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131k bir da\u011f\u0131l\u0131m\u0131n \u015feklini \u00f6l\u00e7menin iki yoludur. \u00c7arp\u0131kl\u0131k , bir da\u011f\u0131l\u0131m\u0131n \u00e7arp\u0131kl\u0131\u011f\u0131n\u0131n bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Bu de\u011fer pozitif ya da negatif olabilir. Negatif \u00e7arp\u0131kl\u0131k, kuyru\u011fun da\u011f\u0131l\u0131m\u0131n sol taraf\u0131nda oldu\u011funu ve daha negatif de\u011ferlere do\u011fru uzand\u0131\u011f\u0131n\u0131 g\u00f6sterir. Pozitif bir \u00e7arp\u0131kl\u0131k, kuyru\u011fun da\u011f\u0131l\u0131m\u0131n sa\u011f taraf\u0131nda oldu\u011funu ve daha pozitif de\u011ferlere do\u011fru uzand\u0131\u011f\u0131n\u0131 g\u00f6sterir. S\u0131f\u0131r de\u011feri, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1145","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R - Statorialsde \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131k nas\u0131l hesaplan\u0131r?<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, R&#039;de belirli bir veri k\u00fcmesi i\u00e7in \u00e7arp\u0131kl\u0131k ve bas\u0131kl\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131 birka\u00e7 \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/tr\/rde-asimetri-basikligi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R - 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