{"id":220,"date":"2023-08-04T01:16:05","date_gmt":"2023-08-04T01:16:05","guid":{"rendered":"https:\/\/statorials.org\/id\/distribusi-siswa\/"},"modified":"2023-08-04T01:16:05","modified_gmt":"2023-08-04T01:16:05","slug":"distribusi-siswa","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/distribusi-siswa\/","title":{"rendered":"Distribusi t siswa"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi Student t dan kegunaannya. Selain itu juga ditampilkan grafik distribusi t Student dan apa saja ciri-ciri dari jenis distribusi probabilitas tersebut. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-t-de-student\"><\/span> Apa distribusi Siswa?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Distribusi t Student<\/strong> adalah distribusi probabilitas yang banyak digunakan dalam statistik. Secara khusus, distribusi t Student digunakan dalam uji t Student untuk menentukan perbedaan antara rata-rata dua sampel dan untuk menetapkan interval kepercayaan.<\/p>\n<p> Distribusi t Student dikembangkan oleh ahli statistik William Sealy Gosset pada tahun 1908 dengan nama samaran &#8220;Student&#8221;.<\/p>\n<p> Distribusi t Student ditentukan oleh jumlah derajat kebebasannya, yang diperoleh dengan mengurangkan satu satuan dari jumlah total observasi. Oleh karena itu, rumus untuk menentukan derajat kebebasan distribusi t Student adalah <em>\u03bd=n-1<\/em> . <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1c805dc2d6ca050feb70dad99de53402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\nu=n-1\\\\[2ex]X\\sim t_\\nu\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"74\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-t-de-student\"><\/span> Grafik distribusi t siswa<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita mengetahui definisi distribusi t Student, mari kita lihat apa grafiknya. Nah, di bawah ini Anda dapat melihat secara grafis beberapa contoh distribusi t Student dengan derajat kebebasan yang berbeda-beda. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/graphique-de-distribution-t-des-etudiants.png\" alt=\"Grafik distribusi t siswa\" class=\"wp-image-4266\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"\"><\/figure>\n<p> Dari grafik distribusi t Student dapat disimpulkan sifat-sifat sebagai berikut:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">Distribusi Student t simetris berpusat pada 0 dan berbentuk lonceng.<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">Distribusi t Student lebih tersebar dibandingkan distribusi normal, yaitu kurva distribusi t Student lebih lebar.<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">Semakin besar derajat kebebasan distribusi t Student, semakin rendah penyebarannya.<\/span><\/li>\n<\/ul>\n<p> Pada grafik di atas, fungsi kepadatan distribusi t Student telah diplot terhadap derajat kebebasannya. Namun, Anda dapat melihat di bawah bagaimana fungsi probabilitas kumulatif dari distribusi t Student bervariasi: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-t-etudiante-cumulative.png\" alt=\"plot distribusi t kumulatif Siswa\" class=\"wp-image-4267\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"\"><\/figure>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <a href=\"https:\/\/statorials.org\/id\/tabel-distribusi-t-siswa\/\">Tabel distribusi siswa<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-t-de-student\"><\/span> Karakteristik distribusi t Student<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Karakteristik terpenting dari distribusi t Student ditunjukkan di bawah ini.<\/p>\n<ul>\n<li> Domain distribusi Student t terdiri dari bilangan real.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd8ca9914bdf447012a1a16f7950ce95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (-\\infty, +\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Untuk distribusi t Student dengan lebih dari satu derajat kebebasan, mean distribusinya sama dengan 0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d4fed5eadcaa1162752aeedb7f8a0906_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] E[X]=0 \\qquad \\text{para }\\nu>1\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;55&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Varians dari distribusi t Student dapat dihitung dengan menggunakan ekspresi berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bfdcbc8a5f071a61e091b0ef6f686a16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] Var(X)=\\cfrac{\\nu}{\\nu-2} \\qquad \\text{para }\\nu>2\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;75&#8243; width=&#8221;245&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Median dan modus distribusi t Student, berapa pun jumlah derajat kebebasannya, selalu 0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8d90790fce0c987648c0b30216c82214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Me=0\\\\[2ex]Mo=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Fungsi kepadatan distribusi Student t ditentukan dengan rumus berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8c0f1e97a8e407e8b9e2b00ba93aee0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\Gamma((\\nu+1)\/2)} {\\sqrt{\\nu\\pi}\\,\\Gamma(\\nu\/2)} (1+x^2\/\\nu)^{-(\\nu+1)\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"339\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Fungsi distribusi probabilitas kumulatif dari distribusi t Student ditentukan dengan rumus berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-da1e3bdf2d87c3a7dcc89c236958dcec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{1}{2} + x \\Gamma \\left( \\frac{\\nu+1}{2} \\right) \\cdot\\frac{\\,_2F_1 \\left ( \\frac{1}{2},\\frac{\\nu+1}{2};\\frac{3}{2};-\\frac{x^2}{\\nu} \\right)}{\\sqrt{\\pi\\nu}\\,\\Gamma \\left(\\frac{\\nu}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"402\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<ul>\n<li> Untuk distribusi t Student dengan derajat kebebasan lebih besar dari 3, koefisien asimetrinya adalah nol karena merupakan distribusi simetris.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6fea0ec5e37ef4db61fb44d6f5eba6fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=0\\qquad \\text{para }\\nu>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;17&#8243; width=&#8221;164&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Jika derajat kebebasan distribusi t Student lebih besar dari empat, maka kurtosis dapat dihitung dengan membagi enam dengan derajat kebebasan dikurangi empat. <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0335e705ad289732dd1be59dc8388dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\cfrac{6}{\\nu-4}\\qquad \\text{para }\\nu>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;38&#8243; width=&#8221;198&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-t-de-student\"><\/span> Penerapan distribusi t Siswa<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Distribusi t Student adalah distribusi probabilitas yang banyak digunakan dalam statistik. Faktanya, terdapat uji-t Student, yang digunakan untuk menguji hipotesis dan interval kepercayaan.<\/p>\n<p> Jadi, distribusi t Student memungkinkan kita menganalisis perbedaan rata-rata dua sampel, lebih tepatnya, digunakan untuk menentukan apakah dua sampel mempunyai rata-rata yang berbeda secara signifikan. Demikian pula uji t Student digunakan untuk mengetahui apakah garis yang diperoleh dari analisis regresi linier mempunyai kemiringan atau tidak.<\/p>\n<p> Singkatnya, penerapan distribusi t Student mengandalkan analisis kumpulan data yang secara teoritis mengikuti distribusi normal tetapi jumlah observasi terlalu kecil untuk menggunakan jenis distribusi ini.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi Student t dan kegunaannya. Selain itu juga ditampilkan grafik distribusi t Student dan apa saja ciri-ciri dari jenis distribusi probabilitas tersebut. Apa distribusi Siswa? Distribusi t Student adalah distribusi probabilitas yang banyak digunakan dalam statistik. Secara khusus, distribusi t Student digunakan dalam uji t Student untuk menentukan perbedaan antara [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribusi siswa<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan menemukan apa itu distribusi t Student, kegunaannya, grafik distribusi t Student dan karakteristiknya.\" \/>\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\/id\/distribusi-siswa\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribusi siswa\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan apa itu distribusi t Student, kegunaannya, grafik distribusi t Student dan karakteristiknya.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/distribusi-siswa\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-04T01:16:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1c805dc2d6ca050feb70dad99de53402_l3.png\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/distribusi-siswa\/\",\"url\":\"https:\/\/statorials.org\/id\/distribusi-siswa\/\",\"name\":\"\u25b7 Distribusi siswa\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-04T01:16:05+00:00\",\"dateModified\":\"2023-08-04T01:16:05+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan menemukan apa itu distribusi t Student, kegunaannya, grafik distribusi t Student dan karakteristiknya.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/distribusi-siswa\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/distribusi-siswa\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/distribusi-siswa\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribusi t siswa\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. 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