{"id":770,"date":"2023-07-28T19:45:12","date_gmt":"2023-07-28T19:45:12","guid":{"rendered":"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-a-la-main\/"},"modified":"2023-07-28T19:45:12","modified_gmt":"2023-07-28T19:45:12","slug":"w-jedna-strone-anova-a-la-main","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-a-la-main\/","title":{"rendered":"Jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 anova"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/pl\/w-jedna-strone,-anova\/\" target=\"_blank\" rel=\"noopener\">Jednoczynnikowa ANOVA<\/a> (\u201eanaliza wariancji\u201d) por\u00f3wnuje \u015brednie trzech lub wi\u0119cej 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;\">W tym samouczku wyja\u015bniono, jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 analiz\u0119 ANOVA.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Przyk\u0142ad: r\u0119czna jednokierunkowa 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;\">Wykonaj poni\u017csze kroki, aby r\u0119cznie wykona\u0107 jednoczynnikow\u0105 analiz\u0119 ANOVA w celu ustalenia, czy \u015bredni wynik egzaminu r\u00f3\u017cni si\u0119 w trzech grupach:<\/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:<\/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 kwadratu b\u0142\u0119du (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;\"><strong>Krok 5: Wype\u0142nij tabel\u0119 ANOVA.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Teraz, gdy mamy SSR, SSE i SST, mo\u017cemy wype\u0142ni\u0107 tabel\u0119 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;\">F<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Leczenie<\/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<\/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<\/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<\/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>leczenie 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>F:<\/strong> Przetwarzanie MS \/ b\u0142\u0105d MS = 96,1 \/ 40,8 = 2,358<\/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;\"><strong>Krok 6: Interpretacja wynik\u00f3w.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Statystyka testu F dla tej jednokierunkowej ANOVA wynosi <strong>2,358<\/strong> . Aby okre\u015bli\u0107, czy jest to wynik istotny statystycznie, nale\u017cy por\u00f3wna\u0107 go z krytyczn\u0105 warto\u015bci\u0105 F znalezion\u0105 w <a href=\"https:\/\/statorials.org\/pl\/f-tablica-rozdzielcza\/\" target=\"_blank\" rel=\"noopener\">tabeli rozk\u0142adu F<\/a> o nast\u0119puj\u0105cych warto\u015bciach:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u03b1 (poziom istotno\u015bci) = 0,05<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF1 (stopnie swobody licznika) = df leczenie = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF2 (stopnie swobody mianownika) = b\u0142\u0105d df = 27<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ustalamy, \u017ce warto\u015b\u0107 krytyczna F wynosi <strong>3,3541<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poniewa\u017c statystyka testu F w tabeli ANOVA jest mniejsza ni\u017c warto\u015b\u0107 krytyczna F w tabeli rozk\u0142adu F, nie uda\u0142o nam si\u0119 odrzuci\u0107 hipotezy zerowej. Oznacza to, \u017ce nie mamy wystarczaj\u0105cych dowod\u00f3w, aby stwierdzi\u0107, \u017ce istnieje statystycznie istotna r\u00f3\u017cnica pomi\u0119dzy \u015brednimi wynikami egzamin\u00f3w trzech grup.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby:<\/strong> U\u017cyj tego <a href=\"https:\/\/statorials.org\/pl\/jednokierunkowy-kalkulator-danova\/\" target=\"_blank\" rel=\"noopener\">jednokierunkowego kalkulatora ANOVA<\/a> , aby automatycznie wykona\u0107 jednokierunkow\u0105 ANOVA dla maksymalnie pi\u0119ciu pr\u00f3bek.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jednoczynnikowa ANOVA (\u201eanaliza wariancji\u201d) por\u00f3wnuje \u015brednie trzech lub wi\u0119cej niezale\u017cnych grup w celu ustalenia, czy istnieje statystycznie istotna r\u00f3\u017cnica mi\u0119dzy \u015brednimi odpowiedniej populacji. W tym samouczku wyja\u015bniono, jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 analiz\u0119 ANOVA. Przyk\u0142ad: r\u0119czna jednokierunkowa ANOVA 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 [&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-770","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 r\u0119cznie wykona\u0107 jednokierunkow\u0105 analiz\u0119 ANOVA \u2013 statoriale<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie, jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 ANOVA.\" \/>\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\/w-jedna-strone-anova-a-la-main\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 analiz\u0119 ANOVA \u2013 statoriale\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie, jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 ANOVA.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-a-la-main\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T19:45:12+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\/w-jedna-strone-anova-a-la-main\/\",\"url\":\"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-a-la-main\/\",\"name\":\"Jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 analiz\u0119 ANOVA \u2013 statoriale\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-28T19:45:12+00:00\",\"dateModified\":\"2023-07-28T19:45:12+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie, jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 ANOVA.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-a-la-main\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-a-la-main\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-a-la-main\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak r\u0119cznie wykona\u0107 jednokierunkow\u0105 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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