{"id":301,"date":"2023-08-02T20:15:08","date_gmt":"2023-08-02T20:15:08","guid":{"rendered":"https:\/\/statorials.org\/pl\/stol-anova\/"},"modified":"2023-08-02T20:15:08","modified_gmt":"2023-08-02T20:15:08","slug":"stol-anova","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/stol-anova\/","title":{"rendered":"Tabela anova"},"content":{"rendered":"<p>W tym artykule znajdziesz wyja\u015bnienie tabeli ANOVA. Wyja\u015bnimy wi\u0119c, czym jest tabela ANOVA, jak zrobi\u0107 tabel\u0119 ANOVA, jakie s\u0105 wzory tabeli ANOVA, a dodatkowo b\u0119dziesz m\u00f3g\u0142 zobaczy\u0107 krok po kroku rozwi\u0105zane \u0107wiczenie. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-tabla-anova\"><\/span> Co to jest tabela ANOVA?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Tabela ANOVA<\/strong> jest tabel\u0105 stosowan\u0105 w statystyce w analizie wariancji. M\u00f3wi\u0105c dok\u0142adniej, tabela ANOVA zawiera wszystkie informacje niezb\u0119dne do analizy wariancji.<\/p>\n<p> Dlatego tabela ANOVA s\u0142u\u017cy do podsumowania analizy wariancji. Wykre\u015blaj\u0105c obliczenia analizy wariancji w tabeli, mo\u017cna \u0142atwo wyci\u0105gn\u0105\u0107 wnioski, a tak\u017ce pozwoli\u0107 na szybkie obliczenie warto\u015bci statystyki testu ANOVA. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-la-tabla-anova\"><\/span> Wzory tabelaryczne ANOVA<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> W jednoczynnikowej tabeli ANOVA znajduj\u0105 si\u0119 trzy wiersze: wsp\u00f3\u0142czynnik, b\u0142\u0105d i suma. Zatem w tabeli ANOVA obliczane s\u0105 sumy kwadrat\u00f3w ka\u017cdego wiersza i ich stopnie swobody. Dodatkowo obliczany jest b\u0142\u0105d \u015bredniokwadratowy wsp\u00f3\u0142czynnika i b\u0142\u0105d, a na koniec wyznaczana jest statystyka testu ANOVA, kt\u00f3ra jest r\u00f3wna stosunkowi kwadrat\u00f3w b\u0142\u0119d\u00f3w.<\/p>\n<p> <strong>Wzory tabeli ANOVA<\/strong> s\u0105 zatem nast\u0119puj\u0105ce: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tableau-anova-formules-.png\" alt=\"Wzory tabelaryczne ANOVA\" class=\"wp-image-6387\" width=\"664\" height=\"397\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:5px\"> Z\u0142oto:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> to wielko\u015b\u0107 pr\u00f3bki, tj.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7354bae77b50b7d1faed3e8ea7a3511a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> to ca\u0142kowita liczba obserwacji.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> jest liczb\u0105 r\u00f3\u017cnych grup w analizie wariancji.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-393bb0c333649c80fe6365339bc42b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> jest warto\u015bci\u0105 j grupy i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8effb66cfe7466ba329c455ccb9289f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> jest \u015bredni\u0105 grupy i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ed5becac4ccb36fec040f449ba9fa52d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> Jest to \u015brednia wszystkich analizowanych danych. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-tabla-anova\"><\/span> Przyk\u0142ad tabeli ANOVA<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Aby dobrze zrozumie\u0107 t\u0119 koncepcj\u0119, zobaczmy, jak utworzy\u0107 tabel\u0119 ANOVA, rozwi\u0105zuj\u0105c przyk\u0142ad krok po kroku.<\/p>\n<ul>\n<li> Przeprowadza si\u0119 badanie statystyczne w celu por\u00f3wnania wynik\u00f3w uzyskanych przez czterech uczni\u00f3w z trzech r\u00f3\u017cnych przedmiot\u00f3w (A, B i C). Poni\u017csza tabela szczeg\u00f3\u0142owo opisuje wyniki uzyskane przez ka\u017cdego ucznia w te\u015bcie, kt\u00f3rego maksymalny wynik wynosi 20. Skonstruuj tabel\u0119 ANOVA, aby por\u00f3wna\u0107 wyniki uzyskane przez ka\u017cdego ucznia z ka\u017cdego przedmiotu. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-anova-donnees.png\" alt=\"\" class=\"wp-image-6389\" width=\"471\" height=\"205\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Pierwsz\u0105 rzecz\u0105, kt\u00f3r\u0105 musimy zrobi\u0107, to obliczy\u0107 \u015bredni\u0105 dla ka\u017cdego przedmiotu i ca\u0142kowit\u0105 \u015bredni\u0105 danych: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-792e2e662519db421d0c9c4d7f831282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_A=\\cfrac{14+12+14+10}{4}=12,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"239\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ace3ea8d1e0ce91dafdf4b5458e9760a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_B=\\cfrac{13+14+10+14}{4}=12,75\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d2781ad166914d48b6d458fe8e326f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_C=\\cfrac{19+17+16+19}{4}=17,75\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-26caf7f83546e9112594e6886e8dccae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}=\\cfrac{14+12+14+10+13+14+10+14+19+17+16+19}{12}=14,33\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"553\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Gdy znamy warto\u015b\u0107 \u015brednich, obliczamy sumy kwadrat\u00f3w, korzystaj\u0105c ze wzor\u00f3w z tabeli ANOVA (patrz wy\u017cej): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-77b3fecdc3b577841da684cd80297288_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_F&amp;=\\sum_{i=1}^k n_i(\\overline{y}_i-\\overline{y})^2\\\\[2ex] SS_F&amp;= 4\\cdot (12,5-14,33)^2+4\\cdot (12,75-14,33)^2+4\\cdot (17,75-14,33)^2\\\\[2ex] SS_F&amp;=70,17\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"546\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-aa02f1b826df45c26ead3537ecc4c7e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_E=&amp;\\sum_{i=1}^k\\sum_{j=1}^{n_i} (y_{ij}-\\overline{y}_i)^2\\\\[2ex] \\displaystyle SS_E=\\ &amp;(14-12,5)^2+(12-12,5)^2+(14-12,5)^2+(10-12,5)^2+\\\\&amp;+(13-12,75)^2+(14-12,75)^2+(10-12,75)^2+(14-12,75)^2+\\\\&amp;+(19-17,75)^2+(17-17,75)^2+(16-17,75)^2+(19-17,75)^2\\\\[2ex] SS_E=\\ &amp;28,50\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"575\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2eb66d1d37653749f38916c905108a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_T=&amp;\\sum_{i=1}^k\\sum_{j=1}^{n_i} (y_{ij}-\\overline{y})^2\\\\[2ex] \\displaystyle SS_T= \\ &amp;(14-14,33)^2+(12-14,33)^2+(14-14,33)^2+(10-14,33)^2+\\\\&amp;+(13-14,33)^2+(14-14,33)^2+(10-14,33)^2+(14-14,33)^2+\\\\&amp;+(19-14,33)^2+(17-14,33)^2+(16-14,33)^2+(19-14,33)^2\\\\[2ex] SS_T= \\ &amp;98,67\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"575\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Nast\u0119pnie wyznaczamy stopnie swobody czynnika, b\u0142\u0105d i sum\u0119: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-481e16a2bd9b99bcd934aa0b6e3bdce7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_F=k-1=3-1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"196\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6c71951c1e79cb2368b941b79387fe82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_E=N-k=12-3=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"213\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c62813e7a06bfd423af43109bfb508d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_F=N-1=12-1=11\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"220\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Teraz obliczamy b\u0142\u0119dy \u015bredniokwadratowe, dziel\u0105c sumy kwadrat\u00f3w wsp\u00f3\u0142czynnika i b\u0142\u0119du przez ich odpowiednie stopnie swobody:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-477d73197865e6166394e3d20732b237_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"MSE_F=\\cfrac{SS_F}{GL_F}=\\cfrac{70,17}{2}=35,08\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"255\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a5b4e07b9ec4135498762b5dbc0f173e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"MSE_R=\\cfrac{SS_R}{GL_R}=\\cfrac{28,50}{9}=3,17\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"245\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Na koniec obliczamy warto\u015b\u0107 statystyki F, dziel\u0105c dwa b\u0142\u0119dy obliczone w poprzednim kroku:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4a30a3a61861deb9f53bd1cfcdb0b664_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F=\\cfrac{MSE_F}{MSE_R}=\\cfrac{35,09}{3,17}=11,08\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"231\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> W skr\u00f3cie, tabela ANOVA dla przyk\u0142adowych danych wygl\u0105da\u0142aby nast\u0119puj\u0105co: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-anova-exemple.png\" alt=\"Przyk\u0142ad tabeli ANOVA\" class=\"wp-image-6408\" width=\"726\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Po obliczeniu wszystkich warto\u015bci w tabeli ANOVA pozostaje tylko je zinterpretowa\u0107. Aby to zrobi\u0107, musimy por\u00f3wna\u0107 prawdopodobie\u0144stwo odpowiadaj\u0105ce warto\u015bci statystyki F, zwanej warto\u015bci\u0105 p. Mo\u017cesz zobaczy\u0107, jak to si\u0119 robi, klikaj\u0105c poni\u017cszy link: <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Patrz:<\/strong> <a href=\"https:\/\/statorials.org\/pl\/wartosc-p\/\">Interpretacja warto\u015bci p<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>W tym artykule znajdziesz wyja\u015bnienie tabeli ANOVA. Wyja\u015bnimy wi\u0119c, czym jest tabela ANOVA, jak zrobi\u0107 tabel\u0119 ANOVA, jakie s\u0105 wzory tabeli ANOVA, a dodatkowo b\u0119dziesz m\u00f3g\u0142 zobaczy\u0107 krok po kroku rozwi\u0105zane \u0107wiczenie. Co to jest tabela ANOVA? Tabela ANOVA jest tabel\u0105 stosowan\u0105 w statystyce w analizie wariancji. M\u00f3wi\u0105c dok\u0142adniej, tabela ANOVA zawiera wszystkie informacje niezb\u0119dne [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-301","post","type-post","status-publish","format-standard","hentry","category-statystyka"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Tabela ANOVA<\/title>\n<meta name=\"description\" content=\"Tutaj dowiesz si\u0119 czym jest tabela ANOVA, jak jest wykonana (wzory), jak j\u0105 interpretowa\u0107, a tak\u017ce konkretny 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\/stol-anova\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Tabela ANOVA\" \/>\n<meta property=\"og:description\" content=\"Tutaj dowiesz si\u0119 czym jest tabela ANOVA, jak jest wykonana (wzory), jak j\u0105 interpretowa\u0107, a tak\u017ce konkretny przyk\u0142ad krok po kroku.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/stol-anova\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-02T20:15:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tableau-anova-formules-.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\/stol-anova\/\",\"url\":\"https:\/\/statorials.org\/pl\/stol-anova\/\",\"name\":\"\u25b7 Tabela ANOVA\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-08-02T20:15:08+00:00\",\"dateModified\":\"2023-08-02T20:15:08+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Tutaj dowiesz si\u0119 czym jest tabela ANOVA, jak jest wykonana (wzory), jak j\u0105 interpretowa\u0107, a tak\u017ce konkretny przyk\u0142ad krok po kroku.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/stol-anova\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/stol-anova\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/stol-anova\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Tabela anova\"}]},{\"@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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