{"id":884,"date":"2023-07-28T10:31:38","date_gmt":"2023-07-28T10:31:38","guid":{"rendered":"https:\/\/statorials.org\/pl\/tukey-kramer-test-post-hoc-w-excelu\/"},"modified":"2023-07-28T10:31:38","modified_gmt":"2023-07-28T10:31:38","slug":"tukey-kramer-test-post-hoc-w-excelu","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/tukey-kramer-test-post-hoc-w-excelu\/","title":{"rendered":"Jak wykona\u0107 test post hoc tukeya-kramera w programie excel"},"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\">Jednoczynnikow\u0105 ANOVA<\/a> stosuje si\u0119 do okre\u015blenia, czy istnieje statystycznie istotna r\u00f3\u017cnica pomi\u0119dzy \u015brednimi z trzech lub wi\u0119cej niezale\u017cnych grup.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener\">Za\u0142o\u017cenia<\/a> stosowane w ANOVA s\u0105 nast\u0119puj\u0105ce:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Hipoteza zerowa (H <sub>0<\/sub> ): \u00b5 <sub>1<\/sub> = \u00b5 <sub>2<\/sub> = \u00b5 <sub>3<\/sub> = \u2026 = \u00b5 <sub>k<\/sub> (\u015brednie s\u0105 r\u00f3wne dla ka\u017cdej grupy)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Hipoteza alternatywna: (Ha): przynajmniej jeden ze \u015brodk\u00f3w r\u00f3\u017cni si\u0119 od pozosta\u0142ych<\/span><\/p>\n<p> <span style=\"color: #000000;\">Je\u017celi <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener\">warto\u015b\u0107 p analizy<\/a> ANOVA jest poni\u017cej poziomu istotno\u015bci, mo\u017cemy odrzuci\u0107 hipotez\u0119 zerow\u0105 i stwierdzi\u0107, \u017ce mamy wystarczaj\u0105ce dowody, aby stwierdzi\u0107, \u017ce przynajmniej jedna ze \u015brednich grupowych r\u00f3\u017cni si\u0119 od pozosta\u0142ych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nie m\u00f3wi nam to jednak <em>, kt\u00f3re<\/em> grupy r\u00f3\u017cni\u0105 si\u0119 od siebie. To po prostu m\u00f3wi nam, \u017ce nie wszystkie \u015brednie grupowe s\u0105 r\u00f3wne. Aby dok\u0142adnie wiedzie\u0107, kt\u00f3re grupy si\u0119 od siebie r\u00f3\u017cni\u0105, nale\u017cy przeprowadzi\u0107 test post hoc.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Najcz\u0119\u015bciej stosowanym testem post hoc jest <strong>test Tukeya-Kramera<\/strong> , kt\u00f3ry por\u00f3wnuje \u015bredni\u0105 pomi\u0119dzy ka\u017cd\u0105 kombinacj\u0105 parami grup.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy przyk\u0142ad pokazuje, jak wykona\u0107 test Tukeya-Kramera w programie Excel.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad: test Tukeya-Kramera w Excelu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce przeprowadzamy jednokierunkow\u0105 ANOVA na trzech grupach: A, B i C. Wyniki jednokierunkowej ANOVA przedstawiono poni\u017cej:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9546 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tukeyexcel1.png\" alt=\"Jednokierunkowe wyniki tabeli ANOVA w programie Excel\" width=\"623\" height=\"360\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Powi\u0105zane:<\/strong> <a href=\"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-excel\/\" target=\"_blank\" rel=\"noopener\">Jak wykona\u0107 jednokierunkow\u0105 analiz\u0119 wariancji w programie Excel<\/a><\/span><\/p>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 p tabeli ANOVA wynosi <strong>0,000588<\/strong> . Poniewa\u017c ta warto\u015b\u0107 p jest mniejsza ni\u017c 0,05, mo\u017cemy odrzuci\u0107 hipotez\u0119 zerow\u0105 i stwierdzi\u0107, \u017ce \u015brednie mi\u0119dzy trzema grupami <em>nie<\/em> s\u0105 r\u00f3wne.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby dok\u0142adnie okre\u015bli\u0107 <em>, kt\u00f3re<\/em> \u015brednie grupowe s\u0105 r\u00f3\u017cne, mo\u017cemy wykona\u0107 test post hoc Tukeya-Kramera, wykonuj\u0105c nast\u0119puj\u0105ce kroki:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 1:<\/strong> <strong>Znajd\u017a \u015bredni\u0105 bezwzgl\u0119dn\u0105 r\u00f3\u017cnic\u0119 mi\u0119dzy ka\u017cd\u0105 grup\u0105.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Najpierw znajdziemy \u015bredni\u0105 bezwzgl\u0119dn\u0105 r\u00f3\u017cnic\u0119 mi\u0119dzy ka\u017cd\u0105 grup\u0105, korzystaj\u0105c ze \u015brednich wymienionych w pierwszej tabeli wyniku ANOVA:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9548 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tukeyexcel2.png\" alt=\"Jednokierunkowy wynik ANOVA w Excelu\" width=\"478\" height=\"383\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 2: Znajd\u017a warto\u015b\u0107 krytyczn\u0105 Q.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie musimy znale\u017a\u0107 warto\u015b\u0107 krytyczn\u0105 Q, korzystaj\u0105c z nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 krytyczna Q = Q*\u221a(s <sup>2<\/sup> <sub>zgrupowane<\/sub> \/ n.)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Q<\/strong> = Warto\u015b\u0107 zakresu Tabeli Studenta Q<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sup>2<\/sup> <sub>po\u0142\u0105czone<\/sub> =<\/strong> wariancja zebrana dla wszystkich grup<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>nie.<\/strong> = Wielko\u015b\u0107 pr\u00f3by dla danej grupy<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Aby znale\u017a\u0107 warto\u015b\u0107 Q, mo\u017cesz skorzysta\u0107 z tabeli Studentized Range Q, kt\u00f3ra wygl\u0105da nast\u0119puj\u0105co:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9549 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tukeyexcel3.png\" alt=\"Q Tabela standardowych zakres\u00f3w\" width=\"318\" height=\"358\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">W naszym przyk\u0142adzie k = liczba grup, tj. k = 3. Stopnie swobody obliczamy nast\u0119puj\u0105co: nk = 30 \u2013 3 = 27. Poniewa\u017c w powy\u017cszej tabeli nie pokazano 27, mo\u017cemy zastosowa\u0107 ostro\u017cne oszacowanie 24 Na podstawie k = 3 i df = 24 stwierdzamy, \u017ce Q = <strong>3,53<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0141\u0105czn\u0105 wariancj\u0119 mo\u017cna obliczy\u0107 jako \u015bredni\u0105 wariancji grup, kt\u00f3ra okazuje si\u0119 wynosi\u0107 <strong>19,056<\/strong> .<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9550 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tukeyexcel4.png\" alt=\"\" width=\"588\" height=\"355\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ostatecznie wielko\u015b\u0107 pr\u00f3by w ka\u017cdej grupie wynosi 10.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zatem nasz\u0105 warto\u015b\u0107 krytyczn\u0105 Q mo\u017cna obliczy\u0107 w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 krytyczna Q = Q*\u221a( <sup>s2<\/sup> <sub>zgrupowane<\/sub> \/ n.) = 3,53*\u221a(19,056\/10) = <strong>4,87<\/strong> .<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9551 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tukeyexcel5.png\" alt=\"\" width=\"555\" height=\"379\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 3: Okre\u015bl, kt\u00f3re \u015brednie grupowe s\u0105 r\u00f3\u017cne<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na koniec mo\u017cemy por\u00f3wna\u0107 \u015bredni\u0105 bezwzgl\u0119dn\u0105 r\u00f3\u017cnic\u0119 mi\u0119dzy ka\u017cd\u0105 grup\u0105 z warto\u015bci\u0105 krytyczn\u0105 Q. Je\u015bli bezwzgl\u0119dna \u015brednia r\u00f3\u017cnica jest wi\u0119ksza ni\u017c warto\u015b\u0107 krytyczna Q, w\u00f3wczas r\u00f3\u017cnica mi\u0119dzy \u015brednimi grupowymi jest istotna statystycznie:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9552 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tukeyexcel6.png\" alt=\"Test Tukeya w Excelu\" width=\"560\" height=\"381\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Na podstawie testu post hoc Tukeya-Kramera stwierdzono, co nast\u0119puje:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">R\u00f3\u017cnica \u015brednich pomi\u0119dzy grup\u0105 A i grup\u0105 B jest istotna statystycznie.<\/span><\/li>\n<li> <span style=\"color: #000000;\">R\u00f3\u017cnica \u015brednich pomi\u0119dzy grup\u0105 B i grup\u0105 C <em>nie jest<\/em> istotna statystycznie.<\/span><\/li>\n<li> <span style=\"color: #000000;\">R\u00f3\u017cnica \u015brednich pomi\u0119dzy grup\u0105 A i grup\u0105 C jest istotna statystycznie.<\/span><\/li>\n<\/ul>\n<h3> <strong>Dodatkowe zasoby<\/strong><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/w-jedna-strone-anova-excel\/\" target=\"_blank\" rel=\"noopener\">Jak wykona\u0107 jednokierunkow\u0105 ANOVA w programie Excel<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/testy-post-hoc-anova\/\" target=\"_blank\" rel=\"noopener\">Przewodnik po korzystaniu z test\u00f3w post-hoc z ANOVA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jednoczynnikow\u0105 ANOVA stosuje si\u0119 do okre\u015blenia, czy istnieje statystycznie istotna r\u00f3\u017cnica pomi\u0119dzy \u015brednimi z trzech lub wi\u0119cej niezale\u017cnych grup. Za\u0142o\u017cenia stosowane w ANOVA s\u0105 nast\u0119puj\u0105ce: Hipoteza zerowa (H 0 ): \u00b5 1 = \u00b5 2 = \u00b5 3 = \u2026 = \u00b5 k (\u015brednie s\u0105 r\u00f3wne dla ka\u017cdej grupy) Hipoteza alternatywna: (Ha): przynajmniej jeden ze [&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-884","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 wykona\u0107 test post hoc Tukeya-Kramera w programie Excel - Statologia<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie, jak wykona\u0107 test post hoc Tukeya-Kramera w Excelu po jednoczynnikowej 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\/tukey-kramer-test-post-hoc-w-excelu\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak wykona\u0107 test post hoc Tukeya-Kramera w programie Excel - Statologia\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie, jak wykona\u0107 test post hoc Tukeya-Kramera w Excelu po jednoczynnikowej ANOVA.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/tukey-kramer-test-post-hoc-w-excelu\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T10:31:38+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tukeyexcel1.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\/tukey-kramer-test-post-hoc-w-excelu\/\",\"url\":\"https:\/\/statorials.org\/pl\/tukey-kramer-test-post-hoc-w-excelu\/\",\"name\":\"Jak wykona\u0107 test post hoc Tukeya-Kramera w programie Excel - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-28T10:31:38+00:00\",\"dateModified\":\"2023-07-28T10:31:38+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie, jak wykona\u0107 test post hoc Tukeya-Kramera w Excelu po jednoczynnikowej ANOVA.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/tukey-kramer-test-post-hoc-w-excelu\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/tukey-kramer-test-post-hoc-w-excelu\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/tukey-kramer-test-post-hoc-w-excelu\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak wykona\u0107 test post hoc tukeya-kramera w programie excel\"}]},{\"@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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