{"id":1563,"date":"2023-07-25T21:00:34","date_gmt":"2023-07-25T21:00:34","guid":{"rendered":"https:\/\/statorials.org\/pl\/indeks-roznorodnosci-simpsonow\/"},"modified":"2023-07-25T21:00:34","modified_gmt":"2023-07-25T21:00:34","slug":"indeks-roznorodnosci-simpsonow","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/indeks-roznorodnosci-simpsonow\/","title":{"rendered":"Indeks r\u00f3\u017cnorodno\u015bci simpsona: definicja i przyk\u0142ady"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Indeks r\u00f3\u017cnorodno\u015bci Simpsona<\/strong> to spos\u00f3b pomiaru r\u00f3\u017cnorodno\u015bci gatunk\u00f3w w spo\u0142eczno\u015bci.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oznaczono <em>D<\/em> , wska\u017anik ten jest obliczany w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>D<\/em> = \u03a3n <sub>ja<\/sub> (n <sub>i<\/sub> -1) \/ N(N-1)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n <sub>i<\/sub> :<\/strong> Liczba organizm\u00f3w nale\u017c\u0105cych do gatunku <em>i<\/em><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>N:<\/strong> Ca\u0142kowita liczba organizm\u00f3w<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 wska\u017anika r\u00f3\u017cnorodno\u015bci Simpsona mie\u015bci si\u0119 w przedziale od 0 do 1. Im wy\u017csza warto\u015b\u0107, tym mniejsze zr\u00f3\u017cnicowanie.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poniewa\u017c interpretacja ta jest nieco sprzeczna z intuicj\u0105, cz\u0119sto obliczamy <strong>Wska\u017anik R\u00f3\u017cnorodno\u015bci Simpsona<\/strong> (czasami nazywany Wska\u017anikiem Dominacji), kt\u00f3ry oblicza si\u0119 jako: 1 \u2013 D. Im wy\u017csza warto\u015b\u0107 tego wska\u017anika, tym wi\u0119ksze jest zr\u00f3\u017cnicowanie gatunk\u00f3w.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017cemy r\u00f3wnie\u017c obliczy\u0107 <strong>odwrotno\u015b\u0107 indeksu Simpsona<\/strong> , kt\u00f3ry jest obliczany jako 1\/D. Najni\u017csza warto\u015b\u0107 tego wska\u017anika wynosi 1, a najwy\u017csza jest r\u00f3wna liczbie gatunk\u00f3w.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad, je\u015bli istnieje 7 r\u00f3\u017cnych gatunk\u00f3w, maksymalna warto\u015b\u0107 tego wska\u017anika wyniesie 7. Im wy\u017csza warto\u015b\u0107 tego wska\u017anika, tym wi\u0119ksza r\u00f3\u017cnorodno\u015b\u0107 gatunkowa.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy przyk\u0142ad pokazuje krok po kroku, jak obliczy\u0107 te r\u00f3\u017cne wska\u017aniki dla danej spo\u0142eczno\u015bci.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Krok 1: Zbierz dane<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce biolog chce zmierzy\u0107 r\u00f3\u017cnorodno\u015b\u0107 gatunkow\u0105 w lokalnym lesie. Gromadzi nast\u0119puj\u0105ce dane:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15477 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon1.png\" alt=\"\" width=\"159\" height=\"188\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 2: Oblicz N<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie mo\u017ce obliczy\u0107 ca\u0142kowit\u0105 liczb\u0119 organizm\u00f3w.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15509 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpson1.png\" alt=\"\" width=\"169\" height=\"236\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">W sumie jest <strong>105<\/strong> organizacji.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 3: Oblicz n <sub>i<\/sub> (n <sub>i<\/sub> -1)<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie mo\u017ce obliczy\u0107 n <sub>i<\/sub> (n <sub>i<\/sub> -1). Na przyk\u0142ad pierwszy gatunek zostanie obliczony w nast\u0119puj\u0105cy spos\u00f3b: 40*(40-1) = 1560. Mo\u017ce powt\u00f3rzy\u0107 to obliczenie dla ka\u017cdego gatunku:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15510 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpson2.png\" alt=\"\" width=\"233\" height=\"237\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 4: Oblicz wska\u017anik r\u00f3\u017cnorodno\u015bci Simpsona<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Na koniec mo\u017cemy u\u017cy\u0107 nast\u0119puj\u0105cego wzoru do obliczenia indeksu Simpsona:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>D<\/em> = \u03a3n <sub>ja<\/sub> (n <sub>i<\/sub> -1) \/ N(N-1)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Korzystaj\u0105c z warto\u015bci, kt\u00f3re znale\u017ali\u015bmy wcze\u015bniej, <strong>Indeks Simpsona<\/strong> mo\u017cna obliczy\u0107 w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>D<\/em> = 2,668 \/ (105*(105-1)) = <strong>0,244<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017cemy r\u00f3wnie\u017c obliczy\u0107 <strong>Indeks R\u00f3\u017cnorodno\u015bci Simpsona<\/strong> w nast\u0119puj\u0105cy spos\u00f3b: 1 \u2013 <em>D<\/em> = 1 \u2013 0,244 = <strong>0,756<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017cemy r\u00f3wnie\u017c obliczy\u0107 <strong>wsp\u00f3\u0142czynnik odwrotno\u015bci Simpsona<\/strong> jako 1\/ <em>D<\/em> = 1\/.244 = <strong>4,09<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Mo\u017cesz skorzysta\u0107 z kalkulatora indeksu r\u00f3\u017cnorodno\u015bci Simpsona, aby automatycznie obliczy\u0107 indeks r\u00f3\u017cnorodno\u015bci Simpsona dla dowolnego zbioru danych.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Indeks r\u00f3\u017cnorodno\u015bci Simpsona to spos\u00f3b pomiaru r\u00f3\u017cnorodno\u015bci gatunk\u00f3w w spo\u0142eczno\u015bci. Oznaczono D , wska\u017anik ten jest obliczany w nast\u0119puj\u0105cy spos\u00f3b: D = \u03a3n ja (n i -1) \/ N(N-1) Z\u0142oto: n i : Liczba organizm\u00f3w nale\u017c\u0105cych do gatunku i N: Ca\u0142kowita liczba organizm\u00f3w Warto\u015b\u0107 wska\u017anika r\u00f3\u017cnorodno\u015bci Simpsona mie\u015bci si\u0119 w przedziale od 0 do 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-1563","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>Indeks r\u00f3\u017cnorodno\u015bci Simpsona: definicja i przyk\u0142ady - Statologia<\/title>\n<meta name=\"description\" content=\"Ten samouczek zawiera wyja\u015bnienie Indeksu R\u00f3\u017cnorodno\u015bci Simpsona, w tym wz\u00f3r i przyk\u0142ad krok po kroku.\" \/>\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\/indeks-roznorodnosci-simpsonow\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Indeks r\u00f3\u017cnorodno\u015bci Simpsona: definicja i przyk\u0142ady - Statologia\" \/>\n<meta property=\"og:description\" content=\"Ten samouczek zawiera wyja\u015bnienie Indeksu R\u00f3\u017cnorodno\u015bci Simpsona, w tym wz\u00f3r i przyk\u0142ad krok po kroku.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/indeks-roznorodnosci-simpsonow\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-25T21:00:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon1.png\" \/>\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\/indeks-roznorodnosci-simpsonow\/\",\"url\":\"https:\/\/statorials.org\/pl\/indeks-roznorodnosci-simpsonow\/\",\"name\":\"Indeks r\u00f3\u017cnorodno\u015bci Simpsona: definicja i przyk\u0142ady - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-25T21:00:34+00:00\",\"dateModified\":\"2023-07-25T21:00:34+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Ten samouczek zawiera wyja\u015bnienie Indeksu R\u00f3\u017cnorodno\u015bci Simpsona, w tym wz\u00f3r i przyk\u0142ad krok po kroku.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/indeks-roznorodnosci-simpsonow\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/indeks-roznorodnosci-simpsonow\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/indeks-roznorodnosci-simpsonow\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Indeks r\u00f3\u017cnorodno\u015bci simpsona: definicja i przyk\u0142ady\"}]},{\"@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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