{"id":218,"date":"2023-08-04T01:54:33","date_gmt":"2023-08-04T01:54:33","guid":{"rendered":"https:\/\/statorials.org\/id\/distribusi-chi-kuadrat\/"},"modified":"2023-08-04T01:54:33","modified_gmt":"2023-08-04T01:54:33","slug":"distribusi-chi-kuadrat","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/distribusi-chi-kuadrat\/","title":{"rendered":"Distribusi chi-kuadrat"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi chi-kuadrat dan kegunaannya. Selain itu, Anda akan menemukan grafik distribusi chi-kuadrat dan propertinya. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-chi-cuadrado\"><\/span> Berapakah distribusi chi-kuadratnya?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Distribusi Chi-kuadrat<\/strong> merupakan distribusi probabilitas yang simbolnya adalah \u03c7\u00b2. Lebih tepatnya, distribusi Chi-kuadrat adalah jumlah kuadrat dari <em>k<\/em> variabel acak independen yang berdistribusi normal.<\/p>\n<p> Jadi, distribusi Chi-kuadrat mempunyai <em>k<\/em> derajat kebebasan. Oleh karena itu, distribusi Chi-kuadrat mempunyai derajat kebebasan yang sama dengan jumlah kuadrat dari variabel-variabel berdistribusi normal yang diwakilinya.<\/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-9ea0bf7a87071883ceae5e419bae9e71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X\\sim\\chi^2_k \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\begin{array}{l}\\text{Distribuci\\'on chi-cuadrado}\\\\[2ex]\\text{con k grados de libertad}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Distribusi Chi-kuadrat juga dikenal sebagai <strong>distribusi Pearson<\/strong> .<\/p>\n<p> Perlu dicatat bahwa distribusi Chi-kuadrat adalah kasus khusus dari distribusi gamma.<\/p>\n<p> Distribusi chi-kuadrat banyak digunakan dalam inferensi statistik, misalnya dalam pengujian hipotesis dan interval kepercayaan. Kita akan melihat di bawah apa saja penerapan jenis distribusi probabilitas ini. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-chi-cuadrado\"><\/span> Grafik distribusi chi-kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita melihat definisi distribusi Chi-kuadrat, kita akan melihat beberapa contoh distribusi jenis ini yang direpresentasikan secara grafis. Jadi di bawah ini Anda dapat melihat bagaimana plot probabilitas distribusi chi-kuadrat bervariasi bergantung pada derajat kebebasan. <\/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\/diagramme-de-distribution-du-chi-carre.png\" alt=\"plot distribusi chi-kuadrat\" class=\"wp-image-4212\" width=\"670\" height=\"405\" srcset=\"\" sizes=\"\"><\/figure>\n<p> Fungsi kepadatan distribusi Chi-kuadrat telah digambarkan pada grafik di atas. Sedangkan grafik fungsi distribusi probabilitas kumulatif chi-kuadrat adalah sebagai berikut: <\/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-du-chi-carre-cumulatif.png\" alt=\"grafik distribusi kumulatif chi-kuadrat\" class=\"wp-image-4215\" width=\"670\" height=\"405\" 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> Tabel distribusi chi-kuadrat <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-chi-cuadrado\"><\/span> Karakteristik distribusi chi-kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Pada bagian ini kita akan melihat sifat terpenting dari distribusi Chi-kuadrat yang berkaitan dengan teori probabilitas dan statistik.<\/p>\n<ul>\n<li> Rata-rata distribusi chi-kuadrat sama dengan derajat kebebasannya.<\/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-8a7926aa60ec788064c47a5a34e641ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim\\chi^2_k\\\\[2ex] E[X]=k\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"73\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Varians suatu distribusi Chi-kuadrat sama dengan dua kali derajat kebebasan distribusi.<\/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-cffd659f19d8ed8260fcaf53dc6dd83f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim\\chi^2_k\\\\[2ex] Var(X)=2\\cdot k\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Modus distribusi chi-kuadrat adalah dua satuan lebih kecil dari derajat kebebasannya, selama distribusi tersebut mempunyai lebih dari satu derajat kebebasan.<\/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-3c10387635aba8249e98afe0ca6f3ea9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=k-2 \\qquad \\text{si } k\\geq 2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"186\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> Fungsi kepadatan distribusi Chi-kuadrat adalah nol jika x=0. Namun, untuk nilai x lebih besar dari 0, fungsi kepadatan distribusi Chi-kuadrat 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-f239003e822b2c8ba44146e94a94ad89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]= \\frac{(1\/2)^{k\/2}}{\\Gamma(k\/2)} x^{k\/2 - 1} e^{-x\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"254\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Fungsi distribusi kumulatif dari distribusi Chi-kuadrat diatur 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-9d39bc2eb949e628c1109501656da4b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{\\gamma(k\/2,x\/2)}{\\Gamma(k\/2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"187\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Koefisien skewness distribusi Chi-kuadrat adalah akar kuadrat dari hasil bagi delapan dibagi jumlah derajat kebebasan distribusi.<\/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-c0113d9ec77836abace7fe06e18d90c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\sqrt{\\frac{8}{k}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"69\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<ul>\n<li> Kurtosis distribusi Chi-kuadrat dihitung menggunakan persamaan 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-a2c6ae2842ea42a7ff31babce8eb778a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=3+\\cfrac{12}{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"88\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Karena teorema limit pusat, distribusi chi-kuadrat dapat didekati dengan distribusi normal jika <em>k<\/em> cukup besar. <\/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-b2c7e4c59f39b5f1910f7a7806c08819_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{k \\to \\infty} \\frac{\\chi^2_k (x)}{ k } = N_{\\left(1,\\sqrt{2\/k}\\right)} (x)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"210\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-chi-cuadrado\"><\/span> Penerapan distribusi chi-kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Distribusi chi-kuadrat memiliki banyak penerapan berbeda dalam statistik. Faktanya, terdapat uji chi-square yang digunakan untuk memeriksa independensi antar variabel dan kesesuaian dengan distribusi teoritis. Misalnya, uji Chi-kuadrat dapat digunakan untuk menentukan apakah data sampel sesuai dengan distribusi Poisson.<\/p>\n<p> Dalam analisis regresi linier, distribusi chi-kuadrat juga digunakan untuk memperkirakan rata-rata populasi yang berdistribusi normal dan memperkirakan kemiringan garis studi regresi linier.<\/p>\n<p> Terakhir, distribusi Chi kuadrat juga ikut serta dalam analisis varians, melalui hubungannya dengan distribusi Snedecor F.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi chi-kuadrat dan kegunaannya. Selain itu, Anda akan menemukan grafik distribusi chi-kuadrat dan propertinya. Berapakah distribusi chi-kuadratnya? Distribusi Chi-kuadrat merupakan distribusi probabilitas yang simbolnya adalah \u03c7\u00b2. Lebih tepatnya, distribusi Chi-kuadrat adalah jumlah kuadrat dari k variabel acak independen yang berdistribusi normal. Jadi, distribusi Chi-kuadrat mempunyai k derajat kebebasan. Oleh karena [&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 chi kuadrat (\u03c7\u00b2)<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan menemukan apa itu sebaran Chi kuadrat, kegunaannya, grafiknya, dan ciri-ciri sebaran Chi kuadrat.\" \/>\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-chi-kuadrat\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribusi chi kuadrat (\u03c7\u00b2)\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan apa itu sebaran Chi kuadrat, kegunaannya, grafiknya, dan ciri-ciri sebaran Chi kuadrat.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/distribusi-chi-kuadrat\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-04T01:54:33+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9ea0bf7a87071883ceae5e419bae9e71_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-chi-kuadrat\/\",\"url\":\"https:\/\/statorials.org\/id\/distribusi-chi-kuadrat\/\",\"name\":\"\u25b7 Distribusi chi kuadrat (\u03c7\u00b2)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-04T01:54:33+00:00\",\"dateModified\":\"2023-08-04T01:54:33+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan menemukan apa itu sebaran Chi kuadrat, kegunaannya, grafiknya, dan ciri-ciri sebaran Chi kuadrat.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/distribusi-chi-kuadrat\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/distribusi-chi-kuadrat\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/distribusi-chi-kuadrat\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribusi chi-kuadrat\"}]},{\"@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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