{"id":1304,"date":"2023-07-26T22:57:59","date_gmt":"2023-07-26T22:57:59","guid":{"rendered":"https:\/\/statorials.org\/id\/perkiraan-satterthwaite\/"},"modified":"2023-07-26T22:57:59","modified_gmt":"2023-07-26T22:57:59","slug":"perkiraan-satterthwaite","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/perkiraan-satterthwaite\/","title":{"rendered":"Perkiraan satterthwaite: definisi &amp; contoh"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Perkiraan Satterthwaite<\/strong> adalah rumus yang digunakan untuk mencari &#8220;derajat kebebasan efektif&#8221; dalam uji-t dua sampel.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Hal ini paling sering digunakan dalam <a href=\"https:\/\/statorials.org\/id\/tes-selamat-datang\/\" target=\"_blank\" rel=\"noopener\">uji-t Welch<\/a> , yang membandingkan rata-rata dua sampel independen tanpa mengasumsikan bahwa populasi dari mana <a href=\"https:\/\/statorials.org\/id\/populasi-vs.-sampel\/\" target=\"_blank\" rel=\"noopener\">sampel<\/a> diambil memiliki varian yang sama.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Rumus pendekatan Satterthwaite adalah sebagai berikut:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #000000;\">Degrees of freedom:<\/span> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ {[(s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> ) <sup>2<\/sup> \/(n <sub>1<\/sub> \u2013 1)] + [(s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/(n <sub>2<\/sub> \u2013 1)]}<\/span>\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> <sup>2<\/sup> , s <sub>2<\/sub> <sup>2<\/sup> :<\/strong> Masing-masing varians sampel dari sampel pertama dan kedua.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n1<\/sub> , <sub>n2<\/sub> :<\/strong> Ukuran sampel masing-masing sampel pertama dan kedua.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Contoh berikut menunjukkan bagaimana menggunakan pendekatan Satterthwaite untuk menghitung derajat kebebasan efektif.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Contoh: Perhitungan perkiraan Satterthwaite<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Misalkan kita ingin mengetahui apakah rata-rata tinggi dua jenis tumbuhan berbeda adalah sama. Jadi kami akan mengumpulkan dua sampel acak sederhana dari setiap spesies dan mengukur tinggi tanaman di setiap sampel.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nilai berikut menunjukkan tinggi (dalam inci) setiap sampel:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Contoh 1:<\/strong> 14, 15, 15, 15, 16, 18, 22, 23, 24, 25, 25<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Contoh 2:<\/strong> 10, 12, 14, 15, 18, 22, 24, 27, 31, 33, 34, 34, 34<\/span><\/p>\n<p> <span style=\"color: #000000;\">Rata-rata, varians dan ukuran sampelnya adalah:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x1<\/span> <sub>=<\/sub><\/strong> 19,27<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x2<\/span> <sub>=<\/sub><\/strong> 23,69<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> <sup>2<\/sup><\/strong> = 20,42<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>2<\/sub> <sup>2<\/sup><\/strong> = 83,23<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n1<\/strong> <sub><strong>=<\/strong><\/sub> 11<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n2<\/strong> = <sub><strong>13<\/strong><\/sub><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Kemudian kita dapat memasukkan nilai varians dan ukuran sampel ke dalam rumus aproksimasi Satterthwaite untuk mencari derajat kebebasan efektif:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #000000;\">df = (s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ {[(s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> ) <sup>2<\/sup> \/(n <sub>1<\/sub> \u2013 1)] + [(s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ (n <sub>2<\/sub> \u2013 1)]} \n\ndf = (20.42\/11 + 83.23\/13) <sup>2<\/sup> \/{[(20.42\/11) <sup>2<\/sup> \/(11 \u2013 1)] + [(83.23\/13) <sup>2<\/sup> \/(13 \u2013 1)]} = 18.137<\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Derajat kebebasan efektifnya adalah <strong>18,137<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Biasanya, kita membulatkan nilai ini ke bilangan bulat terdekat, sehingga derajat kebebasan yang akan kita gunakan dalam uji-t Welch adalah <strong>18<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Terakhir, kita akan menemukan nilai kritis <em>t<\/em> dalam tabel distribusi t yang sesuai dengan pengujian dua sisi dengan alpha = 0,05 untuk 18 derajat kebebasan:<\/span> <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/t_dist.png\" alt=\"Tabel distribusi T\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Nilai kritis t adalah <strong>2,101<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kami kemudian akan menghitung statistik pengujian kami sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Statistik pengujian:<\/strong> ( <span style=\"border-top: 1px solid black;\">x <sub>1<\/sub><\/span> \u2013 <span style=\"border-top: 1px solid black;\">x <sub>2<\/sub><\/span> ) \/ (\u221a <span style=\"border-top: 1px solid black;\">s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub><\/span> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">Statistik pengujian: (19.27 \u2013 23.69) \/ (\u221a <span style=\"border-top: 1px solid black;\">20.42\/11 + 83.23\/13<\/span> ) = -4.42 \/ 2.873 = <strong>-1.538<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Karena nilai absolut statistik pengujian kami (1,538) tidak lebih besar dari nilai kritis t, kami gagal menolak hipotesis nol pengujian tersebut.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tidak ada cukup bukti yang menyatakan bahwa rata-rata kedua populasi berbeda secara signifikan.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Perkiraan Satterthwaite dalam praktiknya<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Dalam praktiknya, Anda jarang perlu menghitung perkiraan Satterthwaite secara manual.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Sebaliknya, perangkat lunak statistik umum seperti R, Python, Excel, SAS, dan Stata semuanya dapat menggunakan perkiraan Satterthwaite untuk secara otomatis menghitung derajat kebebasan efektif untuk Anda.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Sumber daya tambahan<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/id\/pengujian-hipotesis-1\/\" target=\"_blank\" rel=\"noopener\">Pengantar Pengujian Hipotesis<\/a><br \/> <a href=\"https:\/\/statorials.org\/id\/uji-dua-sampel-anda\/\" target=\"_blank\" rel=\"noopener\">Pengantar uji t dua sampel<\/a><br \/> <a href=\"https:\/\/statorials.org\/id\/tes-selamat-datang\/\" target=\"_blank\" rel=\"noopener\">Pengantar uji-t Welch<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Perkiraan Satterthwaite adalah rumus yang digunakan untuk mencari &#8220;derajat kebebasan efektif&#8221; dalam uji-t dua sampel. Hal ini paling sering digunakan dalam uji-t Welch , yang membandingkan rata-rata dua sampel independen tanpa mengasumsikan bahwa populasi dari mana sampel diambil memiliki varian yang sama. Rumus pendekatan Satterthwaite adalah sebagai berikut: Degrees of freedom: (s 1 2 \/n [&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>Perkiraan Satterthwaite: definisi dan contoh<\/title>\n<meta name=\"description\" content=\"Tutorial ini memberikan penjelasan tentang pendekatan Satterthwaite, termasuk rumus dan contohnya.\" \/>\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\/perkiraan-satterthwaite\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Perkiraan Satterthwaite: definisi dan contoh\" \/>\n<meta property=\"og:description\" content=\"Tutorial ini memberikan penjelasan tentang pendekatan Satterthwaite, termasuk rumus dan contohnya.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/perkiraan-satterthwaite\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T22:57:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/t_dist.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\/perkiraan-satterthwaite\/\",\"url\":\"https:\/\/statorials.org\/id\/perkiraan-satterthwaite\/\",\"name\":\"Perkiraan Satterthwaite: definisi dan contoh\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-07-26T22:57:59+00:00\",\"dateModified\":\"2023-07-26T22:57:59+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Tutorial ini memberikan penjelasan tentang pendekatan Satterthwaite, termasuk rumus dan contohnya.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/perkiraan-satterthwaite\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/perkiraan-satterthwaite\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/perkiraan-satterthwaite\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Perkiraan satterthwaite: definisi &amp; contoh\"}]},{\"@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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