{"id":745,"date":"2023-07-28T21:47:40","date_gmt":"2023-07-28T21:47:40","guid":{"rendered":"https:\/\/statorials.org\/my\/welchs-t-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%95%e1%80%b1%e1%80%ab%e1%80%84%e1%80%ba%e1%80%b8%e1%80%85%e1%80%80%e1%80%ba\/"},"modified":"2023-07-28T21:47:40","modified_gmt":"2023-07-28T21:47:40","slug":"welchs-t-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%95%e1%80%b1%e1%80%ab%e1%80%84%e1%80%ba%e1%80%b8%e1%80%85%e1%80%80%e1%80%ba","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/welchs-t-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%95%e1%80%b1%e1%80%ab%e1%80%84%e1%80%ba%e1%80%b8%e1%80%85%e1%80%80%e1%80%ba\/","title":{"rendered":"Welch \u104f t-test \u1002\u100f\u1014\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1000\u103a"},"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\"><b>Welch&#8217;s t-test \u1000\u102d\u102f<\/b> \u101c\u1030\u1026\u1038\u101b\u1031 \u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u101e\u100a\u103a \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038 \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/div>\n<div id=\"words_intro\"> \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u101f\u102f \u1019\u101a\u1030\u1006\u1015\u102b\u104b \u101e\u1004\u103a\u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101c\u102d\u102f\u1015\u102b\u1000\u104a <a href=\"https:\/\/statorials.org\/my\/ta-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1002\u100f\u1014\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1000\u103a-\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\/\" target=\"_blank\" rel=\"noopener\">\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f t-test calculator \u1000\u102d\u102f<\/a> \u101e\u102f\u1036\u1038\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u104b<\/div>\n<div id=\"words_intro\"> Welch t-test \u1000\u102d\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u103c\u100a\u1037\u103a\u1005\u103d\u1000\u103a\u1015\u103c\u102e\u1038 \u201c\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a\u201d \u1001\u101c\u102f\u1010\u103a\u1000\u102d\u102f \u1014\u103e\u102d\u1015\u103a\u1015\u102b\u104b<\/div>\n<div id=\"words\"> <label class=\"label_radio\" for=\"raw\">\u1012\u1031\u1010\u102c\u1021\u1000\u103c\u1019\u103a\u1038\u1011\u100a\u1037\u103a\u1015\u102b\u104b<\/label><input type=\"radio\" id=\"raw\" name=\"tails\" onclick=\"check()\" checked=\"\"> <label class=\"label_radio\" for=\"summary\">\u1021\u1014\u103e\u1005\u103a\u1001\u103b\u102f\u1015\u103a\u1012\u1031\u1010\u102c\u1011\u100a\u1037\u103a\u1015\u102b\u104b<\/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>\u1014\u1019\u1030\u1014\u102c \u1041<\/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>\u1014\u1019\u1030\u1014\u102c \u1042<\/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><span style=\"text-decoration:overline\">x<\/span> <sub>1<\/sub><\/b> (\u1025\u1015\u1019\u102c 1 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e)<\/label><input type=\"number\" id=\"x1\" value=\"300\"><\/div>\n<div id=\"words\"> <label><b>s <sub>1<\/sub><\/b> (\u1005\u1036\u1014\u1019\u1030\u1014\u102c 1 \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a)<\/label><input type=\"number\" id=\"s1\" value=\"18.5\"><\/div>\n<div id=\"words\"> <label><b>n <sub>1<\/sub><\/b> (\u1014\u1019\u1030\u1014\u102c 1 \u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038)<\/label><input type=\"number\" id=\"n1\" value=\"40\"><\/div>\n<div id=\"words\"> <label><b><span style=\"text-decoration:overline\">x<\/span> <sub>2<\/sub><\/b> (\u1025\u1015\u1019\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e 2)<\/label><input type=\"number\" id=\"x2\" value=\"305\"><\/div>\n<div id=\"words\"> <label><b>s <sub>2<\/sub><\/b> (\u1014\u1019\u1030\u1014\u102c 1 \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a)<\/label><input type=\"number\" id=\"s2\" value=\"16.7\"><\/div>\n<div id=\"words\"> <label><b>n <sub>2<\/sub><\/b> (\u1014\u1019\u1030\u1014\u102c 2 \u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038)<\/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>t =<\/b> <span id=\"t\">-1.608761<\/span><\/p>\n<\/div>\n<div id=\"words\">\n<p> <b>df =<\/b> <span id=\"df\">\u1041\u1047<\/span><\/p>\n<\/div>\n<div id=\"words\">\n<p> <b>p-value (\u1010\u1005\u103a\u1016\u1000\u103a\u101e\u1010\u103a) =<\/b> <span id=\"p1\">0.063040<\/span><\/p>\n<\/div>\n<div id=\"words\">\n<p> <b>p-value (2-\u1010\u1016\u1000\u103a\u101e\u1010\u103a) =<\/b> <span id=\"p2\">0.126080<\/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 x1 = +document.getElementById('x1').value;\nvar s1 = +document.getElementById('s1').value;\nvar n1 = +document.getElementById('n1').value;\nvar x2 = +document.getElementById('x2').value;\nvar s2 = +document.getElementById('s2').value;\nvar n2 = +document.getElementById('n2').value;\nvar s12 = Math.pow(s1,2);\nvar s22 = Math.pow(s2,2);<\/p>\n<p>var df1 = (Math.pow(s12\/n1 - (-1*s22\/n2),2)) \/ ((Math.pow(s12\/n1,2)\/(n1-1)) - (-1*Math.pow(s22\/n2,2)\/(n2-1)));\nvar df = Math.floor(df1);\nvar t = (x1-x2)\/(Math.sqrt(Math.pow(s1,2)\/n1 - (-1*Math.pow(s2,2)\/n2)));<\/p>\n<p>if (t<0) {\nvar p1 = jStat.studentt.cdf(t, df);\nvar p2 = p1*2;\n} else {\nvar p1 = 1-jStat.studentt.cdf(t, df);\nvar p2 = p1*2;\n}\n\ndocument.getElementById('t').innerHTML = t.toFixed(6);\ndocument.getElementById('df').innerHTML = df;\ndocument.getElementById('p1').innerHTML = p1.toFixed(6);\ndocument.getElementById('p2').innerHTML = p2.toFixed(6);\n\t} else {\nvar raw1 = document.getElementById('rawData1').value.split(',').map(Number);\nvar raw2 = document.getElementById('rawData2').value.split(',').map(Number);\nvar x1 = math.mean(raw1)\nvar s1 = math.std(raw1)\nvar n1 = raw1.length;\nvar x2 = math.mean(raw2)\nvar s2 = math.std(raw2)\nvar n2 = raw2.length;\nvar s12 = Math.pow(s1,2);\nvar s22 = Math.pow(s2,2);\n\nvar df1 = (Math.pow(s12\/n1 - (-1*s22\/n2),2)) \/ ((Math.pow(s12\/n1,2)\/(n1-1)) - (-1*Math.pow(s22\/n2,2)\/(n2-1)));\nvar df = Math.floor(df1);\nvar t = (x1-x2)\/(Math.sqrt(Math.pow(s1,2)\/n1 - (-1*Math.pow(s2,2)\/n2)));\n\nif (t<0) {\nvar p1 = jStat.studentt.cdf(t, df);\nvar p2 = p1*2;\n} else {\nvar p1 = 1-jStat.studentt.cdf(t, df);\nvar p2 = p1*2;\n}\n\ndocument.getElementById('t').innerHTML = t.toFixed(6);\ndocument.getElementById('df').innerHTML = df;\ndocument.getElementById('p1').innerHTML = p1.toFixed(6);\ndocument.getElementById('p2').innerHTML = p2.toFixed(6);\n\t}\n\n\/\/output results\n}\n\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Welch&#8217;s t-test \u1000\u102d\u102f \u101c\u1030\u1026\u1038\u101b\u1031 \u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u101e\u100a\u103a \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038 \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u101f\u102f \u1019\u101a\u1030\u1006\u1015\u102b\u104b \u101e\u1004\u103a\u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101c\u102d\u102f\u1015\u102b\u1000\u104a \u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f t-test calculator \u1000\u102d\u102f \u101e\u102f\u1036\u1038\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u104b Welch t-test \u1000\u102d\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u103c\u100a\u1037\u103a\u1005\u103d\u1000\u103a\u1015\u103c\u102e\u1038 \u201c\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a\u201d \u1001\u101c\u102f\u1010\u103a\u1000\u102d\u102f \u1014\u103e\u102d\u1015\u103a\u1015\u102b\u104b \u1012\u1031\u1010\u102c\u1021\u1000\u103c\u1019\u103a\u1038\u1011\u100a\u1037\u103a\u1015\u102b\u104b \u1021\u1014\u103e\u1005\u103a\u1001\u103b\u102f\u1015\u103a\u1012\u1031\u1010\u102c\u1011\u100a\u1037\u103a\u1015\u102b\u104b \u1014\u1019\u1030\u1014\u102c \u1041 301, 298, 295, 297, 304, 305, 309, 298, 291, 299, 293, 304 \u1014\u1019\u1030\u1014\u102c \u1042 302, 309, 324, 313, 312, 310, 305, 298, [&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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Welch \u104f t-test \u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a - Statology<\/title>\n<meta name=\"description\" content=\"\u1024\u1002\u100f\u1014\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1000\u103a\u101e\u100a\u103a \u101e\u102f\u1036\u1038\u1005\u103d\u1032\u101e\u1030\u1019\u103e\u1015\u1031\u1038\u101e\u1031\u102c \u101e\u103d\u1004\u103a\u1038\u1021\u102c\u1038\u1005\u102f\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\u103a \u1021\u1001\u103c\u1031\u1001\u1036\u104d Welch \u104f t-test \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u103a\u104b\" \/>\n<meta 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