{"id":3133,"date":"2023-07-19T01:29:22","date_gmt":"2023-07-19T01:29:22","guid":{"rendered":"https:\/\/statorials.org\/id\/jumlah-kuadrat-anova\/"},"modified":"2023-07-19T01:29:22","modified_gmt":"2023-07-19T01:29:22","slug":"jumlah-kuadrat-anova","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/jumlah-kuadrat-anova\/","title":{"rendered":"Cara menghitung jumlah kuadrat di anova (dengan contoh)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Dalam statistik, <a href=\"https:\/\/statorials.org\/id\/anova-satu-arah\/\" target=\"_blank\" rel=\"noopener\">ANOVA satu arah<\/a> digunakan untuk membandingkan rata-rata tiga atau lebih kelompok independen untuk menentukan apakah terdapat perbedaan yang signifikan secara statistik antara rata-rata populasi yang bersangkutan.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Setiap kali Anda melakukan ANOVA satu arah, Anda akan selalu menghitung tiga jumlah nilai kuadrat:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Regresi Jumlah Kuadrat (SSR)<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Ini adalah jumlah kuadrat selisih antara rata-rata masing-masing kelompok dan <a href=\"https:\/\/statorials.org\/id\/anova-sedang-besar\/\" target=\"_blank\" rel=\"noopener\">rata-rata umum<\/a> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. Kesalahan Jumlah Kuadrat (SSE)<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Ini adalah jumlah kuadrat perbedaan antara masing-masing observasi individu dan rata-rata kelompok dari observasi tersebut.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>3. Jumlah Kuadrat Total (SST)<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Ini adalah jumlah kuadrat selisih antara masing-masing pengamatan dan rata-rata keseluruhan.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Masing-masing dari ketiga nilai ini ditempatkan dalam tabel ANOVA akhir, yang kami gunakan untuk menentukan ada atau tidaknya perbedaan yang signifikan secara statistik antara rata-rata kelompok.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Contoh berikut menunjukkan cara menghitung masing-masing jumlah nilai kuadrat ini untuk ANOVA satu arah dalam praktiknya.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Contoh: Cara menghitung jumlah kuadrat di ANOVA<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Misalkan kita ingin mengetahui apakah tiga program persiapan ujian yang berbeda menghasilkan nilai rata-rata yang berbeda pada ujian tertentu. Untuk mengujinya, kami merekrut 30 siswa untuk berpartisipasi dalam penelitian dan membagi mereka menjadi tiga kelompok.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Siswa di setiap kelompok secara acak ditugaskan untuk menggunakan salah satu dari tiga program persiapan ujian selama tiga minggu berikutnya untuk mempersiapkan ujian. Pada akhir tiga minggu, semua siswa mengikuti ujian yang sama.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Hasil ujian masing-masing kelompok ditunjukkan di bawah ini:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8258 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aller-simple2.png\" sizes=\"\" srcset=\"\" alt=\"Contoh data ANOVA satu arah\" width=\"237\" height=\"246\"><\/p>\n<p> <span style=\"color: #000000;\">Langkah-langkah berikut menunjukkan cara menghitung jumlah nilai kuadrat untuk ANOVA satu arah ini.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Langkah 1: Hitung rata-rata kelompok dan rata-rata keseluruhan.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Pertama, kami akan menghitung rata-rata ketiga kelompok serta rata-rata keseluruhan (atau \u201ckeseluruhan\u201d):<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8434 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/anovamain1-1.png\" alt=\"\" width=\"300\" height=\"257\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Langkah 2: Hitung SSR.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Selanjutnya kita akan menghitung jumlah regresi kuadrat (SSR) dengan menggunakan rumus sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\">n\u03a3(X <sub>j<\/sub> \u2013 <span style=\"text-decoration: overline;\">X<\/span> ..) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : ukuran sampel kelompok j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : simbol Yunani yang berarti \u201cjumlah\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>j<\/sub><\/strong> : rata-rata kelompok j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> ..<\/strong> : rata-rata keseluruhan<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Dalam contoh kita, kita menghitung SSR = 10(83.4-85.8) <sup>2<\/sup> + 10(89.3-85.8) <sup>2<\/sup> + 10(84.7-85.8) <sup>2<\/sup> = <strong>192.2<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Langkah 3: Hitung SES.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Selanjutnya kita akan menghitung jumlah kesalahan kuadrat (SSE) dengan menggunakan rumus berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3(X <sub>ij<\/sub> \u2013 <span style=\"text-decoration: overline;\">Xj<\/span> <sub>)<\/sub> <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : simbol Yunani yang berarti \u201cjumlah\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>ij<\/sub><\/strong> : observasi <sup>ke-i<\/sup> kelompok j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/sub><\/strong> : rata-rata kelompok j<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Dalam contoh kami, kami menghitung SSE sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 1:<\/strong> (85-83.4) <sup>2<\/sup> + (86-83.4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-83.4) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (75-83.4) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (78-83.4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (94-83.4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (98-83.4) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (79-83.4) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (71-83.4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (80-83.4) <sup>2<\/sup> = <strong>640.4<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 2:<\/strong> (91-89.3) <sup>2<\/sup> + (92-89.3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (93-89.3) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (85-89.3) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (87-89.3) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (84-89.3) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (82-89.3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-89.3) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (95-89.3) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (96-89.3) <sup>2<\/sup> = <strong>208.1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 3:<\/strong> (79-84.7) <sup>2<\/sup> + (78-84.7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-84.7) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (94-84.7) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (92-84.7) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (85-84.7) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (83-84.7) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (85-84.7) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (82-84.7) <sup>2+<\/sup> <strong>&nbsp;<\/strong> (81-84.7) <sup>2<\/sup> = <strong>252.1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>ESS:<\/strong> 640,4 + 208,1 + 252,1 = <strong>1.100,6<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Langkah 4: Hitung SST.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Selanjutnya kita akan menghitung jumlah kuadrat total (SST) dengan menggunakan rumus berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SST = SSR + SSE<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dalam contoh kita, SST = 192,2 + 1100,6 = <strong>1292,8<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Setelah kita menghitung nilai SSR, SSE dan SST, masing-masing nilai tersebut akhirnya akan ditempatkan pada tabel ANOVA:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>Sumber<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jumlah kuadrat (SS)<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">df<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Kuadrat rata-rata (MS)<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">nilai-F<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">nilai p<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Regresi<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">192.2<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">96.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2.358<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,1138<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Kesalahan<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1100.6<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">40.8<\/span><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Total<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1292.8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">29<\/span><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Inilah cara kami menghitung angka-angka berbeda dalam tabel:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>df regresi:<\/strong> k-1 = 3-1 = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>kesalahan df:<\/strong> nk = 30-3 = 27<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>jumlah df:<\/strong> n-1 = 30-1 = 29<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Perlakuan SEP :<\/strong> Perlakuan SST\/df = 192,2 \/ 2 = 96,1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Kesalahan MS:<\/strong> Kesalahan SSE \/ df = 1100.6 \/ 27 = 40.8<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Nilai F :<\/strong> MS pemrosesan \/ MS error = 96,1 \/ 40,8 = 2,358<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p-value<\/strong> : nilai p yang sesuai dengan nilai F.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><em><strong>Catatan:<\/strong> n = jumlah observasi, k = jumlah kelompok<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">Lihat <a href=\"https:\/\/statorials.org\/id\/anova-nilai-f-nilai-p\/\" target=\"_blank\" rel=\"noopener\">tutorial ini<\/a> untuk mempelajari cara menginterpretasikan nilai F dan nilai p pada tabel ANOVA.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dalam statistik, ANOVA satu arah digunakan untuk membandingkan rata-rata tiga atau lebih kelompok independen untuk menentukan apakah terdapat perbedaan yang signifikan secara statistik antara rata-rata populasi yang bersangkutan. Setiap kali Anda melakukan ANOVA satu arah, Anda akan selalu menghitung tiga jumlah nilai kuadrat: 1. Regresi Jumlah Kuadrat (SSR) Ini adalah jumlah kuadrat selisih antara rata-rata [&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>Cara menghitung jumlah kuadrat di ANOVA (dengan contoh) - Statologi<\/title>\n<meta name=\"description\" content=\"Tutorial ini menjelaskan cara menghitung jumlah kuadrat di ANOVA, disertai contoh lengkap.\" \/>\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\/jumlah-kuadrat-anova\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cara menghitung jumlah kuadrat di ANOVA (dengan contoh) - Statologi\" \/>\n<meta property=\"og:description\" content=\"Tutorial ini menjelaskan cara menghitung jumlah kuadrat di ANOVA, disertai contoh lengkap.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/jumlah-kuadrat-anova\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-19T01:29:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aller-simple2.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=\"3 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/jumlah-kuadrat-anova\/\",\"url\":\"https:\/\/statorials.org\/id\/jumlah-kuadrat-anova\/\",\"name\":\"Cara menghitung jumlah kuadrat di ANOVA (dengan contoh) - Statologi\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-07-19T01:29:22+00:00\",\"dateModified\":\"2023-07-19T01:29:22+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Tutorial ini menjelaskan cara menghitung jumlah kuadrat di ANOVA, disertai contoh lengkap.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/jumlah-kuadrat-anova\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/jumlah-kuadrat-anova\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/jumlah-kuadrat-anova\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Cara menghitung jumlah kuadrat di anova (dengan 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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