{"id":434,"date":"2023-07-29T22:51:45","date_gmt":"2023-07-29T22:51:45","guid":{"rendered":"https:\/\/statorials.org\/de\/bartletts-testrechner\/"},"modified":"2023-07-29T22:51:45","modified_gmt":"2023-07-29T22:51:45","slug":"bartletts-testrechner","status":"publish","type":"post","link":"https:\/\/statorials.org\/de\/bartletts-testrechner\/","title":{"rendered":"Bartletts testrechner"},"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><script type=\"text\/javascript\" src=\"https:\/\/www.Statorials.org\/wp-content\/themes\/wisteria\/mannwhitneyu.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;\ntext-align: center;\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_text {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_text_area {\ndisplay:inline-block;\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#calcTitle {\ntext-align: center;\nfont-size: 20px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\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, input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #button {\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>    #button:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>\t.label_radio {\n\ttext-align: center;\n    }<\/p>\n<p>td, tr, th {\n    border: 1px solid black;\n}\ntable {\n    border-collapse: collapse;\n}\ntd, th {\n    min-width: 50px;\n    height: 21px;\n}\n.table_span_x, .table_span_y {\n    width: 100%;\n    display: block;\n}<\/p>\n<p>#words_table {\ncolor: black;\nfont-family: Raleway;\nmax-width: 350px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 20px;\n}<\/p>\n<p>#summary_table {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 20px;\n}<\/p>\n<p>    .label_radio {\n\ttext-align: center;\n}<\/p>\n<p>#text_area_input {\n\tpadding-left: 5%;\n\tfloat: left;\n}<\/p>\n<p>textarea, textarea:focus {\n\tmargin-right: 5px;\n\twidth: 85px;\n\toutline: 1px solid #aeaeae;\n}\n<\/style>\n<div id=\"words_text\">\n<p style=\"text-align: left\"><b>Mit dem Bartlett-Test<\/b> wird getestet, ob Stichproben aus Populationen mit gleichen Varianzen stammen. Einige statistische Tests, wie z <a href=\"https:\/\/statorials.org\/de\/einweg-anova\/\" target=\"_blank\" rel=\"noopener\">. B. die einfaktorielle ANOVA<\/a> , gehen davon aus, dass die Varianzen zwischen den Stichproben gleich sind. Zur \u00dcberpr\u00fcfung dieser Hypothese kann der Bartlett-Test verwendet werden.<\/p>\n<p style=\"text-align: left\"> Um einen Bartlett-Test an bis zu f\u00fcnf Proben durchzuf\u00fchren, geben Sie einfach die folgenden Datenwerte ein und klicken Sie auf die Schaltfl\u00e4che \u201eBerechnen\u201c. Eine Teststatistik und der entsprechende p-Wert werden unten dargestellt. Ein p-Wert von weniger als 0,05 ist ein starker Beweis daf\u00fcr, dass die Varianzen zwischen den Stichproben nicht gleich sind.<\/p>\n<\/div>\n<div id=\"words_text\">\n<div id=\"text_area_input\"> Probe 1 || Probe 2 || Probe 3 || Probe 4 || Probe 5 <\/div>\n<div id=\"text_area_input\"><textarea id=\"a\" name=\"a\" rows=\"15\" cols=\"4\"><\/textarea><textarea id=\"b\" name=\"b\" rows=\"15\" cols=\"4\"><\/textarea><textarea id=\"c\" name=\"c\" rows=\"15\" cols=\"4\"><\/textarea><textarea id=\"d\" name=\"d\" rows=\"15\" cols=\"4\"><\/textarea><textarea id=\"e\" name=\"e\" rows=\"15\" cols=\"4\"><\/textarea><\/div>\n<\/div>\n<div id=\"words\"><input type=\"button\" id=\"button\" onclick=\"calc()\" value=\"Calculate\"><\/div>\n<div>\n<p><span id=\"B\"><\/span><\/p>\n<\/div>\n<div>\n<p><span id=\"p\"><\/span><\/p>\n<\/div>\n<p><script><\/p>\n<p>\/\/create function that performs t test calculations\nfunction calc() {<\/p>\n<p>\/\/define addition function\n\t\tfunction add(a, b) {\n\t\t    return a + b;\n\t\t}<\/p>\n<p>\/\/get raw data\n    \/\/group a\n    \/\/    var values_a_input = document.getElementsByClassName('a');\n\t\/\/var values_a_array = [];\n\t\/\/for (var i = 0; i < values_a_input.length; i++) {\n    \/\/  \tvalues_a_array[i] = values_a_input[i].innerText;\n    \/\/    }\n\t\/\/values_a_array = values_a_array.filter(n => n);\n\t\/\/var group_a = values_a_array.map(Number);\n\tif(document.getElementById(\"a\").value == '') {\n\t    var group_a = '';\n\t} else {\n\t    var group_a = document.getElementById('a').value.match(\/\\d+\/g).map(Number);\n\t}<\/p>\n<p>\tif(document.getElementById(\"b\").value == '') {\n\t    var group_b = '';\n\t} else {\n\t    var group_b = document.getElementById('b').value.match(\/\\d+\/g).map(Number);\n\t}<\/p>\n<p>\tif(document.getElementById(\"c\").value == '') {\n\t    var group_c = '';\n\t} else {\n\t    var group_c = document.getElementById('c').value.match(\/\\d+\/g).map(Number);\n\t}<\/p>\n<p>\tif(document.getElementById(\"d\").value == '') {\n\t    var group_d = '';\n\t} else {\n\t    var group_d = document.getElementById('d').value.match(\/\\d+\/g).map(Number);\n\t}<\/p>\n<p>\tif(document.getElementById(\"e\").value == '') {\n\t    var group_e = '';\n\t} else {\n\t    var group_e = document.getElementById('e').value.match(\/\\d+\/g).map(Number);\n\t}<\/p>\n<p>\tvar all_groups = (group_a.concat(group_b, group_c, group_d, group_e)).filter(n => n);<\/p>\n<p>\t\/\/get summary stats of each group\n\tif (group_a.length > 0) { var mean_group_a = math.mean(group_a); };\n\tif (group_b.length > 0) { var mean_group_b = math.mean(group_b); };\n\tif (group_c.length > 0) { var mean_group_c = math.mean(group_c); };\n\tif (group_d.length > 0) { var mean_group_d = math.mean(group_d); };\n\tif (group_e.length > 0) { var mean_group_e = math.mean(group_e); };<\/p>\n<p>\tif (group_a.length > 0) { var var_group_a = math.var(group_a); };\n\tif (group_b.length > 0) { var var_group_b = math.var(group_b); };\n\tif (group_c.length > 0) { var var_group_c = math.var(group_c); };\n\tif (group_d.length > 0) { var var_group_d = math.var(group_d); };\n\tif (group_e.length > 0) { var var_group_e = math.var(group_e); };<\/p>\n<p>\tif (group_a.length > 0) { var lnvar_group_a = Math.log(var_group_a); } else { var lnvar_group_a = 0;};\n\tif (group_b.length > 0) { var lnvar_group_b = Math.log(var_group_b); } else { var lnvar_group_b = 0;};\n\tif (group_c.length > 0) { var lnvar_group_c = Math.log(var_group_c); } else { var lnvar_group_c = 0;};\n\tif (group_d.length > 0) { var lnvar_group_d = Math.log(var_group_d); } else { var lnvar_group_d = 0;};\n\tif (group_e.length > 0) { var lnvar_group_e = Math.log(var_group_e); } else { var lnvar_group_e = 0;};<\/p>\n<p>\tif (group_a.length > 0) { var df_group_a = group_a.length-1; } else { var df_group_a = 0;};\n\tif (group_b.length > 0) { var df_group_b = group_b.length-1; } else { var df_group_b = 0;};\n\tif (group_c.length > 0) { var df_group_c = group_c.length-1; } else { var df_group_c = 0;};\n\tif (group_d.length > 0) { var df_group_d = group_d.length-1; } else { var df_group_d = 0;};\n\tif (group_e.length > 0) { var df_group_e = group_e.length-1; } else { var df_group_e = 0;};<\/p>\n<p>\tvar total_df = [df_group_a, df_group_b, df_group_c, df_group_d, df_group_e].reduce(add, 0);\n\tvar total_df1 = 1 \/ total_df;<\/p>\n<p>\tvar lnvar_array = [lnvar_group_a, lnvar_group_b, lnvar_group_c, lnvar_group_d, lnvar_group_e];\n\tvar df_array = [df_group_a, df_group_b, df_group_c, df_group_d, df_group_e];\n\tvar lnvar_df_array = []\n\tfor (var i = 0; i < lnvar_array.length; i++) {\n\t    lnvar_df_array.push(lnvar_array[i] * df_array[i]);\n\t}\n\t\n\tvar sum_lnvar_df_array = lnvar_df_array.reduce(add, 0);\n\t\n\tif (group_a.length > 0) { var flag_group_a = 1; } else { var flag_group_a = 0;};\n\tif (group_b.length > 0) { var flag_group_b = 1; } else { var flag_group_b = 0;};\n\tif (group_c.length > 0) { var flag_group_c = 1; } else { var flag_group_c = 0;};\n\tif (group_d.length > 0) { var flag_group_d = 1; } else { var flag_group_d = 0;};\n\tif (group_e.length > 0) { var flag_group_e = 1; } else { var flag_group_e = 0;};<\/p>\n<p>\tif (group_a.length > 0) { var df1_group_a = 1\/df_group_a; } else { var df1_group_a = 0;};\n\tif (group_b.length > 0) { var df1_group_b = 1\/df_group_b; } else { var df1_group_b = 0;};\n\tif (group_c.length > 0) { var df1_group_c = 1\/df_group_c; } else { var df1_group_c = 0;};\n\tif (group_d.length > 0) { var df1_group_d = 1\/df_group_d; } else { var df1_group_d = 0;};\n\tif (group_e.length > 0) { var df1_group_e = 1\/df_group_e; } else { var df1_group_e = 0;};<\/p>\n<p>\tvar df1_array = [df1_group_a, df1_group_b, df1_group_c, df1_group_d, df1_group_e];\n\tvar df1_array_sum = df1_array.reduce(add, 0);<\/p>\n<p>\tvar treatments = [flag_group_a, flag_group_b, flag_group_c, flag_group_d, flag_group_e].reduce(add, 0) - 1;<\/p>\n<p>\tif (treatments == 1) {\n    \tvar total_var = jStat.pooledvariance([group_a, group_b]);\n    \tvar total_lnvar = Math.log(total_var);\n\t} else if (treatments == 2) {\n\t   var total_var = jStat.pooledvariance([group_a, group_b, group_c]);\n\t   var total_lnvar = Math.log(total_var);\n\t} else if (treatments == 3) {\n\t   var total_var = jStat.pooledvariance([group_a, group_b, group_c, group_d]);\n\t   var total_lnvar = Math.log(total_var);\n\t} else if (treatments == 4) {\n\t   var total_var = jStat.pooledvariance([group_a, group_b, group_c, group_d, group_e]);\n\t   var total_lnvar = Math.log(total_var);\n\t}\n\/\/calculate test statistic\n    var b_numerator = total_df * total_lnvar - sum_lnvar_df_array;\n    var b_denominator = 1 - (-1 \/ (3*treatments)) * (df1_array_sum - total_df1);\n    var b = b_numerator \/ b_denominator;\n    var p = 1 - jStat.chisquare.cdf(b, treatments);\nconsole.log(df1_array, lnvar_array, total_df, total_var, total_lnvar, total_df1);\n\/\/output results\ndocument.getElementById('B').innerHTML = \"Test Statistic B: \" + b.toFixed(5);\ndocument.getElementById('p').innerHTML = \"p-value: \" + p.toFixed(5);\n}<\/p>\n<p><\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mit dem Bartlett-Test wird getestet, ob Stichproben aus Populationen mit gleichen Varianzen stammen. Einige statistische Tests, wie z . B. die einfaktorielle ANOVA , gehen davon aus, dass die Varianzen zwischen den Stichproben gleich sind. Zur \u00dcberpr\u00fcfung dieser Hypothese kann der Bartlett-Test verwendet werden. Um einen Bartlett-Test an bis zu f\u00fcnf Proben durchzuf\u00fchren, geben Sie [&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>Bartlett-Testrechner \u2013 Statorials<\/title>\n<meta name=\"description\" content=\"Dieser Rechner f\u00fchrt einen Bartlett-Test durch, mit dem \u00fcberpr\u00fcft wird, ob Stichproben aus Populationen mit gleichen Varianzen stammen.\" \/>\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\/bartletts-testrechner\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bartlett-Testrechner \u2013 Statorials\" \/>\n<meta property=\"og:description\" content=\"Dieser Rechner f\u00fchrt einen Bartlett-Test durch, mit dem \u00fcberpr\u00fcft wird, ob Stichproben aus Populationen mit gleichen Varianzen stammen.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/de\/bartletts-testrechner\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T22:51:45+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\t<meta name=\"twitter:label2\" content=\"Gesch\u00e4tzte Lesezeit\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 Minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/de\/bartletts-testrechner\/\",\"url\":\"https:\/\/statorials.org\/de\/bartletts-testrechner\/\",\"name\":\"Bartlett-Testrechner \u2013 Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/de\/#website\"},\"datePublished\":\"2023-07-29T22:51:45+00:00\",\"dateModified\":\"2023-07-29T22:51:45+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/de\/#\/schema\/person\/ec75c4d6365f2708f8a0ad3a42121aa0\"},\"description\":\"Dieser Rechner f\u00fchrt einen Bartlett-Test durch, mit dem \u00fcberpr\u00fcft wird, ob Stichproben aus Populationen mit gleichen Varianzen stammen.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/de\/bartletts-testrechner\/#breadcrumb\"},\"inLanguage\":\"de-DE\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/de\/bartletts-testrechner\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/de\/bartletts-testrechner\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Heim\",\"item\":\"https:\/\/statorials.org\/de\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Bartletts testrechner\"}]},{\"@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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