{"id":1197,"date":"2024-09-05T23:05:36","date_gmt":"2024-09-05T21:05:36","guid":{"rendered":"https:\/\/site.ellistat.com\/?p=1197"},"modified":"2024-10-23T15:16:29","modified_gmt":"2024-10-23T13:16:29","slug":"outlier-teszteles","status":"publish","type":"post","link":"https:\/\/ellistat.com\/hu\/tests-de-valeurs-aberrantes\/","title":{"rendered":"Kiugr\u00f3 \u00e9rt\u00e9kek vizsg\u00e1lata"},"content":{"rendered":"<p class=\"wp-block-paragraph\">Adatsorok elemz\u00e9sekor n\u00e9ha tal\u00e1lkozunk olyan \u00e9rt\u00e9kekkel, amelyek nem t\u0171nnek az adatok norm\u00e1lis eloszl\u00e1s\u00e1nak r\u00e9sz\u00e9nek. Ezeket a pontokat kiugr\u00f3 \u00e9rt\u00e9keknek nevezz\u00fck, \u00e9s mint \u00e1ltal\u00e1ban, nem szabad mindig az intu\u00edci\u00f3j\u00e1ra hagyatkoznia, hogy felismerje, hogy egy \u00e9rt\u00e9k kiugr\u00f3 \u00e9rt\u00e9k-e. Vannak olyan tesztek, amelyek k\u00e9pesek kiemelni \u0151ket, \u00e9s az olyan statisztikai szoftverek, mint p\u00e9ld\u00e1ul a(z)&nbsp;<a href=\"https:\/\/ellistat.com\/hu\/adatelemzesi-megoldasok\/\">Ellistat<\/a>&nbsp;hogy seg\u00edtsen a sz\u00e1m\u00edt\u00e1sokban.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Statisztikai szempontb\u00f3l a kiugr\u00f3 \u00e9rt\u00e9k olyan \u00e9rt\u00e9k, amely nem tartozik az adatok norm\u00e1lis eloszl\u00e1s\u00e1hoz. Ez sz\u00e1rmazhat :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>M\u00e9r\u00e9si vagy m\u00e1sol\u00e1si hiba (a tizedesvessz\u0151 elfelejt\u00e9se).<\/li>\n\n\n\n<li>K\u00fcl\u00f6nleges ok, p\u00e9ld\u00e1ul ha egy darabot nem mostak meg a m\u00e9r\u00e9s el\u0151tt.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">A norm\u00e1lis eloszl\u00e1s tulajdons\u00e1gait haszn\u00e1l\u00f3 valamennyi statisztikai sz\u00e1m\u00edt\u00e1s (statisztikai tesztek, k\u00e9pess\u00e9gsz\u00e1m\u00edt\u00e1sok, t\u0171r\u00e9shat\u00e1ron k\u00edv\u00fcli % sz\u00e1m\u00edt\u00e1sok) nagyon \u00e9rz\u00e9keny a kiugr\u00f3 \u00e9rt\u00e9kek jelenl\u00e9t\u00e9re, ez\u00e9rt fontos, hogy meg\u00e9rts\u00fck eredet\u00fcket \u00e9s kik\u00fcsz\u00f6b\u00f6lj\u00fck \u0151ket, miel\u0151tt ezeket a sz\u00e1m\u00edt\u00e1sokat haszn\u00e1ln\u00e1nk. Haszn\u00e1lhat\u00f3k nem parametrikus statisztikai tesztek is, amelyek sokkal kev\u00e9sb\u00e9 \u00e9rz\u00e9kenyek a kiugr\u00f3 \u00e9rt\u00e9kekre.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">K\u00e9t f\u0151 tesztet haszn\u00e1lnak:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Test_Q\">Dixon tesztje<\/a>\u00a0: nagyon \u00e9rdekes, ha az adatok sz\u00e1ma alacsony (&lt;30)<\/li>\n\n\n\n<li><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Test_de_Grubbs\">Grubbs teszt<\/a>\u00a0minden esetben haszn\u00e1lhat\u00f3.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Dixon tesztje<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"73\" src=\"https:\/\/ellistat.com\/wp-content\/uploads\/2024\/09\/Test-de-Dixon.png\" alt=\"\" class=\"wp-image-1199\" srcset=\"https:\/\/ellistat.com\/wp-content\/uploads\/2024\/09\/Test-de-Dixon.png 300w, https:\/\/ellistat.com\/wp-content\/uploads\/2024\/09\/Test-de-Dixon-18x4.png 18w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">A Dixon-teszt alkalmaz\u00e1s\u00e1hoz sz\u00e1m\u00edtsa ki az ar\u00e1nyt :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>b = A m\u00e9r\u00e9sek teljes terjedelme (itt 14.1.)<\/li>\n\n\n\n<li>a = A kiugr\u00f3nak v\u00e9lt r\u00e9sz \u00e9s a legk\u00f6zelebbi szomsz\u00e9dja k\u00f6z\u00f6tti t\u00e1vols\u00e1g (itt 8,6).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Az ar\u00e1nyt %-ben kell kisz\u00e1m\u00edtani.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ezt a jelent\u00e9st ezut\u00e1n \u00f6sszehasonl\u00edtjuk Dixon t\u00e1bl\u00e1zat\u00e1val:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>&nbsp;<\/th><th>&nbsp;<\/th><th>&nbsp;<\/th><th>&nbsp;<\/th><th>&nbsp;<\/th><th>&nbsp;<\/th><th>&nbsp;<\/th><\/tr><\/thead><tbody><tr><td>Darabsz\u00e1m<\/td><td>3<\/td><td>5<\/td><td>10<\/td><td>16<\/td><td>20<\/td><td>30<\/td><\/tr><tr><td>Maxim\u00e1lis ar\u00e1ny<\/td><td>0.94<\/td><td>0.72<\/td><td>0.46<\/td><td>0.38<\/td><td>0.34<\/td><td>0.30<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ha az \u00e9rt\u00e9k kisebb, mint a t\u00e1bl\u00e1zat \u00e1ltal javasolt maxim\u00e1lis ar\u00e1ny, akkor az \u00e9rt\u00e9k nem sz\u00e1m\u00edt kiugr\u00f3nak. Itt a 62% ar\u00e1ny 5 darab eset\u00e9ben kisebb, mint a 72%. A pont teh\u00e1t nem sz\u00e1m\u00edt kiugr\u00f3nak.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Grubb-teszt<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A Grubb-teszt haszn\u00e1lat\u00e1hoz el\u0151sz\u00f6r kisz\u00e1m\u00edtjuk :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>X: Az \u00f6sszes m\u00e9r\u00e9s \u00e1tlaga<\/li>\n\n\n\n<li>S: Az \u00f6sszes m\u00e9r\u00e9s sz\u00f3r\u00e1sa<\/li>\n\n\n\n<li>G: a kiugr\u00f3nak v\u00e9lt \u00e9rt\u00e9k \u00e9s a G \u00e1tlag k\u00f6z\u00f6tti t\u00e1vols\u00e1g.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><span class=\"wp-katex-eq\" data-display=\"false\">G=\\frac{(Value - X)}{S}<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"166\" src=\"https:\/\/ellistat.com\/wp-content\/uploads\/2024\/09\/Test-de-Grubb.png\" alt=\"\" class=\"wp-image-1198\" srcset=\"https:\/\/ellistat.com\/wp-content\/uploads\/2024\/09\/Test-de-Grubb.png 300w, https:\/\/ellistat.com\/wp-content\/uploads\/2024\/09\/Test-de-Grubb-18x10.png 18w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">A kapott G \u00e9rt\u00e9ket ezut\u00e1n \u00f6sszehasonl\u00edtjuk egy G hat\u00e1r\u00e9rt\u00e9kkel:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><span class=\"wp-katex-eq\" data-display=\"false\">G_{limite}=\\frac{N-1}{\\sqrt{N}}.\\sqrt{\\frac{t^2_{\\frac{a}{N},N-2}{}}{N-2 +t^2{}_{\\frac{a}{n}}{,} N-2}}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ha G&gt;G hat\u00e1r\u00e9rt\u00e9k, az \u00e9rt\u00e9ket kiugr\u00f3nak tekintj\u00fck, \u00e9s ford\u00edtva.<\/p>","protected":false},"excerpt":{"rendered":"<p>Lorsque l\u2019on analyse une s\u00e9rie de donn\u00e9es, il arrive que l\u2019on se retrouve confront\u00e9 \u00e0 des valeurs qui nous semblent ne pas faire partie de la distribution normale des donn\u00e9es. On appelle ces points des valeurs aberrantes et comme d\u2019habitude, il ne faut pas toujours se fier \u00e0 son intuition pour pouvoir d\u00e9tecter si une [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":1202,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-1197","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-analysis"],"acf":[],"_links":{"self":[{"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/posts\/1197","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/comments?post=1197"}],"version-history":[{"count":1,"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/posts\/1197\/revisions"}],"predecessor-version":[{"id":1200,"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/posts\/1197\/revisions\/1200"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/media\/1202"}],"wp:attachment":[{"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/media?parent=1197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/categories?post=1197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ellistat.com\/hu\/wp-json\/wp\/v2\/tags?post=1197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}