{"id":4385,"date":"2026-05-25T10:30:18","date_gmt":"2026-05-25T08:30:18","guid":{"rendered":"https:\/\/ellistat.com\/?p=4385"},"modified":"2026-05-27T10:32:05","modified_gmt":"2026-05-27T08:32:05","slug":"hasonlitsa-ossze-a-cramer-von-mises-teszt-es-az-energia-teszt-eloszlasait","status":"publish","type":"post","link":"https:\/\/ellistat.com\/hu\/comparer-des-distributions-test-de-cramer-von-mises-et-test-energie\/","title":{"rendered":"Eloszl\u00e1sok \u00f6sszehasonl\u00edt\u00e1sa: Cram\u00e9r-von Mises-teszt \u00e9s Energy-teszt"},"content":{"rendered":"<h2 class=\"wp-block-heading\">Eloszl\u00e1sok \u00f6sszehasonl\u00edt\u00e1sa az \u00e1tlagok helyett: a Cram\u00e9e-von Mises- \u00e9s az Energy-tesztnek k\u00f6sz\u00f6nhet\u0151en a min\u0151s\u00e9gellen\u0151rz\u00e9sben el\u00e9rt kulcsfontoss\u00e1g\u00fa el\u0151rel\u00e9p\u00e9s.<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">K\u00e9t t\u00e9tel alkatr\u00e9sz. Ugyanaz az \u00e1tlag. Ugyanaz a l\u00e1tsz\u00f3lagos sz\u00f3r\u00e1s. <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"547\" height=\"568\" src=\"https:\/\/ellistat.com\/wp-content\/uploads\/t1xOgQeJwdjWtepZ.png\" alt=\"\" class=\"wp-image-4386\" style=\"aspect-ratio:0.9630546614948695;width:434px;height:auto\" srcset=\"https:\/\/ellistat.com\/wp-content\/uploads\/t1xOgQeJwdjWtepZ.png 547w, https:\/\/ellistat.com\/wp-content\/uploads\/t1xOgQeJwdjWtepZ-289x300.png 289w, https:\/\/ellistat.com\/wp-content\/uploads\/t1xOgQeJwdjWtepZ-12x12.png 12w\" sizes=\"auto, (max-width: 547px) 100vw, 547px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Az \u00e1tlagok \u00e9s a sz\u00f3r\u00e1sok itt gyakorlatilag azonosak, m\u00e9gis intuit\u00edve \u00e9rezhet\u0151 a k\u00fcl\u00f6nbs\u00e9g a k\u00e9t g\u00e9p k\u00f6z\u00f6tt.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A hagyom\u00e1nyos hipot\u00e9zisvizsg\u00e1lat azonban nem mutat k\u00fcl\u00f6nbs\u00e9get a k\u00e9t eloszl\u00e1s k\u00f6z\u00f6tt.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-27-a-10.13.46-722x1024.png\" alt=\"\" class=\"wp-image-4387\" style=\"width:287px;height:auto\" srcset=\"https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-27-a-10.13.46-722x1024.png 722w, https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-27-a-10.13.46-212x300.png 212w, https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-27-a-10.13.46-8x12.png 8w, https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-27-a-10.13.46.png 738w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Az \u00e1tlag \u00e9s a sz\u00f3r\u00e1s azonban csak egy r\u00e9sz\u00e9t mondja el a megmunk\u00e1l\u00e1si folyamat t\u00f6rt\u00e9net\u00e9nek. A m\u00e9r\u00e9sek csoportjai k\u00f6z\u00f6tti val\u00f3di k\u00fcl\u00f6nbs\u00e9gek kimutat\u00e1s\u00e1hoz, k\u00e9t besz\u00e1ll\u00edt\u00f3, k\u00e9t g\u00e9p, k\u00e9t csapat, k\u00e9t gy\u00e1rt\u00e1si id\u0151szak k\u00f6z\u00f6tt... a teljes eloszl\u00e1sokat kell \u00f6sszehasonl\u00edtani. Pontosan ez az, amit k\u00e9t statisztikai teszt integr\u00e1lt <a href=\"https:\/\/ellistat.com\/hu\/adatelemzesi-megoldasok\/\" type=\"page\" id=\"905\">Ellistat adatelemz\u00e9s<\/a> teszt: a <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Test_de_Cramer-Von_Mises\" type=\"link\" id=\"https:\/\/fr.wikipedia.org\/wiki\/Test_de_Cramer-Von_Mises\">Cram\u00e9r-von Mises<\/a> \u00e9s az Energia teszt.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">A Cram\u00e9r-von Mises-teszt<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Ez a teszt \u00f6sszehasonl\u00edtja :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>vagy egy elm\u00e9leti eloszl\u00e1s\u00fa minta<\/li>\n\n\n\n<li>vagy k\u00e9t minta k\u00f6z\u00f6tt\u00fck<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Az elv:<\/strong> a teszt a k\u00e9t eloszl\u00e1s kumulat\u00edv eloszl\u00e1sf\u00fcggv\u00e9nyeit (ogives) hasonl\u00edtja \u00f6ssze.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M\u00e1s sz\u00f3val azt m\u00e9ri, hogy \u00abmilyen messze vannak egym\u00e1st\u00f3l a kumulat\u00edv g\u00f6rb\u00e9k\u00bb?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ha a k\u00e9t eloszl\u00e1s k\u00f6zel van egym\u00e1shoz, a robban\u00f3fejek \u00e1tfedik egym\u00e1st. Ha k\u00fcl\u00f6nb\u00f6znek, a kumulat\u00edv k\u00fcl\u00f6nbs\u00e9g n\u0151.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"964\" height=\"687\" src=\"https:\/\/ellistat.com\/wp-content\/uploads\/wR0hkKcvY2ndV6Nq.png\" alt=\"\" class=\"wp-image-4388\" style=\"aspect-ratio:1.4032157026519105;width:704px;height:auto\" srcset=\"https:\/\/ellistat.com\/wp-content\/uploads\/wR0hkKcvY2ndV6Nq.png 964w, https:\/\/ellistat.com\/wp-content\/uploads\/wR0hkKcvY2ndV6Nq-300x214.png 300w, https:\/\/ellistat.com\/wp-content\/uploads\/wR0hkKcvY2ndV6Nq-768x547.png 768w, https:\/\/ellistat.com\/wp-content\/uploads\/wR0hkKcvY2ndV6Nq-18x12.png 18w\" sizes=\"auto, (max-width: 964px) 100vw, 964px\" \/><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">Az energiateszt<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Ez a vizsg\u00e1lat ezt a megk\u00f6zel\u00edt\u00e9st t\u00f6bb csoportra \u00e1ltal\u00e1nos\u00edtja. K\u00fcl\u00f6n\u00f6sen alkalmas, ha :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>kett\u0151n\u00e9l t\u00f6bb popul\u00e1ci\u00f3t hasonl\u00edtanak \u00f6ssze<\/li>\n\n\n\n<li>az eloszl\u00e1sok ismeretlenek<\/li>\n\n\n\n<li>az adatok t\u00f6bbdimenzi\u00f3sak<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Az elv <\/strong>A teszt egy intuit\u00edv \u00f6tleten alapul: a pontok k\u00f6z\u00f6tti t\u00e1vols\u00e1gok \u00f6sszehasonl\u00edt\u00e1s\u00e1n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M\u00e9ri :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a csoportokon bel\u00fcli \u00e1tlagos t\u00e1vols\u00e1gok<\/li>\n\n\n\n<li>akkor a csoportok k\u00f6z\u00f6tti t\u00e1vols\u00e1gok <\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ha a csoportok ugyanabb\u00f3l az eloszl\u00e1sb\u00f3l sz\u00e1rmaznak, akkor a csoporton bel\u00fcli \u00e9s a csoportok k\u00f6z\u00f6tti t\u00e1vols\u00e1gok hasonl\u00f3ak. Ha nem, akkor a csoportok k\u00f6z\u00f6tti t\u00e1vols\u00e1gok nagyobbak lesznek.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Mit jelent ez a gyakorlatban<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Hasonl\u00edtson \u00f6ssze k\u00e9t besz\u00e1ll\u00edt\u00f3t egy kritikus \u00e1tm\u00e9r\u0151n. A g\u00e9pbe\u00e1ll\u00edt\u00e1s megv\u00e1ltoztat\u00e1s\u00e1nak valid\u00e1l\u00e1sa. Egy instabil folyamat el\u0151tte\/ut\u00e1na elemz\u00e9se. K\u00fcl\u00f6nbs\u00e9gt\u00e9tel k\u00e9t olyan megmunk\u00e1l\u00f3k\u00f6zpont k\u00f6z\u00f6tt, amelyek ugyanazt az alkatr\u00e9szt gy\u00e1rtj\u00e1k... megjelen\u00e9s\u00fckben.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mindezekben az esetekben f\u00e9lrevezet\u0151 lehet, ha csak az \u00e1tlagot \u00e9s a sz\u00f3r\u00e1st n\u00e9zz\u00fck.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A teljes eloszl\u00e1sok \u00f6sszehasonl\u00edt\u00e1sa val\u00f3s k\u00e9pet ad arr\u00f3l, hogy mi t\u00f6rt\u00e9nik val\u00f3j\u00e1ban.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Az Ellistat adatelemz\u0151 modulj\u00e1ban ezek a tesztek vizualiz\u00e1ci\u00f3val p\u00e1rosulnak: ogives, KDE, egym\u00e1sra helyezett hisztogramok, mivel egy p-\u00e9rt\u00e9k vizu\u00e1lis kontextus n\u00e9lk\u00fcl senkit sem gy\u0151z meg a m\u0171helyben.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"566\" src=\"https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-19-a-17.10.12-1024x566.png\" alt=\"\" class=\"wp-image-4389\" srcset=\"https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-19-a-17.10.12-1024x566.png 1024w, https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-19-a-17.10.12-300x166.png 300w, https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-19-a-17.10.12-768x425.png 768w, https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-19-a-17.10.12-1536x850.png 1536w, https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-19-a-17.10.12-2048x1133.png 2048w, https:\/\/ellistat.com\/wp-content\/uploads\/Capture-decran-2026-05-19-a-17.10.12-18x10.png 18w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A c\u00e9l nem a statisztikai eredm\u00e9nyek el\u0151\u00e1ll\u00edt\u00e1sa, hanem annak meg\u00e9rt\u00e9se, hogy k\u00e9t folyamat mi\u00e9rt viselkedik elt\u00e9r\u0151en, \u00e9s a cselekv\u00e9s.<\/p>","protected":false},"excerpt":{"rendered":"<p>Comparer les distributions plut\u00f4t que les moyennes : une avanc\u00e9e cl\u00e9 pour le contr\u00f4le qualit\u00e9 gr\u00e2ce aux test de Cram\u00e9e-von Mises et test Energie Deux lots de pi\u00e8ces. M\u00eame moyenne. M\u00eame \u00e9cart-type apparent. Les moyennes et les variances sont ici sensiblement identiques, et pourtant, intuitivement, on peut sentir une diff\u00e9rence entre ces deux machines. Les [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-4385","post","type-post","status-publish","format-standard","hentry","category-data-analysis"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Comparer des distributions : Test de Cram\u00e9r\u2013von Mises et test Energie - Ellistat<\/title>\n<meta name=\"description\" content=\"Moyenne identique, qualit\u00e9 diff\u00e9rente : d\u00e9couvrez pourquoi comparer les distributions compl\u00e8tes est plus fiable que la moyenne ou la variance.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ellistat.com\/hu\/hasonlitsa-ossze-a-cramer-von-mises-teszt-es-az-energia-teszt-eloszlasait\/\" \/>\n<meta property=\"og:locale\" content=\"hu_HU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Comparer des distributions : Test de Cram\u00e9r\u2013von Mises et test Energie - 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