{"id":3132,"date":"2023-07-19T01:29:22","date_gmt":"2023-07-19T01:29:22","guid":{"rendered":"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/"},"modified":"2023-07-19T01:29:22","modified_gmt":"2023-07-19T01:29:22","slug":"suma-kwadratow-anova","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/","title":{"rendered":"Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w anova (z przyk\u0142adem)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">W statystyce <a href=\"https:\/\/statorials.org\/pl\/w-jedna-strone,-anova\/\" target=\"_blank\" rel=\"noopener\">jednoczynnikow\u0105 analiz\u0119 ANOVA<\/a> stosuje si\u0119 do por\u00f3wnania \u015brednich trzech lub wi\u0119kszej liczby niezale\u017cnych grup w celu ustalenia, czy istnieje statystycznie istotna r\u00f3\u017cnica mi\u0119dzy \u015brednimi odpowiedniej populacji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Za ka\u017cdym razem, gdy przeprowadzasz jednokierunkow\u0105 analiz\u0119 ANOVA, zawsze obliczysz trzy sumy warto\u015bci kwadrat\u00f3w:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Regresja sumy kwadrat\u00f3w (SSR)<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Jest to suma kwadrat\u00f3w r\u00f3\u017cnic pomi\u0119dzy \u015bredni\u0105 ka\u017cdej grupy a <a href=\"https:\/\/statorials.org\/pl\/duza-srednia-anova\/\" target=\"_blank\" rel=\"noopener\">\u015bredni\u0105 og\u00f3ln\u0105<\/a> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. B\u0142\u0105d sumy kwadrat\u00f3w (SSE)<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Jest to suma kwadrat\u00f3w r\u00f3\u017cnic mi\u0119dzy ka\u017cd\u0105 indywidualn\u0105 obserwacj\u0105 a \u015bredni\u0105 grupow\u0105 tej obserwacji.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>3. Suma wszystkich kwadrat\u00f3w (SST)<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Jest to suma kwadrat\u00f3w r\u00f3\u017cnic mi\u0119dzy ka\u017cd\u0105 indywidualn\u0105 obserwacj\u0105 a \u015bredni\u0105 og\u00f3ln\u0105.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ka\u017cda z tych trzech warto\u015bci jest umieszczana w ko\u0144cowej tabeli ANOVA, kt\u00f3rej u\u017cywamy do okre\u015blenia, czy istnieje statystycznie istotna r\u00f3\u017cnica mi\u0119dzy \u015brednimi grupowymi.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy przyk\u0142ad pokazuje, jak w praktyce obliczy\u0107 ka\u017cd\u0105 z tych sum warto\u015bci kwadrat\u00f3w dla jednokierunkowej ANOVA.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Przyk\u0142ad: Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce chcemy wiedzie\u0107, czy trzy r\u00f3\u017cne programy przygotowuj\u0105ce do test\u00f3w prowadz\u0105 do r\u00f3\u017cnych \u015brednich wynik\u00f3w na danym egzaminie. Aby to przetestowa\u0107, rekrutujemy 30 student\u00f3w do udzia\u0142u w badaniu i dzielimy ich na trzy grupy.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Uczniowie w ka\u017cdej grupie s\u0105 losowo przydzielani do korzystania z jednego z trzech program\u00f3w przygotowuj\u0105cych do test\u00f3w przez kolejne trzy tygodnie w celu przygotowania si\u0119 do egzaminu. Po trzech tygodniach wszyscy uczniowie przyst\u0119puj\u0105 do tego samego egzaminu.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cej wyniki egzamin\u00f3w dla poszczeg\u00f3lnych grup:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8258 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aller-simple2.png\" sizes=\"auto, \" srcset=\"\" alt=\"Przyk\u0142ad jednokierunkowych danych ANOVA\" width=\"237\" height=\"246\"><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017csze kroki pokazuj\u0105, jak obliczy\u0107 sum\u0119 warto\u015bci kwadrat\u00f3w dla tej jednokierunkowej ANOVA.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 1: Oblicz \u015bredni\u0105 grupow\u0105 i \u015bredni\u0105 og\u00f3ln\u0105.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Najpierw obliczymy \u015bredni\u0105 z trzech grup, a tak\u017ce \u015bredni\u0105 og\u00f3ln\u0105 (lub \u201eog\u00f3ln\u0105\u201d):<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8434 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/anovamain1-1.png\" alt=\"\" width=\"300\" height=\"257\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 2: Oblicz SSR.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie obliczymy sum\u0119 kwadrat\u00f3w regresji (SSR) korzystaj\u0105c z nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <span style=\"color: #000000;\">n\u03a3(X <sub>j<\/sub> \u2013 <span style=\"text-decoration: overline;\">X<\/span> ..) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : liczebno\u015b\u0107 pr\u00f3by grupy j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : grecki symbol oznaczaj\u0105cy \u201esum\u0119\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>j<\/sub><\/strong> : \u015brednia grupy j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> ..<\/strong> : \u015brednia og\u00f3lna<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">W naszym przyk\u0142adzie obliczamy, \u017ce SSR = 10(83,4-85,8) <sup>2<\/sup> + 10(89,3-85,8) <sup>2<\/sup> + 10(84,7-85,8) <sup>2<\/sup> = <strong>192,2<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 3: Oblicz SES.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie obliczymy sum\u0119 b\u0142\u0119d\u00f3w kwadrat\u00f3w (SSE), korzystaj\u0105c z nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3(X <sub>ij<\/sub> \u2013 <span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/sub> ) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : grecki symbol oznaczaj\u0105cy \u201esum\u0119\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>ij<\/sub><\/strong> : <sup>i-ta<\/sup> obserwacja grupy j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/sub><\/strong> : \u015brednia grupy j<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">W naszym przyk\u0142adzie obliczamy SSE w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grupa 1:<\/strong> (85-83,4) <sup>2<\/sup> + (86-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (75-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (78-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (94-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (98-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (79-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (71-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (80-83,4) <sup>2<\/sup> = <strong>640,4<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grupa 2:<\/strong> (91-89,3) <sup>2<\/sup> + (92-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (93-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (87-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (84-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (82-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (95-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (96-89,3) <sup>2<\/sup> = <strong>208,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grupa 3:<\/strong> (79-84,7) <sup>2<\/sup> + (78-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (94-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (92-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (83-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (82-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (81-84,7) <sup>2<\/sup> = <strong>252,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>ESS:<\/strong> 640,4 + 208,1 + 252,1 = <strong>1100,6<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 4: Oblicz SST.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie obliczymy ca\u0142kowit\u0105 sum\u0119 kwadrat\u00f3w (SST) za pomoc\u0105 nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SST = SSR + SSE<\/span><\/p>\n<p> <span style=\"color: #000000;\">W naszym przyk\u0142adzie SST = 192,2 + 1100,6 = <strong>1292,8<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Kiedy ju\u017c obliczymy warto\u015bci SSR, SSE i SST, ka\u017cda z tych warto\u015bci zostanie ostatecznie umieszczona w tabeli ANOVA:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>\u0179r\u00f3d\u0142o<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Suma kwadrat\u00f3w (SS)<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">zm<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">\u015arednie kwadraty (MS)<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Warto\u015b\u0107 F<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">warto\u015b\u0107 p<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Regresja<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">192.2<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">96.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2358<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,1138<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>B\u0142\u0105d<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1100,6<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">40,8<\/span><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Ca\u0142kowity<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1292,8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">29<\/span><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Oto jak obliczyli\u015bmy r\u00f3\u017cne liczby w tabeli:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>regresja df:<\/strong> k-1 = 3-1 = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b\u0142\u0105d df:<\/strong> nk = 30-3 = 27<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>ca\u0142kowity df:<\/strong> n-1 = 30-1 = 29<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Obr\u00f3bka SEP:<\/strong> Obr\u00f3bka SST\/df = 192,2 \/ 2 = 96,1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>B\u0142\u0105d MS:<\/strong> b\u0142\u0105d SSE \/ df = 1100,6 \/ 27 = 40,8<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Warto\u015b\u0107 F:<\/strong> przetwarzanie MS \/ b\u0142\u0105d MS = 96,1 \/ 40,8 = 2,358<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>warto\u015b\u0107 p<\/strong> : warto\u015b\u0107 p odpowiadaj\u0105ca warto\u015bci F.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><em><strong>Uwaga:<\/strong> n = ca\u0142kowita liczba obserwacji, k = liczba grup<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">Sprawd\u017a <a href=\"https:\/\/statorials.org\/pl\/anova-wartosc-f-wartosc-p\/\" target=\"_blank\" rel=\"noopener\">ten samouczek,<\/a> aby dowiedzie\u0107 si\u0119, jak interpretowa\u0107 warto\u015bci F i warto\u015b\u0107 p w tabeli ANOVA.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>W statystyce jednoczynnikow\u0105 analiz\u0119 ANOVA stosuje si\u0119 do por\u00f3wnania \u015brednich trzech lub wi\u0119kszej liczby niezale\u017cnych grup w celu ustalenia, czy istnieje statystycznie istotna r\u00f3\u017cnica mi\u0119dzy \u015brednimi odpowiedniej populacji. Za ka\u017cdym razem, gdy przeprowadzasz jednokierunkow\u0105 analiz\u0119 ANOVA, zawsze obliczysz trzy sumy warto\u015bci kwadrat\u00f3w: 1. Regresja sumy kwadrat\u00f3w (SSR) Jest to suma kwadrat\u00f3w r\u00f3\u017cnic pomi\u0119dzy \u015bredni\u0105 ka\u017cdej [&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-3132","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 sum\u0119 kwadrat\u00f3w w ANOVA (na przyk\u0142adzie) - Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA, podaj\u0105c pe\u0142ny przyk\u0142ad.\" \/>\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\/suma-kwadratow-anova\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA (na przyk\u0142adzie) - Statologia\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA, podaj\u0105c pe\u0142ny przyk\u0142ad.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-19T01:29:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aller-simple2.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=\"3 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/\",\"url\":\"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/\",\"name\":\"Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA (na przyk\u0142adzie) - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-19T01:29:22+00:00\",\"dateModified\":\"2023-07-19T01:29:22+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA, podaj\u0105c pe\u0142ny przyk\u0142ad.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w anova (z przyk\u0142adem)\"}]},{\"@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. Dzi\u0119ki bogatemu do\u015bwiadczeniu i wiedzy specjalistycznej w dziedzinie statystyki ch\u0119tnie dziel\u0119 si\u0119 swoj\u0105 wiedz\u0105, aby wzmocni\u0107 pozycj\u0119 uczni\u00f3w za po\u015brednictwem Statorials. Wiedzie\u0107 wi\u0119cej\",\"sameAs\":[\"https:\/\/statorials.org\/pl\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA (na przyk\u0142adzie) - Statologia","description":"W tym samouczku wyja\u015bniono, jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA, podaj\u0105c pe\u0142ny przyk\u0142ad.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/","og_locale":"pl_PL","og_type":"article","og_title":"Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA (na przyk\u0142adzie) - Statologia","og_description":"W tym samouczku wyja\u015bniono, jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA, podaj\u0105c pe\u0142ny przyk\u0142ad.","og_url":"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/","og_site_name":"Statorials","article_published_time":"2023-07-19T01:29:22+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aller-simple2.png"}],"author":"Benjamin Anderson","twitter_card":"summary_large_image","twitter_misc":{"Napisane przez":"Benjamin Anderson","Szacowany czas czytania":"3 minuty"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/","url":"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/","name":"Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA (na przyk\u0142adzie) - Statologia","isPartOf":{"@id":"https:\/\/statorials.org\/pl\/#website"},"datePublished":"2023-07-19T01:29:22+00:00","dateModified":"2023-07-19T01:29:22+00:00","author":{"@id":"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965"},"description":"W tym samouczku wyja\u015bniono, jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w ANOVA, podaj\u0105c pe\u0142ny przyk\u0142ad.","breadcrumb":{"@id":"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/#breadcrumb"},"inLanguage":"pl-PL","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/pl\/suma-kwadratow-anova\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Dom","item":"https:\/\/statorials.org\/pl\/"},{"@type":"ListItem","position":2,"name":"Jak obliczy\u0107 sum\u0119 kwadrat\u00f3w w anova (z przyk\u0142adem)"}]},{"@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. Dzi\u0119ki bogatemu do\u015bwiadczeniu i wiedzy specjalistycznej w dziedzinie statystyki ch\u0119tnie dziel\u0119 si\u0119 swoj\u0105 wiedz\u0105, aby wzmocni\u0107 pozycj\u0119 uczni\u00f3w za po\u015brednictwem Statorials. Wiedzie\u0107 wi\u0119cej","sameAs":["https:\/\/statorials.org\/pl"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts\/3132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/comments?post=3132"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts\/3132\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/media?parent=3132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/categories?post=3132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/tags?post=3132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}