{"id":1495,"date":"2023-07-26T03:59:37","date_gmt":"2023-07-26T03:59:37","guid":{"rendered":"https:\/\/statorials.org\/de\/gruppenvarianzrechner\/"},"modified":"2023-07-26T03:59:37","modified_gmt":"2023-07-26T03:59:37","slug":"gruppenvarianzrechner","status":"publish","type":"post","link":"https:\/\/statorials.org\/de\/gruppenvarianzrechner\/","title":{"rendered":"Geb\u00fcndelter gap-rechner"},"content":{"rendered":"<p><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjs\/5.1.1\/math.js\"><\/script><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/jstat@latest\/dist\/jstat.min.js\"><\/script><\/p>\n<style>\n@import url('https:\/\/fonts.googleapis.com\/css?family=Droid+Serif|Raleway');<\/p>\n<p>.axis--y .domain {\n  display: none;\n}<\/p>\n<p>h1 {\ntext-align: center;\nfont-size: 50px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\n}<\/p>\n<p>p {\ncolor: black;\nmargin-bottom: 15px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>#words {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#words_calc {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#words_calc input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n    max-height: 35px;\n}<\/p>\n<p>#hr_top {\nwidth: 30%;\nmargin-bottom: 0px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#hr_bottom {\nwidth: 30%;\nmargin-top: 15px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#words label, #words input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n    max-height: 35px;\n}<\/p>\n<p>    #buttonCalc {\n      border: 1px solid;\n      border-radius: 10px;\n      margin-top: 20px;\n      padding: 10px 10px;\n      cursor: pointer;\n      outline: none;\n      background-color: white;\n      color: black;\n      font-family: 'Work Sans', sans-serif;\n      border: 1px solid grey;\n      \/* Green *\/\n    }<\/p>\n<p>    #buttonCalc:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>#words_output {\ntext-align: center;\n}<\/p>\n<p>#solution_div {\ntext-align: center;\n}<\/p>\n<p>#words_intro {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_table {\ncolor: black;\nfont-family: Raleway;\nmax-width: 350px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>.text_areas {\ncolor: black;\nfont-family: Raleway;\nmax-width: 350px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>.label_radio {\ntext-align: center;\n}\n<\/style>\n<div id=\"words_intro\">Wenn wir einen <a href=\"https:\/\/statorials.org\/de\/testen-sie-ihre-beiden-proben\/\" target=\"_blank\" rel=\"noopener\">t-Test bei zwei Stichproben<\/a> durchf\u00fchren, gehen wir im Allgemeinen davon aus, dass die Varianzen zwischen den beiden Stichproben gleich sind. Unter dieser Annahme k\u00f6nnen wir die <a href=\"https:\/\/statorials.org\/de\/gruppenvarianz\/\" target=\"_blank\" rel=\"noopener\">gepoolte Varianz<\/a> berechnen, die im T-Test bei zwei Stichproben verwendet werden soll.<\/div>\n<div id=\"words_intro\"> Um die gepoolte Varianz f\u00fcr zwei Stichproben zu berechnen, geben Sie einfach die folgenden Informationen ein und klicken Sie dann auf die Schaltfl\u00e4che \u201eBerechnen\u201c.<\/div>\n<div id=\"words\"> <label class=\"label_radio\" for=\"raw\">Geben Sie Rohdaten ein<\/label><input type=\"radio\" id=\"raw\" name=\"tails\" onclick=\"check()\" checked=\"\"> <label class=\"label_radio\" for=\"summary\">Geben Sie zusammenfassende Daten ein<\/label> <input type=\"radio\" id=\"summary\" name=\"tails\" onclick=\"check()\"><\/div>\n<div id=\"words_table\">\n<div class=\"text_areas\">\n<p style=\"text-align:center\"> <b>Probe 1<\/b><\/p>\n<p><textarea id=\"rawData1\" rows=\"5\" cols=\"40\"> 301, 298, 295, 297, 304, 305, 309, 298, 291, 299, 293, 304<\/textarea><\/p>\n<\/div>\n<div class=\"text_areas\">\n<p style=\"text-align:center\"> <b>Probe 2<\/b><\/p>\n<p><textarea id=\"rawData2\" rows=\"5\" cols=\"40\"> 302, 309, 324, 313, 312, 310, 305, 298, 299, 300, 289, 294<\/textarea><\/p>\n<\/div>\n<\/div>\n<div id=\"summary_table\">\n<div id=\"words\"> <label><b>s <sub>1<\/sub><\/b> (Standardabweichung von Probe 1)<\/label><input type=\"number\" id=\"s1\" value=\"18.5\"><\/div>\n<div id=\"words\"> <label><b>n <sub>1<\/sub><\/b> (Probe 1 Gr\u00f6\u00dfe)<\/label><input type=\"number\" id=\"n1\" value=\"40\"><\/div>\n<div id=\"words\"> <label><b>s <sub>2<\/sub><\/b> (Standardabweichung von Probe 2)<\/label><input type=\"number\" id=\"s2\" value=\"16.7\"><\/div>\n<div id=\"words\"> <label><b>n <sub>2<\/sub><\/b> (Probengr\u00f6\u00dfe 2)<\/label> <input type=\"number\" id=\"n2\" value=\"38\"><\/div>\n<\/div>\n<div id=\"words_calc\"><input class=\"input_label_calc\" type=\"button\" id=\"buttonCalc\" onclick=\"calc()\" value=\"Calculate\"><\/div>\n<div id=\"words\">\n<p> <b>Gepoolte Varianz =<\/b> <span id=\"pooled\">59,905303<\/span><\/p>\n<\/div>\n<p><script><\/p>\n<p>\/\/set summary table to hidden to start\nvar summary_display = document.getElementById(\"summary_table\");\nsummary_display.style.display = \"none\";<\/p>\n<p>\/\/find which radio button is checked\nfunction check() {\nif (document.getElementById('raw').checked) {\n\tvar table_display = document.getElementById(\"words_table\");\n        table_display.style.display = \"block\";\n        var summary_display = document.getElementById(\"summary_table\");\n        summary_display.style.display = \"none\";\n\t} else {\n\tvar table_display = document.getElementById(\"words_table\");\n        table_display.style.display = \"none\";\n        var summary_display = document.getElementById(\"summary_table\");\n        summary_display.style.display = \"block\";\n\t}<\/p>\n<p>} \/\/end check<\/p>\n<p>\/\/perform one-sample t-test\nfunction calc() {\nif (document.getElementById('summary').checked) {\nvar s1 = +document.getElementById('s1').value;\nvar n1 = +document.getElementById('n1').value;\nvar s2 = +document.getElementById('s2').value;\nvar n2 = +document.getElementById('n2').value;<\/p>\n<p>var df = n1-(-1*n2)-2;\nvar pooled = Math.sqrt(((n1-1)*Math.pow(s1,2) - (-1*((n2-1)*Math.pow(s2,2))))\/df);\nvar pooled2 = pooled*pooled;<\/p>\n<p>document.getElementById('pooled').innerHTML = pooled2.toFixed(6);\n\t} else {\nvar raw1 = document.getElementById('rawData1').value.split(',').map(Number);\nvar raw2 = document.getElementById('rawData2').value.split(',').map(Number);\nvar s1 = math.std(raw1);\nvar n1 = raw1.length;\nvar s2 = math.std(raw2);\nvar n2 = raw2.length;<\/p>\n<p>var df = n1-(-1*n2)-2;\nvar pooled = Math.sqrt(((n1-1)*Math.pow(s1,2) - (-1*((n2-1)*Math.pow(s2,2))))\/df);\nvar pooled2 = pooled*pooled;<\/p>\n<p>document.getElementById('pooled').innerHTML = pooled2.toFixed(6);\n\t}<\/p>\n<p>\/\/output results\n}<\/p>\n<p><\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Wenn wir einen t-Test bei zwei Stichproben durchf\u00fchren, gehen wir im Allgemeinen davon aus, dass die Varianzen zwischen den beiden Stichproben gleich sind. Unter dieser Annahme k\u00f6nnen wir die gepoolte Varianz berechnen, die im T-Test bei zwei Stichproben verwendet werden soll. Um die gepoolte Varianz f\u00fcr zwei Stichproben zu berechnen, geben Sie einfach die folgenden [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Gepoolter Varianzrechner \u2013 Statistik<\/title>\n<meta name=\"description\" content=\"Dieser Rechner ermittelt automatisch die gepoolte Varianz zwischen zwei Stichproben.\" \/>\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\/de\/gruppenvarianzrechner\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Gepoolter Varianzrechner \u2013 Statistik\" \/>\n<meta property=\"og:description\" content=\"Dieser Rechner ermittelt automatisch die gepoolte Varianz zwischen zwei Stichproben.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/de\/gruppenvarianzrechner\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T03:59:37+00:00\" \/>\n<meta name=\"author\" content=\"Dr. Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Verfasst von\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. Benjamin Anderson\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/de\/gruppenvarianzrechner\/\",\"url\":\"https:\/\/statorials.org\/de\/gruppenvarianzrechner\/\",\"name\":\"Gepoolter Varianzrechner \u2013 Statistik\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/de\/#website\"},\"datePublished\":\"2023-07-26T03:59:37+00:00\",\"dateModified\":\"2023-07-26T03:59:37+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/de\/#\/schema\/person\/ec75c4d6365f2708f8a0ad3a42121aa0\"},\"description\":\"Dieser Rechner ermittelt automatisch die gepoolte Varianz zwischen zwei Stichproben.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/de\/gruppenvarianzrechner\/#breadcrumb\"},\"inLanguage\":\"de-DE\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/de\/gruppenvarianzrechner\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/de\/gruppenvarianzrechner\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Heim\",\"item\":\"https:\/\/statorials.org\/de\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Geb\u00fcndelter gap-rechner\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/de\/#website\",\"url\":\"https:\/\/statorials.org\/de\/\",\"name\":\"Statorials\",\"description\":\"Ihr Leitfaden f\u00fcr statistische Kompetenz !\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/de\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"de-DE\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/de\/#\/schema\/person\/ec75c4d6365f2708f8a0ad3a42121aa0\",\"name\":\"Dr. Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"de-DE\",\"@id\":\"https:\/\/statorials.org\/de\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/de\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/de\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. Benjamin Anderson\"},\"description\":\"Hallo, ich bin Benjamin, ein pensionierter Statistikprofessor, der sich zum engagierten Statorials-Lehrer entwickelt hat. 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