{"id":1282,"date":"2023-07-27T00:41:54","date_gmt":"2023-07-27T00:41:54","guid":{"rendered":"https:\/\/statorials.org\/pl\/niektore-z\/"},"modified":"2023-07-27T00:41:54","modified_gmt":"2023-07-27T00:41:54","slug":"niektore-z","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/niektore-z\/","title":{"rendered":"Co to jest d somersa? (definicja \u2013 przyk\u0142ad)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Somers&#8217; D<\/strong> , skr\u00f3t od Somers&#8217; Delta, jest miar\u0105 si\u0142y i kierunku powi\u0105zania mi\u0119dzy porz\u0105dkow\u0105 zmienn\u0105 zale\u017cn\u0105 a porz\u0105dkow\u0105 zmienn\u0105 niezale\u017cn\u0105.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zmienna <em>porz\u0105dkowa<\/em> to taka, w kt\u00f3rej warto\u015bci maj\u0105 naturalny porz\u0105dek (np. \u201ez\u0142y\u201d, \u201eneutralny\u201d, \u201edobry\u201d).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 D Somersa mie\u015bci si\u0119 w przedziale od -1 do 1, gdzie:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>-1:<\/strong> Wskazuje, \u017ce wszystkie pary zmiennych nie s\u0105 zgodne<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>1:<\/strong> wskazuje, \u017ce wszystkie pary zmiennych s\u0105 zgodne<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">D Somersa jest stosowany w praktyce w wielu nieparametrycznych metodach statystycznych.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Somersa D: definicja<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Maj\u0105c dwie zmienne X i Y, mo\u017cemy powiedzie\u0107:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Dwie pary (x <sub>i<\/sub> , y <sub>i<\/sub> ) i (x <sub>j<\/sub> , y <sub>j<\/sub> ) s\u0105 <strong>zgodne<\/strong> , je\u015bli szeregi obu element\u00f3w s\u0105 zgodne.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Dwie pary (x<\/span> <sub>i<\/sub> <span style=\"color: #000000;\">, y<\/span> <sub>i<\/sub> <span style=\"color: #000000;\">) i (x<\/span> <sub>j<\/sub> <span style=\"color: #000000;\">, y<\/span> <sub>j<\/sub> <span style=\"color: #000000;\">) s\u0105 <b>niezgodne<\/b><\/span><b> <\/b><span style=\"color: #000000;\">je\u015bli szeregi dw\u00f3ch element\u00f3w s\u0105 zgodne.<\/span><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie mo\u017cemy obliczy\u0107 D Somersa, korzystaj\u0105c z nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">Somers&#8217; D = ( <sub>NC<\/sub> &#8211; N <sub>re<\/sub> ) \/ ( <sub>NC<\/sub> + N <sub>re<\/sub> + N <sub>T<\/sub> )<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><sub>NC<\/sub> :<\/strong> Liczba pasuj\u0105cych par<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>ND<\/sub> :<\/strong> Liczba niezgodnych par<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>NT<\/sub> :<\/strong> Liczba powi\u0105zanych par<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Wynikowa warto\u015b\u0107 b\u0119dzie zawsze wynosi\u0107 od -1 do 1.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Somers&#8217; D: przyk\u0142ad w R<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce sklep spo\u017cywczy chce oceni\u0107 zwi\u0105zek mi\u0119dzy nast\u0119puj\u0105cymi dwiema zmiennymi porz\u0105dkowymi:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Og\u00f3lna \u017cyczliwo\u015b\u0107 kasjera (ocena od 1 do 3)<\/span><\/li>\n<li> <span style=\"color: #000000;\">Og\u00f3lna satysfakcja z do\u015bwiadczenia klienta (r\u00f3wnie\u017c w rankingu od 1 do 3)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Zbieraj\u0105 nast\u0119puj\u0105ce oceny na <a href=\"https:\/\/statorials.org\/pl\/populacja-vs.-probka\/\" target=\"_blank\" rel=\"noopener\">pr\u00f3bie<\/a> 10 klient\u00f3w:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12605 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quelquun1.png\" alt=\"Przyk\u0142ad D Somersa\" width=\"261\" height=\"306\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Aby okre\u015bli\u0107 ilo\u015bciowo zwi\u0105zek mi\u0119dzy dwiema zmiennymi, mo\u017cemy obliczy\u0107 D Somersa, u\u017cywaj\u0105c nast\u0119puj\u0105cego kodu w R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#enter data<\/span>\nnice &lt;- c(1, 1, 1, 2, 2, 2, 3, 3, 3, 3)\nsatisfaction &lt;- c(2, 2, 1, 2, 3, 2, 2, 3, 3, 3)\n\n<span style=\"color: #008080;\">#load <em>DescTools<\/em> package\n<\/span>library(DescTools)\n\n<span style=\"color: #008080;\">#calculate Somers' D\n<\/span>SomersDelta(nice, satisfaction)\n\n[1] 0.6896552<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Okazuje si\u0119, \u017ce D Somersa wynosi <strong>0,6896552<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 ta, b\u0119d\u0105ca do\u015b\u0107 bliska 1, oznacza, \u017ce istnieje do\u015b\u0107 silna dodatnia zale\u017cno\u015b\u0107 pomi\u0119dzy obiema zmiennymi.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ma to intuicyjny sens: klienci, kt\u00f3rzy oceniaj\u0105 kasjer\u00f3w jako milszych, r\u00f3wnie\u017c cz\u0119\u015bciej oceniaj\u0105 swoje og\u00f3lne zadowolenie.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/wspo\u0142czynnik-korelacji-pearsona-1\/\" target=\"_blank\" rel=\"noopener\">Wprowadzenie do wsp\u00f3\u0142czynnika korelacji Pearsona<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/kendalls-tau\/\" target=\"_blank\" rel=\"noopener\">Wprowadzenie do Tau Kendalla<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Somers&#8217; D , skr\u00f3t od Somers&#8217; Delta, jest miar\u0105 si\u0142y i kierunku powi\u0105zania mi\u0119dzy porz\u0105dkow\u0105 zmienn\u0105 zale\u017cn\u0105 a porz\u0105dkow\u0105 zmienn\u0105 niezale\u017cn\u0105. Zmienna porz\u0105dkowa to taka, w kt\u00f3rej warto\u015bci maj\u0105 naturalny porz\u0105dek (np. \u201ez\u0142y\u201d, \u201eneutralny\u201d, \u201edobry\u201d). Warto\u015b\u0107 D Somersa mie\u015bci si\u0119 w przedziale od -1 do 1, gdzie: -1: Wskazuje, \u017ce wszystkie pary zmiennych nie s\u0105 [&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-1282","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>Co to jest D Somersa? 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