{"id":1162,"date":"2024-09-05T22:25:42","date_gmt":"2024-09-05T20:25:42","guid":{"rendered":"https:\/\/site.ellistat.com\/?p=1162"},"modified":"2024-10-23T15:22:55","modified_gmt":"2024-10-23T13:22:55","slug":"normalitasvizsgalatok","status":"publish","type":"post","link":"https:\/\/clooma.ai\/hu\/normalitasvizsgalatok\/","title":{"rendered":"Normalit\u00e1svizsg\u00e1latok"},"content":{"rendered":"<p>A normalit\u00e1s vizsg\u00e1lat\u00e1hoz t\u00f6bbf\u00e9le teszt is haszn\u00e1lhat\u00f3 annak a hipot\u00e9zisnek az igazol\u00e1s\u00e1ra vagy \u00e9rv\u00e9nytelen\u00edt\u00e9s\u00e9re, hogy az \u00e9rm\u00e9k eloszl\u00e1sa norm\u00e1lis eloszl\u00e1st k\u00f6vet. A leggyakrabban haszn\u00e1lt tesztek a k\u00f6vetkez\u0151k:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A Chi2 teszt<\/li>\n\n\n\n<li>Az Anderson-Darling teszt<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Normalit\u00e1svizsg\u00e1lat a Chi2-teszt seg\u00edts\u00e9g\u00e9vel<\/h2>\n\n\n\n<p>Az eloszl\u00e1s normalit\u00e1s\u00e1nak ellen\u0151rz\u00e9s\u00e9hez az els\u0151 meg\u00e9rz\u00e9s\u00fcnk az lenne, hogy a megfigyelt v\u00e1ltoz\u00f3k eloszl\u00e1s\u00e1nak hisztogramj\u00e1t \u00e1br\u00e1zoljuk. Ezut\u00e1n \u00f6sszehasonl\u00edtan\u00e1nk, hogy ez a hisztogram jobban vagy kev\u00e9sb\u00e9 hasonl\u00edt-e a\u00a0<a href=\"https:\/\/fr.wikipedia.org\/wiki\/Fonction_gaussienne\">Gauss-g\u00f6rbe<\/a> szok\u00e1sos.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/2024\/09\/chi21.png\" alt=\"\" class=\"wp-image-1164\"\/><\/figure><\/div>\n\n\n<p>Pontosan ez az elv \u00e1ll a Chi2 teszt m\u00f6g\u00f6tt. Ez az intu\u00edci\u00f3t kieg\u00e9sz\u00edti egy kis adag statisztikai sz\u00e1m\u00edt\u00e1ssal. Az elv a k\u00f6vetkez\u0151:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/2024\/09\/chi22.png\" alt=\"\" class=\"wp-image-1165\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">d_i=\\frac{(N_i-NP_i)^{2}}{NP_i}<\/span><\/p>\n\n\n\n<p>A hisztogram minden egyes s\u00e1vj\u00e1ra kisz\u00e1m\u00edthatjuk :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ni : A t\u00e9nylegesen megfigyelt alkatr\u00e9szek sz\u00e1ma (ebben az esetben 10).<\/li>\n\n\n\n<li>Npi: Az elm\u00e9letileg megfigyelt r\u00e9szek sz\u00e1ma, ha az eloszl\u00e1s norm\u00e1lis lenne (itt 9,2).<\/li>\n\n\n\n<li>di a \"rosszul elhelyezett alkatr\u00e9szek sz\u00e1m\u00e1t\" jel\u00f6li.<\/li>\n<\/ul>\n\n\n\n<p>Ezut\u00e1n kisz\u00e1m\u00edtjuk<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">D=\\sum_{}^{}D_i<\/span><\/p>\n\n\n\n<p>\u00e9s kider\u00fcl, hogy D egy n-2 szabads\u00e1gi fok\u00fa eloszl\u00e1si t\u00f6rv\u00e9nyt k\u00f6vet (N az oszt\u00e1lyok sz\u00e1ma). Ezut\u00e1n kisz\u00e1m\u00edthatjuk, hogy milyen val\u00f3sz\u00edn\u0171s\u00e9ggel kapunk ilyen \u00e9rt\u00e9ket.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"197\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/2024\/09\/courbe-chi2.jpg\" alt=\"\" class=\"wp-image-1166\" srcset=\"https:\/\/clooma.ai\/wp-content\/uploads\/2024\/09\/courbe-chi2.jpg 300w, https:\/\/clooma.ai\/wp-content\/uploads\/2024\/09\/courbe-chi2-18x12.jpg 18w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure><\/div>\n\n\n<p>P\u00e9ld\u00e1ul egy 7 oszt\u00e1lyt tartalmaz\u00f3 hisztogram eset\u00e9ben, ha kisz\u00e1m\u00edtottuk a 11,07-es D \u00e9rt\u00e9ket, akkor kisz\u00e1m\u00edtjuk, hogy 5% van ahhoz, hogy ilyen vagy enn\u00e9l t\u00f6bb \u00e9rt\u00e9ket kapjunk, ha a r\u00e9szek eloszl\u00e1sa val\u00f3ban norm\u00e1lis.<\/p>\n\n\n\n<p>A vizsg\u00e1lat eredm\u00e9nye teh\u00e1t 5% lesz, \u00e9s az \u00e1ltal\u00e1nos k\u00f6vetkeztet\u00e9s a k\u00f6vetkez\u0151:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ha X &lt; 5%: a v\u00e1ltoz\u00f3k eloszl\u00e1sa nem tekinthet\u0151 norm\u00e1lis eloszl\u00e1s\u00fanak.<\/li>\n\n\n\n<li>Ha X &gt;= 5%: a normalit\u00e1s felt\u00e9telez\u00e9se elfogadhat\u00f3, \u00e9s az eloszl\u00e1s norm\u00e1lis eloszl\u00e1s\u00fanak tekinthet\u0151.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Mi a teend\u0151 nem norm\u00e1lis esetben?<\/h2>\n\n\n\n<p>A k\u00f6zponti hat\u00e1r\u00e9rt\u00e9kt\u00e9tel szerint :<\/p>\n\n\n\n<p>B\u00e1rmely rendszer, amely sok, egym\u00e1st\u00f3l f\u00fcggetlen \u00e9s azonos nagys\u00e1grend\u0171 t\u00e9nyez\u0151 \u00f6sszeg\u00e9b\u0151l ad\u00f3dik, olyan eloszl\u00e1si t\u00f6rv\u00e9nyt hoz l\u00e9tre, amely a norm\u00e1lis eloszl\u00e1s fel\u00e9 tend\u00e1l.<\/p>\n\n\n\n<p>De ellenkez\u0151leg is gondolkodhatunk. Ha olyan eloszl\u00e1st figyel\u00fcnk meg, amely nem norm\u00e1lis, akkor a t\u00e9tel egyik hipot\u00e9zise nem \u00e9rv\u00e9nyes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1. eset: a rendszer nem sok t\u00e9nyez\u0151 \u00f6sszege: lehet sok t\u00e9nyez\u0151 vagy m\u00e1s t\u00e9nyez\u0151 szorzata. Ebben az esetben az eloszl\u00e1si t\u00f6rv\u00e9ny elt\u00e9r\u0151 lehet, \u00e9s \u00e1ltal\u00e1ban egy transzform\u00e1ci\u00f3 (p\u00e9ld\u00e1ul az eredm\u00e9ny logaritmus\u00e1nak felv\u00e9tele) vissza\u00e1ll\u00edtja a norm\u00e1lis eloszl\u00e1st.<\/li>\n\n\n\n<li>2. eset: A t\u00e9nyez\u0151k nem f\u00fcggetlenek egym\u00e1st\u00f3l<\/li>\n\n\n\n<li>3. eset: A t\u00e9nyez\u0151k nem azonos nagys\u00e1grend\u0171ek :\n<ul class=\"wp-block-list\">\n<li>Egy t\u00e9nyez\u0151 fel\u00fclm\u00falja a t\u00f6bbit. Ebben az esetben meg kell tal\u00e1lnunk a sz\u00f3ban forg\u00f3 t\u00e9nyez\u0151t, mert egyed\u00fcl ez gener\u00e1lja a v\u00e1ltoz\u00e9konys\u00e1g egyik f\u0151 forr\u00e1s\u00e1t.<\/li>\n\n\n\n<li>Egy kiugr\u00f3 szennyezi az eloszl\u00e1st. Ebben az esetben meg kell tal\u00e1lnunk a kiugr\u00f3 \u00e9rt\u00e9k ok\u00e1t, \u00e9s ki kell k\u00fcsz\u00f6b\u00f6ln\u00fcnk, ha az ok megmagyar\u00e1zhat\u00f3.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>Ebben a k\u00e9t esetben nem sz\u00fcks\u00e9ges a megfigyelt v\u00e1ltoz\u00e9konys\u00e1gnak megfelel\u0151 eloszl\u00e1si t\u00f6rv\u00e9nyt tal\u00e1lni. Val\u00f3j\u00e1ban ez az eloszl\u00e1si t\u00f6rv\u00e9ny nem lesz id\u0151vel megism\u00e9telhet\u0151, mivel egyetlen param\u00e9terre vezethet\u0151 vissza, \u00edgy nem rendelkezik el\u0151rejelz\u0151 tulajdons\u00e1gokkal.<\/p>\n\n\n\n<p>Ha a nemnormalit\u00e1s eredete az 1. esetre vezethet\u0151 vissza, akkor meg kell tal\u00e1lnia a megfelel\u0151 eloszl\u00e1si t\u00f6rv\u00e9nyt, k\u00fcl\u00f6n\u00f6sen akkor, ha a t\u0171r\u00e9shat\u00e1ron k\u00edv\u00fcli \u00e9rt\u00e9kek sz\u00e1zal\u00e9kos ar\u00e1ny\u00e1t szeretn\u00e9 megj\u00f3solni. Ehhez haszn\u00e1lhatja a javasolt eloszl\u00e1si t\u00f6rv\u00e9nyeket az ablak alj\u00e1n tal\u00e1lhat\u00f3&nbsp;<a href=\"https:\/\/clooma.ai\/hu\/adatelemzesi-megoldasok\/\">az Adatelemz\u00e9s modul<\/a>&nbsp;hogy megn\u00e9zz\u00fck, hogy az egyik eloszl\u00e1s j\u00f3l t\u00fckr\u00f6zi-e a megfigyelt adatokat:<\/p>","protected":false},"excerpt":{"rendered":"<p>Pour tester la normalit\u00e9, il existe plusieurs tests qui permettent de valider ou non l\u2019hypoth\u00e8se selon laquelle la r\u00e9partition des pi\u00e8ces suit une loi normale. Les tests habituellement utilis\u00e9s sont : Test de normalit\u00e9 avec le test de Chi2 Pour v\u00e9rifier la normalit\u00e9 d\u2019une distribution, notre premi\u00e8re intuition serait de tracer l\u2019histogramme de la r\u00e9partition [&hellip;]<\/p>","protected":false},"author":2,"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-1162","post","type-post","status-publish","format-standard","hentry","category-data-analysis"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Les tests de normalit\u00e9 - Clooma<\/title>\n<meta name=\"description\" content=\"Dans cet article nous verrons comment utiliser les test de normalit\u00e9 et comment r\u00e9agir en cas de d\u00e9tection d&#039;une non normalit\u00e9.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/clooma.ai\/hu\/normalitasvizsgalatok\/\" \/>\n<meta property=\"og:locale\" content=\"hu_HU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Les tests de normalit\u00e9 - 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