{"id":1001,"date":"2023-07-28T01:01:14","date_gmt":"2023-07-28T01:01:14","guid":{"rendered":"https:\/\/statorials.org\/pl\/jak-znalezc-z-alfa-2-za-2\/"},"modified":"2023-07-28T01:01:14","modified_gmt":"2023-07-28T01:01:14","slug":"jak-znalezc-z-alfa-2-za-2","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/jak-znalezc-z-alfa-2-za-2\/","title":{"rendered":"Jak znale\u017a\u0107 z alpha\/2 (za\/2)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Ilekro\u0107 w statystyce spotykasz termin <strong>z <sub>\u03b1\/2<\/sub><\/strong> , odnosi si\u0119 on po prostu do <strong>krytycznej warto\u015bci z<\/strong> w tabeli z, kt\u00f3ra odpowiada \u03b1\/2.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym samouczku wyja\u015bniono nast\u0119puj\u0105ce kwestie:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Jak znale\u017a\u0107 z <sub>\u03b1\/2<\/sub> za pomoc\u0105 tabeli az.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Jak znale\u017a\u0107 z <sub>\u03b1\/2<\/sub> za pomoc\u0105 kalkulatora.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Najcz\u0119stsze warto\u015bci dla z <sub>\u03b1\/2<\/sub> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Chod\u017amy!<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Jak znale\u017a\u0107 z <sub>\u03b1\/2<\/sub> za pomoc\u0105 tabeli az<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce chcemy znale\u017a\u0107 z <sub>\u03b1\/2<\/sub> dla testu przy poziomie ufno\u015bci 90%.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym przypadku \u03b1 b\u0119dzie wynosi\u0107 1 \u2013 0,9 = <strong>0,1<\/strong> . Zatem \u03b1\/2 = 0,1\/2 = <strong>0,05<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby znale\u017a\u0107 odpowiedni\u0105 krytyczn\u0105 warto\u015b\u0107 z, po prostu szukamy <strong>0,05<\/strong> w tablicy az:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-10393 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/za2.png\" alt=\"za\/2 w tabeli z\" width=\"619\" height=\"611\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Nale\u017cy zauwa\u017cy\u0107, \u017ce dok\u0142adna warto\u015b\u0107 <strong>0,05<\/strong> nie pojawia si\u0119 w tabeli, ale mie\u015bci si\u0119 bezpo\u015brednio pomi\u0119dzy warto\u015bciami <strong>0,0505<\/strong> i <strong>0,0495<\/strong> . Odpowiednie krytyczne warto\u015bci z poza tabel\u0105 to <strong>-1,64<\/strong> i <strong>-1,65<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dziel\u0105c r\u00f3\u017cnic\u0119, widzimy, \u017ce warto\u015b\u0107 krytyczna z wyniesie <strong>-1,645<\/strong> . I zazwyczaj, gdy u\u017cywamy z <sub>\u03b1\/2,<\/sub> przyjmujemy warto\u015b\u0107 bezwzgl\u0119dn\u0105. Zatem z <sub>0,01\/2<\/sub> = <strong>1,645<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Jak znale\u017a\u0107 z <sub>\u03b1\/2<\/sub> za pomoc\u0105 kalkulatora<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Mo\u017cemy r\u00f3wnie\u017c u\u017cy\u0107<\/span> krytycznego kalkulatora warto\u015bci Z <span style=\"color: #000000;\">, aby znale\u017a\u0107 z <sub>\u03b1\/2<\/sub> dla niekt\u00f3rych test\u00f3w.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad w przypadku niekt\u00f3rych test\u00f3w wykorzystuj\u0105cych poziom ufno\u015bci 90% mo\u017cemy po prostu wprowadzi\u0107 <strong>0,1<\/strong> jako poziom istotno\u015bci, a kalkulator automatycznie zwr\u00f3ci warto\u015b\u0107 <strong>1,645<\/strong> jako odpowiadaj\u0105c\u0105 krytyczn\u0105 warto\u015b\u0107 z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-10394 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/za2_2.png\" alt=\"Kalkulator krytycznej warto\u015bci Z\" width=\"392\" height=\"310\" srcset=\"\" sizes=\"auto, \"><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Wsp\u00f3lne warto\u015bci dla z <sub>\u03b1\/2<\/sub><\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csza tabela przedstawia najcz\u0119stsze warto\u015bci krytyczne dla r\u00f3\u017cnych warto\u015bci \u03b1:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-10395 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/za2_3.png\" alt=\"Typowe warto\u015bci za\/2\" width=\"206\" height=\"191\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Spos\u00f3b interpretacji tej tabeli jest nast\u0119puj\u0105cy:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">W przypadku testu wykorzystuj\u0105cego poziom ufno\u015bci 90% (np. \u03b1 = 0,1) warto\u015b\u0107 krytyczna z wynosi <strong>1,645<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">W przypadku testu wykorzystuj\u0105cego poziom ufno\u015bci 95% (np. \u03b1 = 0,05) krytyczna warto\u015b\u0107 z wynosi <strong>1,96<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">W przypadku testu wykorzystuj\u0105cego 99% poziom ufno\u015bci (np. \u03b1 = 0,01) krytyczna warto\u015b\u0107 z wynosi <strong>5,576<\/strong> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">I tak dalej.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/pl\/jak-korzystac-z-tabeli-z\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak korzysta\u0107 z tabeli Z (z przyk\u0142adami)<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/z-kalkulator-wartosci-krytycznej-ti-84\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak znale\u017a\u0107 krytyczn\u0105 warto\u015b\u0107 Z na kalkulatorze TI-84<\/a><br \/><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ilekro\u0107 w statystyce spotykasz termin z \u03b1\/2 , odnosi si\u0119 on po prostu do krytycznej warto\u015bci z w tabeli z, kt\u00f3ra odpowiada \u03b1\/2. W tym samouczku wyja\u015bniono nast\u0119puj\u0105ce kwestie: Jak znale\u017a\u0107 z \u03b1\/2 za pomoc\u0105 tabeli az. Jak znale\u017a\u0107 z \u03b1\/2 za pomoc\u0105 kalkulatora. Najcz\u0119stsze warto\u015bci dla z \u03b1\/2 . Chod\u017amy! Jak znale\u017a\u0107 z \u03b1\/2 [&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-1001","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 znale\u017a\u0107 Z Alpha\/2 (za\/2) \u2013 Statologia<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie terminu za\/2 w statystyce, \u0142\u0105cznie z przyk\u0142adami, jak go znale\u017a\u0107.\" \/>\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\/jak-znalezc-z-alfa-2-za-2\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak znale\u017a\u0107 Z Alpha\/2 (za\/2) \u2013 Statologia\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie terminu za\/2 w statystyce, \u0142\u0105cznie z przyk\u0142adami, jak go znale\u017a\u0107.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/jak-znalezc-z-alfa-2-za-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T01:01:14+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/za2.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=\"1 minuta\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/jak-znalezc-z-alfa-2-za-2\/\",\"url\":\"https:\/\/statorials.org\/pl\/jak-znalezc-z-alfa-2-za-2\/\",\"name\":\"Jak znale\u017a\u0107 Z Alpha\/2 (za\/2) \u2013 Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-28T01:01:14+00:00\",\"dateModified\":\"2023-07-28T01:01:14+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie terminu za\/2 w statystyce, \u0142\u0105cznie z przyk\u0142adami, jak go znale\u017a\u0107.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/jak-znalezc-z-alfa-2-za-2\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/jak-znalezc-z-alfa-2-za-2\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/jak-znalezc-z-alfa-2-za-2\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak znale\u017a\u0107 z alpha\/2 (za\/2)\"}]},{\"@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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