{"id":1395,"date":"2023-07-26T13:44:31","date_gmt":"2023-07-26T13:44:31","guid":{"rendered":"https:\/\/statorials.org\/tr\/morans-ben\/"},"modified":"2023-07-26T13:44:31","modified_gmt":"2023-07-26T13:44:31","slug":"morans-ben","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/morans-ben\/","title":{"rendered":"Moran&#39;\u0131n benli\u011fi nedir? (tan\u0131m &amp; #038; \u00f6rnek)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Moran&#8217;s I,<\/strong> uzaysal otokorelasyonu \u00f6l\u00e7menin bir yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Basit\u00e7e s\u00f6ylemek gerekirse, de\u011ferlerin 2 boyutlu alanda ne kadar yak\u0131n k\u00fcmelendi\u011fini \u00f6l\u00e7menin bir yoludur. Co\u011frafya ve <a href=\"https:\/\/en.wikipedia.org\/wiki\/Geographic_information_science\" target=\"_blank\" rel=\"noopener\">co\u011frafi bilgi biliminde (GIS),<\/a> hane geliri, e\u011fitim d\u00fczeyi vb. gibi farkl\u0131 \u00f6zelliklerin bir harita \u00fczerinde ne kadar yak\u0131ndan grupland\u0131r\u0131ld\u0131\u011f\u0131n\u0131 \u00f6l\u00e7mek i\u00e7in s\u0131kl\u0131kla kullan\u0131l\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Moran&#8217;\u0131n I: form\u00fcl\u00fc<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Moran&#8217;\u0131n I&#8217;ini hesaplamak i\u00e7in form\u00fcl:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>ben<\/em> = (N\/W)*\u03a3\u03a3w <sub>ij<\/sub> ( <sub>x<\/sub> ben \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> )(x <sub>j<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> )\/\u03a3(x <sub>i<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> ) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>N:<\/strong> <em>i<\/em> ve <em>j<\/em> taraf\u0131ndan indekslenen mekansal birimlerin say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>W:<\/strong> T\u00fcm w <sub>ij&#8217;lerin<\/sub> toplam\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x:<\/strong> \u0130lgi de\u011fi\u015fkeni (hane halk\u0131 geliri, e\u011fitim y\u0131l\u0131 vb.)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span> :<\/strong> x&#8217;in ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>w <sub>ij<\/sub> :<\/strong> Uzaysal a\u011f\u0131rl\u0131klar\u0131n matrisi<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00c7o\u011fu istatistik yaz\u0131l\u0131m\u0131 bunu sizin i\u00e7in hesaplayabilece\u011finden muhtemelen bu \u00f6l\u00e7\u00fcm\u00fc hi\u00e7bir zaman elle hesaplamak zorunda kalmayacaks\u0131n\u0131z, ancak temel olarak kullan\u0131lan form\u00fcl\u00fc bilmek yard\u0131mc\u0131 olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Moran I&#8217;in de\u011feri -1 ile 1 aras\u0131nda de\u011fi\u015febilir; burada:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>-1:<\/strong> \u0130lgilenilen de\u011fi\u015fken m\u00fckemmel \u015fekilde da\u011f\u0131lm\u0131\u015ft\u0131r<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>0:<\/strong> ilgilenilen de\u011fi\u015fken rastgele da\u011f\u0131lm\u0131\u015ft\u0131r<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>1:<\/strong> \u0130lgilenilen de\u011fi\u015fken m\u00fckemmel \u015fekilde grupland\u0131r\u0131lm\u0131\u015ft\u0131r<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00c7o\u011fu istatistiksel yaz\u0131l\u0131m, Moran I&#8217;in hesaplanmas\u0131n\u0131n yan\u0131 s\u0131ra, verilerin rastgele da\u011f\u0131l\u0131p da\u011f\u0131lmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131labilecek kar\u015f\u0131l\u0131k gelen bir p de\u011ferini de hesaplar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Moran testi a\u015fa\u011f\u0131daki bo\u015f ve alternatif hipotezleri kullan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bo\u015f hipotez (H <sub>0<\/sub> ):<\/strong> veriler rastgele da\u011f\u0131lm\u0131\u015ft\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Alternatif hipotez ( <sub>HA<\/sub> ):<\/strong> Veriler rastgele <em>da\u011f\u0131lmam\u0131\u015ft\u0131r<\/em> , yani g\u00f6r\u00fcn\u00fcr kal\u0131plar halinde grupland\u0131r\u0131lm\u0131\u015ft\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Moran&#8217;\u0131n I&#8217;ine kar\u015f\u0131l\u0131k gelen p de\u011feri belirli bir anlaml\u0131l\u0131k seviyesinin alt\u0131ndaysa (yani \u03b1 = 0,05), o zaman bo\u015f hipotezi reddedebilir ve verilerin mekansal olarak k\u00fcmelenme ihtimalinin d\u00fc\u015f\u00fck olaca\u011f\u0131 \u015fekilde mekansal olarak k\u00fcmelendi\u011fi sonucuna varabiliriz. tesad\u00fcfen meydana geldi.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Moran&#8217;\u0131n I: baz\u0131 \u00f6rnekler<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler Moran&#8217;\u0131n I&#8217;i i\u00e7in farkl\u0131 de\u011ferlere sahip sahte kartlar\u0131 temsil etmektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Haritadaki her karenin bir il\u00e7eyi temsil etti\u011fini ve ortalama hane geliri 50.000 dolar\u0131n \u00fczerinde olan il\u00e7elerin mavi renkle g\u00f6sterildi\u011fini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Moran&#8217;s I = 0:<\/strong> Ortalama hane geliri rastgele da\u011f\u0131lm\u0131\u015ft\u0131r (yani rastgele alanlardaki rastgele k\u00fcmeler).<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13852 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/morani1.png\" alt=\"Moran'\u0131n I \u00f6rne\u011fi\" width=\"336\" height=\"323\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Moran&#8217;\u0131n I = -1:<\/strong> Ortalama hane geliri m\u00fckemmel bir \u015fekilde da\u011f\u0131lm\u0131\u015ft\u0131r.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13853 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/morani2.png\" alt=\"Mekansal istatistikte Moran'\u0131n I'i\" width=\"337\" height=\"334\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Moran&#8217;\u0131n I = 1:<\/strong> ortalama hane geliri m\u00fckemmel bir \u015fekilde grupland\u0131r\u0131lm\u0131\u015ft\u0131r.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13854 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/morani3.png\" alt=\"Moran taraf\u0131ndan ben\" width=\"336\" height=\"331\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">R istatistik yaz\u0131l\u0131m\u0131nda Moran I&#8217;in hesaplanmas\u0131na ili\u015fkin somut bir <a href=\"https:\/\/mgimond.github.io\/Spatial\/spatial-autocorrelation-in-r.html#app8_5\" target=\"_blank\" rel=\"noopener\">\u00f6rnek i\u00e7in bu \u00f6rne\u011fe<\/a> bak\u0131n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Moran&#8217;s I, uzaysal otokorelasyonu \u00f6l\u00e7menin bir yoludur. Basit\u00e7e s\u00f6ylemek gerekirse, de\u011ferlerin 2 boyutlu alanda ne kadar yak\u0131n k\u00fcmelendi\u011fini \u00f6l\u00e7menin bir yoludur. Co\u011frafya ve co\u011frafi bilgi biliminde (GIS), hane geliri, e\u011fitim d\u00fczeyi vb. gibi farkl\u0131 \u00f6zelliklerin bir harita \u00fczerinde ne kadar yak\u0131ndan grupland\u0131r\u0131ld\u0131\u011f\u0131n\u0131 \u00f6l\u00e7mek i\u00e7in s\u0131kl\u0131kla kullan\u0131l\u0131r. Moran&#8217;\u0131n I: form\u00fcl\u00fc Moran&#8217;\u0131n I&#8217;ini hesaplamak i\u00e7in form\u00fcl: ben [&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-1395","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>Moran&#039;\u0131n Benli\u011fi Nedir? 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