{"id":2081,"date":"2023-07-23T19:04:22","date_gmt":"2023-07-23T19:04:22","guid":{"rendered":"https:\/\/statorials.org\/pl\/grupowe-odchylenie-standardowe-w-r\/"},"modified":"2023-07-23T19:04:22","modified_gmt":"2023-07-23T19:04:22","slug":"grupowe-odchylenie-standardowe-w-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/grupowe-odchylenie-standardowe-w-r\/","title":{"rendered":"Jak obliczy\u0107 skupione odchylenie standardowe w r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u0141\u0105czne odchylenie standardowe<\/strong> to po prostu \u015brednia wa\u017cona odchyle\u0144 standardowych dw\u00f3ch lub wi\u0119cej niezale\u017cnych grup.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W statystyce najcz\u0119\u015bciej pojawia si\u0119 w <a href=\"https:\/\/statorials.org\/pl\/przetestuj-dwie-probki\/\" target=\"_blank\" rel=\"noopener noreferrer\">te\u015bcie t dla dw\u00f3ch pr\u00f3b<\/a> , kt\u00f3ry s\u0142u\u017cy do sprawdzenia, czy \u015brednie z dw\u00f3ch populacji s\u0105 r\u00f3wne.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Wz\u00f3r na obliczenie skupionego odchylenia standardowego dla dw\u00f3ch grup jest nast\u0119puj\u0105cy:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">Po\u0142\u0105czone odchylenie standardowe = \u221a <span style=\"border-top: 1px solid black;\">(n <sub>1<\/sub> -1) s <sub>1<\/sub> <sup>2<\/sup> + (n <sub>2<\/sub> -1) s <sub>2<\/sub> <sup>2<\/sup> \/ (n <sub>1<\/sub> + n <sub>2<\/sub> -2)<\/span><\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><sub>n1<\/sub> , <sub>n2<\/sub> :<\/strong> Wielko\u015b\u0107 pr\u00f3by odpowiednio dla grupy 1 i grupy 2.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> , s <sub>2<\/sub> :<\/strong> Odchylenie standardowe odpowiednio dla grupy 1 i grupy 2.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105 dwie metody obliczania skupionego odchylenia standardowego mi\u0119dzy dwiema grupami w R.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Metoda 1: R\u0119cznie oblicz skupione odchylenie standardowe<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105ce warto\u015bci danych dla dw\u00f3ch pr\u00f3bek:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Pr\u00f3bka 1<\/strong> : 6, 6, 7, 8, 8, 10, 11, 13, 15, 15, 16, 17, 19, 19, 21<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Pr\u00f3bka 2<\/strong> : 10, 11, 13, 13, 15, 17, 17, 19, 20, 22, 24, 25, 27, 29, 29<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak obliczy\u0107 zbiorcze odchylenie standardowe mi\u0119dzy tymi dwiema pr\u00f3bami:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define two samples\n<\/span>data1 &lt;- c(6, 6, 7, 8, 8, 10, 11, 13, 15, 15, 16, 17, 19, 19, 21)\ndata2 &lt;- c(10, 11, 13, 13, 15, 17, 17, 19, 20, 22, 24, 25, 27, 29, 29)\n\n<span style=\"color: #008080;\">#find sample standard deviation of each sample\n<\/span>s1 &lt;- <span style=\"color: #3366ff;\">sd<\/span> (data1)\ns2 &lt; <span style=\"color: #3366ff;\">-sd<\/span> (data2)\n\n<span style=\"color: #008080;\">#find sample size of each sample\n<\/span>n1 &lt;- <span style=\"color: #3366ff;\">length<\/span> (data1)\nn2 &lt;- <span style=\"color: #3366ff;\">length<\/span> (data2)\n\n<span style=\"color: #008080;\">#calculate pooled standard deviation\n<\/span>pooled &lt;- <span style=\"color: #3366ff;\">sqrt<\/span> (((n1-1)*s1^2 + (n2-1)*s2^2) \/ (n1+n1-2))\n\n<span style=\"color: #008080;\">#view pooled standard deviation\n<\/span>pooled\n\n[1] 5.789564\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0141\u0105czne odchylenie standardowe wynosi <strong>5,789564<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Metoda 2: Oblicz skupione odchylenie standardowe za pomoc\u0105 pakietu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Innym sposobem obliczenia zbiorczego odchylenia standardowego mi\u0119dzy dwiema pr\u00f3bkami w R jest u\u017cycie funkcji <strong>sd_pooled()<\/strong> z pakietu <strong>Effectize<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak w praktyce wykorzysta\u0107 t\u0119 funkcj\u0119:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #ff0000;\">library<\/span> (effectsize)<\/span>\n\n#define two samples\n<\/span>data1 &lt;- c(6, 6, 7, 8, 8, 10, 11, 13, 15, 15, 16, 17, 19, 19, 21)\ndata2 &lt;- c(10, 11, 13, 13, 15, 17, 17, 19, 20, 22, 24, 25, 27, 29, 29)\n\n<span style=\"color: #008080;\">#calculate pooled standard deviation between two samples\n<\/span>sd_pooled(data1, data2)\n\n[1] 5.789564\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0141\u0105czne odchylenie standardowe wynosi <strong>5,789564<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nale\u017cy pami\u0119ta\u0107, \u017ce odpowiada to warto\u015bci obliczonej r\u0119cznie w poprzednim przyk\u0142adzie.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csze samouczki zawieraj\u0105 wi\u0119cej informacji na temat obliczania skupionego odchylenia standardowego:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pl\/odchylenie-standardowe-grupy\/\" target=\"_blank\" rel=\"noopener\">Wprowadzenie do skupionego odchylenia standardowego<\/a><br \/> Skupiony kalkulator odchylenia standardowego<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0141\u0105czne odchylenie standardowe to po prostu \u015brednia wa\u017cona odchyle\u0144 standardowych dw\u00f3ch lub wi\u0119cej niezale\u017cnych grup. W statystyce najcz\u0119\u015bciej pojawia si\u0119 w te\u015bcie t dla dw\u00f3ch pr\u00f3b , kt\u00f3ry s\u0142u\u017cy do sprawdzenia, czy \u015brednie z dw\u00f3ch populacji s\u0105 r\u00f3wne. Wz\u00f3r na obliczenie skupionego odchylenia standardowego dla dw\u00f3ch grup jest nast\u0119puj\u0105cy: Po\u0142\u0105czone odchylenie standardowe = \u221a (n [&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-2081","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>Jak obliczy\u0107 skupione odchylenie standardowe w R - Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, na przyk\u0142adzie, jak obliczy\u0107 skupione odchylenie standardowe w j\u0119zyku R.\" \/>\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\/grupowe-odchylenie-standardowe-w-r\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 skupione odchylenie standardowe w R - Statologia\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, na przyk\u0142adzie, jak obliczy\u0107 skupione odchylenie standardowe w j\u0119zyku R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/grupowe-odchylenie-standardowe-w-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-23T19:04:22+00:00\" \/>\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\/grupowe-odchylenie-standardowe-w-r\/\",\"url\":\"https:\/\/statorials.org\/pl\/grupowe-odchylenie-standardowe-w-r\/\",\"name\":\"Jak obliczy\u0107 skupione odchylenie standardowe w R - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-23T19:04:22+00:00\",\"dateModified\":\"2023-07-23T19:04:22+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, na przyk\u0142adzie, jak obliczy\u0107 skupione odchylenie standardowe w j\u0119zyku R.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/grupowe-odchylenie-standardowe-w-r\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/grupowe-odchylenie-standardowe-w-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/grupowe-odchylenie-standardowe-w-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 skupione odchylenie standardowe w r\"}]},{\"@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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