{"id":3229,"date":"2023-07-18T13:59:04","date_gmt":"2023-07-18T13:59:04","guid":{"rendered":"https:\/\/statorials.org\/tr\/python-normallik-testi\/"},"modified":"2023-07-18T13:59:04","modified_gmt":"2023-07-18T13:59:04","slug":"python-normallik-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/python-normallik-testi\/","title":{"rendered":"Python&#39;da normallik nas\u0131l test edilir (4 y\u00f6ntem)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Bir\u00e7ok istatistiksel test, veri setlerinin normal \u015fekilde da\u011f\u0131ld\u0131\u011f\u0131n\u0131 <a href=\"https:\/\/statorials.org\/tr\/normallik-hipotezi\/\" target=\"_blank\" rel=\"noopener\">varsayar<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Python&#8217;da bu hipotezi kontrol etmenin d\u00f6rt yayg\u0131n yolu vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. (G\u00f6rsel y\u00f6ntem) Bir histogram olu\u015fturun.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Histogram yakla\u015f\u0131k olarak &#8220;\u00e7an&#8221; \u015feklindeyse verilerin normal da\u011f\u0131ld\u0131\u011f\u0131 varsay\u0131l\u0131r.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. (G\u00f6rsel y\u00f6ntem) Bir QQ grafi\u011fi olu\u015fturun.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Grafikteki noktalar kabaca d\u00fcz bir \u00e7apraz \u00e7izgi boyunca uzan\u0131yorsa, verilerin normal da\u011f\u0131ld\u0131\u011f\u0131 varsay\u0131l\u0131r.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>3. (Resmi istatistiksel test) Shapiro-Wilk testi yap\u0131n.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Testin p de\u011feri \u03b1 = 0,05&#8217;ten b\u00fcy\u00fckse verilerin normal da\u011f\u0131ld\u0131\u011f\u0131 varsay\u0131l\u0131r.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>4. (Resmi istatistiksel test) Kolmogorov-Smirnov testini yap\u0131n.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Testin p de\u011feri \u03b1 = 0,05&#8217;ten b\u00fcy\u00fckse verilerin normal da\u011f\u0131ld\u0131\u011f\u0131 varsay\u0131l\u0131r.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler bu y\u00f6ntemlerin her birinin pratikte nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Y\u00f6ntem 1: Histogram Olu\u015fturma<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, <a href=\"https:\/\/statorials.org\/tr\/normal-gunluk-python-dagilimi\/\" target=\"_blank\" rel=\"noopener\">log-normal da\u011f\u0131l\u0131m\u0131<\/a> izleyen bir veri k\u00fcmesi i\u00e7in histogram\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> math\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> lognorm\n<span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>n.p. <span style=\"color: #3366ff;\">random<\/span> . <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#generate dataset that contains 1000 log-normal distributed values\n<\/span>lognorm_dataset = lognorm. <span style=\"color: #3366ff;\">rvs<\/span> (s=.5, scale= <span style=\"color: #3366ff;\">math.exp<\/span> (1), size=1000)\n\n<span style=\"color: #008080;\">#create histogram to visualize values in dataset\n<\/span>plt. <span style=\"color: #3366ff;\">hist<\/span> (lognorm_dataset, edgecolor=' <span style=\"color: #ff0000;\">black<\/span> ', bins=20)<\/span><\/span><\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-27387 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normalitepython1.jpg\" alt=\"\" width=\"559\" height=\"364\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Sadece bu histograma bakarak veri setinin \u201c\u00e7an \u015fekli\u201d sergilemedi\u011fini ve normal da\u011f\u0131lmad\u0131\u011f\u0131n\u0131 s\u00f6yleyebiliriz.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Y\u00f6ntem 2: QQ Grafi\u011fi Olu\u015fturma<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, log-normal da\u011f\u0131l\u0131m\u0131 izleyen bir veri k\u00fcmesi i\u00e7in QQ grafi\u011finin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> math\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> lognorm\n<span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n<span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>n.p. <span style=\"color: #3366ff;\">random<\/span> . <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#generate dataset that contains 1000 log-normal distributed values\n<\/span>lognorm_dataset = lognorm. <span style=\"color: #3366ff;\">rvs<\/span> (s=.5, scale= <span style=\"color: #3366ff;\">math.exp<\/span> (1), size=1000)\n\n<span style=\"color: #008080;\">#create QQ plot with 45-degree line added to plot\n<\/span>fig = sm. <span style=\"color: #3366ff;\">qqplot<\/span> (lognorm_dataset, line=' <span style=\"color: #ff0000;\">45<\/span> ')\n\nplt. <span style=\"color: #3366ff;\">show<\/span> ()\n<\/span><\/span><\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-27390 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normalitepython2.jpg\" alt=\"\" width=\"533\" height=\"359\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u00c7izim noktalar\u0131 yakla\u015f\u0131k olarak d\u00fcz bir \u00e7apraz \u00e7izgi boyunca uzan\u0131yorsa, genellikle bir veri k\u00fcmesinin normal \u015fekilde da\u011f\u0131ld\u0131\u011f\u0131n\u0131 varsayar\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak bu grafikteki noktalar a\u00e7\u0131k\u00e7a k\u0131rm\u0131z\u0131 \u00e7izgiye kar\u015f\u0131l\u0131k gelmiyor, dolay\u0131s\u0131yla bu veri setinin normal da\u011f\u0131ld\u0131\u011f\u0131n\u0131 varsayamay\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Verileri log-normal da\u011f\u0131l\u0131m fonksiyonunu kullanarak olu\u015fturdu\u011fumuz g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, bu mant\u0131kl\u0131 olmal\u0131d\u0131r.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Y\u00f6ntem 3: Shapiro-Wilk testi ger\u00e7ekle\u015ftirin<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, log-normal da\u011f\u0131l\u0131m\u0131 izleyen bir veri k\u00fcmesi i\u00e7in Shapiro-Wilk&#8217;in nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> math\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy.stats <span style=\"color: #008000;\">import<\/span> shapiro \n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> lognorm\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>n.p. <span style=\"color: #3366ff;\">random<\/span> . <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#generate dataset that contains 1000 log-normal distributed values\n<\/span>lognorm_dataset = lognorm. <span style=\"color: #3366ff;\">rvs<\/span> (s=.5, scale= <span style=\"color: #3366ff;\">math.exp<\/span> (1), size=1000)\n\n<span style=\"color: #008080;\">#perform Shapiro-Wilk test for normality\n<\/span>shapiro(lognorm_dataset)\n\nShapiroResult(statistic=0.8573324680328369, pvalue=3.880663073872444e-29)\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Sonu\u00e7tan test istatisti\u011finin <strong>0,857<\/strong> oldu\u011funu ve buna kar\u015f\u0131l\u0131k gelen p de\u011ferinin <strong>3,88e-29<\/strong> (s\u0131f\u0131ra son derece yak\u0131n) oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">P de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan Shapiro-Wilk testinin s\u0131f\u0131r hipotezini reddediyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u00f6rnek verilerin normal da\u011f\u0131l\u0131mdan gelmedi\u011fini s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Y\u00f6ntem 4: Kolmogorov-Smirnov testi yap\u0131n<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, log-normal da\u011f\u0131l\u0131m\u0131 izleyen bir veri k\u00fcmesi i\u00e7in Kolmogorov-Smirnov testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> math\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy.stats <span style=\"color: #008000;\">import<\/span> kstest\n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> lognorm\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>n.p. <span style=\"color: #3366ff;\">random<\/span> . <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#generate dataset that contains 1000 log-normal distributed values\n<\/span>lognorm_dataset = lognorm. <span style=\"color: #3366ff;\">rvs<\/span> (s=.5, scale= <span style=\"color: #3366ff;\">math.exp<\/span> (1), size=1000)\n\n<span style=\"color: #008080;\">#perform Kolmogorov-Smirnov test for normality\n<\/span>kstest(lognorm_dataset, ' <span style=\"color: #ff0000;\">norm<\/span> ')\n\nKstestResult(statistic=0.84125708308077, pvalue=0.0)\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Sonu\u00e7tan test istatisti\u011finin <strong>0,841<\/strong> ve buna kar\u015f\u0131l\u0131k gelen p de\u011ferinin <strong>0,0<\/strong> oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">P de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan Kolmogorov-Smirnov testinin s\u0131f\u0131r hipotezini reddediyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u00f6rnek verilerin normal da\u011f\u0131l\u0131mdan gelmedi\u011fini s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<h3> <strong>Normal olmayan veriler nas\u0131l i\u015flenir?<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir veri k\u00fcmesi normal \u015fekilde <em>da\u011f\u0131lm\u0131yorsa<\/em> , onu daha normal bir \u015fekilde da\u011f\u0131tmak i\u00e7in genellikle a\u015fa\u011f\u0131daki d\u00f6n\u00fc\u015f\u00fcmlerden birini ger\u00e7ekle\u015ftirebiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Log d\u00f6n\u00fc\u015f\u00fcm\u00fc:<\/strong> x de\u011ferlerini <strong>log(x)&#8217;<\/strong> e d\u00f6n\u00fc\u015ft\u00fcr\u00fcn.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Karek\u00f6k d\u00f6n\u00fc\u015f\u00fcm\u00fc:<\/strong> x&#8217;in de\u011ferlerini <strong><span style=\"border-top: 1px solid black;\">\u221ax&#8217;e<\/span><\/strong> d\u00f6n\u00fc\u015ft\u00fcr\u00fcn.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. K\u00fcp k\u00f6k d\u00f6n\u00fc\u015f\u00fcm\u00fc:<\/strong> x&#8217;in de\u011ferlerini <strong>x <sup>1\/3&#8217;e<\/sup><\/strong> d\u00f6n\u00fc\u015ft\u00fcr\u00fcn.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu d\u00f6n\u00fc\u015f\u00fcmlerin ger\u00e7ekle\u015ftirilmesiyle veri k\u00fcmesi genel olarak daha normal da\u011f\u0131lm\u0131\u015f hale gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu d\u00f6n\u00fc\u015f\u00fcmlerin Python&#8217;da nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6rmek i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/pythonda-verileri-donusturme\/\" target=\"_blank\" rel=\"noopener noreferrer\">bu \u00f6\u011freticiyi<\/a> okuyun.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir\u00e7ok istatistiksel test, veri setlerinin normal \u015fekilde da\u011f\u0131ld\u0131\u011f\u0131n\u0131 varsayar . Python&#8217;da bu hipotezi kontrol etmenin d\u00f6rt yayg\u0131n yolu vard\u0131r: 1. (G\u00f6rsel y\u00f6ntem) Bir histogram olu\u015fturun. Histogram yakla\u015f\u0131k olarak &#8220;\u00e7an&#8221; \u015feklindeyse verilerin normal da\u011f\u0131ld\u0131\u011f\u0131 varsay\u0131l\u0131r. 2. (G\u00f6rsel y\u00f6ntem) Bir QQ grafi\u011fi olu\u015fturun. Grafikteki noktalar kabaca d\u00fcz bir \u00e7apraz \u00e7izgi boyunca uzan\u0131yorsa, verilerin normal da\u011f\u0131ld\u0131\u011f\u0131 varsay\u0131l\u0131r. 3. [&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-3229","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>Python&#039;da Normallik Nas\u0131l Test Edilir (4 Y\u00f6ntem) - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde Python&#039;da normalli\u011fin nas\u0131l test edilece\u011fi 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\/python-normallik-testi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python&#039;da Normallik Nas\u0131l Test Edilir (4 Y\u00f6ntem) - Statorials\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde Python&#039;da normalli\u011fin nas\u0131l test edilece\u011fi birka\u00e7 \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/python-normallik-testi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-18T13:59:04+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normalitepython1.jpg\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/python-normallik-testi\/\",\"url\":\"https:\/\/statorials.org\/tr\/python-normallik-testi\/\",\"name\":\"Python&#39;da Normallik Nas\u0131l Test Edilir (4 Y\u00f6ntem) - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-18T13:59:04+00:00\",\"dateModified\":\"2023-07-18T13:59:04+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde Python&#39;da normalli\u011fin nas\u0131l test edilece\u011fi birka\u00e7 \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/python-normallik-testi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/python-normallik-testi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/python-normallik-testi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Python&#39;da normallik nas\u0131l test edilir (4 y\u00f6ntem)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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