{"id":955,"date":"2018-12-21T16:05:48","date_gmt":"2018-12-21T14:05:48","guid":{"rendered":"http:\/\/biostatistics.med.uoa.gr\/?p=955"},"modified":"2022-06-08T15:22:04","modified_gmt":"2022-06-08T12:22:04","slug":"aparametriki_statistiki","status":"publish","type":"post","link":"https:\/\/biostatistics.med.uoa.gr\/en\/aparametriki_statistiki\/","title":{"rendered":"Non-Parametric Statistics"},"content":{"rendered":"<p><strong>\u03a3\u03ba\u03bf\u03c0\u03cc\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/strong><\/p>\n<p>\u039f \u03b2\u03b1\u03c3\u03b9\u03ba\u03cc\u03c2 \u03c3\u03c4\u03cc\u03c7\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03ba\u03b1\u03c4\u03b1\u03bd\u03cc\u03b7\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b4\u03b9\u03ac\u03ba\u03c1\u03b9\u03c3\u03b7\u03c2 \u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03ba\u03b1\u03b9 \u03bc\u03b7 \u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03c3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ce\u03bd \u03b4\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03b9\u03ce\u03bd, \u03c4\u03b1 \u03b5\u03af\u03b4\u03b7 \u03c4\u03c9\u03bd \u03b1\u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03bc\u03b5\u03b8\u03cc\u03b4\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c0\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03c0\u03cc\u03c4\u03b5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9.<\/p>\n<p><strong>\u03a0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/strong><\/p>\n<ul>\n<li>\u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03ba\u03b1\u03b9 \u0391\u03bd\u03b1\u03c3\u03ba\u03cc\u03c0\u03b7\u03c3\u03b7 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03a0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd: \u03a0\u03bb\u03b5\u03bf\u03bd\u03b5\u03ba\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03ba\u03b1\u03b9 \u039c\u03b5\u03b9\u03bf\u03bd\u03b5\u03ba\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c4\u03c9\u03bd \u03b1\u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03bc\u03b5\u03b8\u03cc\u03b4\u03c9\u03bd. \u0391\u03bd\u03b1\u03bc\u03b5\u03bd\u03cc\u03bc\u03b5\u03bd\u03b5\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03b4\u03b9\u03b1\u03ba\u03c5\u03bc\u03ac\u03bd\u03c3\u03b5\u03b9\u03c2 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03c3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c3\u03b5 \u03b4\u03b9\u03b1\u03c4\u03ac\u03be\u03b9\u03bc\u03b1 \u03bc\u03b5\u03b3\u03ad\u03b8\u03b7. \u03a3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ad\u03c2 \u03b4\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03af\u03b5\u03c2 \u03c4\u03ac\u03be\u03b7\u03c2 (rank statistical tests)<\/li>\n<li>\u03a0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03b1 \u03b8\u03ad\u03c3\u03b5\u03c9\u03c2 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ce\u03bd \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03b4\u03b5\u03af\u03b3\u03bc\u03b1 (\u03ae \u03c3\u03b5 \u03b4\u03cd\u03bf \u03c3\u03c5\u03c3\u03c7\u03b5\u03c4\u03b9\u03c3\u03bc\u03ad\u03bd\u03b1 \u03b6\u03b5\u03c5\u03b3\u03b1\u03c1\u03c9\u03c4\u03ac \u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1): \u03a0\u03c1\u03bf\u03c3\u03b7\u03bc\u03b9\u03ba\u03cc\u03c2 \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 (sign t test) \u03ba\u03b1\u03b9 \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 \u03b4\u03b9\u03b1\u03bc\u03ad\u03c3\u03bf\u03c5. \u0388\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7 \u03bc\u03ad\u03c3\u03b7 \u03c4\u03b9\u03bc\u03ae. \u039a\u03c1\u03b9\u03c4\u03ae\u03c1\u03b9\u03bf Wilcoxon \u03b3\u03b9\u03b1 \u03c0\u03b1\u03c1\u03b1\u03c4\u03b7\u03c1\u03ae\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03c4\u03ac \u03b6\u03b5\u03cd\u03b3\u03b7 (Wilcoxon signed rank statistic) \u03ba\u03b1\u03b9 \u03b7 \u03b5\u03ba\u03c4\u03af\u03bc\u03b7\u03c3\u03b7 Hodges-Lehmann. \u0392\u03ad\u03bb\u03c4\u03b9\u03c3\u03c4\u03b7 \u03b5\u03c0\u03b9\u03bb\u03bf\u03b3\u03ae \u03c3\u03b5\u03c3\u03b7\u03bc\u03b1\u03c3\u03bc\u03ad\u03bd\u03c9\u03bd \u03b8\u03ad\u03c3\u03b5\u03c9\u03bd (scores)\u2013(normalscores). \u0388\u03bb\u03b5\u03b3\u03c7\u03bf\u03b9 \u03ba\u03b1\u03bb\u03ae\u03c2 \u03c0\u03c1\u03bf\u03c3\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae\u03c2 (\u0394\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03af\u03b5\u03c2 Kolmogorov, Lilliefors, Shapiro-Wilk).<\/li>\n<li>\u0388\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 \u03b3\u03b9\u03b1 \u03b4\u03cd\u03bf (\u03ae \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1) \u03b1\u03bd\u03b5\u03be\u03ac\u03c1\u03c4\u03b7\u03c4\u03b1 \u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1: \u0392\u03b1\u03c3\u03b9\u03ba\u03ad\u03c2 \u03b1\u03c1\u03c7\u03ad\u03c2 \u03c4\u03c5\u03c7\u03b1\u03b9\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7\u03c2. \u0388\u03bb\u03b5\u03b3\u03c7\u03bf\u03b9 \u03bc\u03ad\u03c3\u03c9\u03bd \u03c4\u03b9\u03bc\u03ce\u03bd-\u03b4\u03b9\u03b1\u03bc\u03ad\u03c3\u03c9\u03bd \u03b3\u03b9\u03b1 \u03b4\u03cd\u03bf \u03b1\u03bd\u03b5\u03be\u03ac\u03c1\u03c4\u03b7\u03c4\u03b1 \u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1 (two sample sign test, Wilcoxon rank sum statistic). \u0392\u03ad\u03bb\u03c4\u03b9\u03c3\u03c4\u03b7 \u03b5\u03c0\u03b9\u03bb\u03bf\u03b3\u03ae \u03c3\u03b5\u03c3\u03b7\u03bc\u03b1\u03c3\u03bc\u03ad\u03bd\u03c9\u03bd \u03b8\u03ad\u03c3\u03b5\u03c9\u03bd (normal scores, Savage scores). \u0388\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 \u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03b4\u03b9\u03b1\u03ba\u03c5\u03bc\u03ac\u03bd\u03c3\u03b5\u03c9\u03bd (Siegel-Turkey \u03ba.\u03bb\u03c0.). \u0388\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 \u03ba\u03bf\u03b9\u03bd\u03ae\u03c2 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ae\u03c2 (Kolmogorov-Smirnov). \u0393\u03b5\u03bd\u03af\u03ba\u03b5\u03c5\u03c3\u03b7 \u03c3\u03b5 \u03c4\u03c1\u03af\u03b1 \u03ae \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1 \u03bc\u03b7 \u03b4\u03b9\u03b1\u03c4\u03ac\u03be\u03b9\u03bc\u03b1 \u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1 (Kruskal-Wallis, \u03ba.\u03bb\u03c0.). \u0394\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03af\u03b1 Jonchkeere-Terpstra \u03b3\u03b9\u03b1 \u03b4\u03b9\u03b1\u03c4\u03ac\u03be\u03b9\u03bc\u03b1 \u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1. \u0391\u03ba\u03c1\u03b9\u03b2\u03ae\u03c2, \u03b1\u03c3\u03c5\u03bc\u03c0\u03c4\u03c9\u03c4\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 Monte Carlo \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1<\/li>\n<li>\u03a3\u03c4\u03c1\u03c9\u03bc\u03b1\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03ba\u03b1\u03b9 \u039f\u03bc\u03b1\u03b4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7: \u0394\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03af\u03b5\u03c2 \u03b1\u03bd\u03ac \u03c3\u03c4\u03c1\u03ce\u03bc\u03b1\u03c4\u03b1. \u0394\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03af\u03b1 Friedman<\/li>\n<li>\u03a3\u03c5\u03c3\u03c7\u03ad\u03c4\u03b9\u03c3\u03b7, \u03a3\u03c5\u03bc\u03c6\u03c9\u03bd\u03af\u03b1 \u03ba\u03b1\u03b9 \u03a0\u03b1\u03bb\u03b9\u03bd\u03b4\u03c1\u03cc\u03bc\u03b7\u03c3\u03b7: \u039c\u03b7 \u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03cc\u03c2 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae\u03c2 \u03c3\u03c5\u03c3\u03c7\u03ad\u03c4\u03b9\u03c3\u03b7\u03c2 \u03c4\u03bf\u03c5 Spearman. \u039c\u03b7 \u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03cc\u03c2 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae\u03c2 \u03c3\u03c5\u03c3\u03c7\u03ad\u03c4\u03b9\u03c3\u03b7\u03c2 \u03c4\u03bf\u03c5 Kendall (\u03c4). \u039c\u03ad\u03c4\u03c1\u03bf \u03c3\u03c5\u03bc\u03c6\u03c9\u03bd\u03af\u03b1\u03c2 (\u03ba\u03ac\u03c0\u03b1 \u03c4\u03bf\u03c5 Cohen). \u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03c3\u03b5 \u03b1\u03bd\u03b8\u03b5\u03ba\u03c4\u03b9\u03ba\u03ad\u03c2 (robust) \u03bc\u03b5\u03b8\u03cc\u03b4\u03bf\u03c5\u03c2 \u03c0\u03b1\u03bb\u03b9\u03bd\u03b4\u03c1\u03cc\u03bc\u03b7\u03c3\u03b7\u03c2 \u03ba\u03b1\u03b9 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b5\u03be\u03bf\u03bc\u03ac\u03bb\u03c5\u03bd\u03c3\u03b7\u03c2 (smoothing).<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>\u03a3\u03ba\u03bf\u03c0\u03cc\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u039f \u03b2\u03b1\u03c3\u03b9\u03ba\u03cc\u03c2 \u03c3\u03c4\u03cc\u03c7\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03ba\u03b1\u03c4\u03b1\u03bd\u03cc\u03b7\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b4\u03b9\u03ac\u03ba\u03c1\u03b9\u03c3\u03b7\u03c2 \u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03ba\u03b1\u03b9 \u03bc\u03b7 \u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03c3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ce\u03bd \u03b4\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03b9\u03ce\u03bd, \u03c4\u03b1 \u03b5\u03af\u03b4\u03b7 \u03c4\u03c9\u03bd \u03b1\u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03bc\u03b5\u03b8\u03cc\u03b4\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c0\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03c0\u03cc\u03c4\u03b5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9. \u03a0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03ba\u03b1\u03b9 \u0391\u03bd\u03b1\u03c3\u03ba\u03cc\u03c0\u03b7\u03c3\u03b7 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03a0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd: \u03a0\u03bb\u03b5\u03bf\u03bd\u03b5\u03ba\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03ba\u03b1\u03b9 \u039c\u03b5\u03b9\u03bf\u03bd\u03b5\u03ba\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c4\u03c9\u03bd \u03b1\u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03bc\u03b5\u03b8\u03cc\u03b4\u03c9\u03bd. \u0391\u03bd\u03b1\u03bc\u03b5\u03bd\u03cc\u03bc\u03b5\u03bd\u03b5\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03b4\u03b9\u03b1\u03ba\u03c5\u03bc\u03ac\u03bd\u03c3\u03b5\u03b9\u03c2 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03c3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c3\u03b5 \u03b4\u03b9\u03b1\u03c4\u03ac\u03be\u03b9\u03bc\u03b1 \u03bc\u03b5\u03b3\u03ad\u03b8\u03b7. \u03a3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ad\u03c2 \u03b4\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03af\u03b5\u03c2 \u03c4\u03ac\u03be\u03b7\u03c2 (rank statistical <a href=\"https:\/\/biostatistics.med.uoa.gr\/en\/aparametriki_statistiki\/\" rel=\"nofollow\"><span class=\"sr-only\">Read more about \u0391\u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ae \u03a3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae<\/span>[&hellip;]<\/a><\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"_links":{"self":[{"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/posts\/955"}],"collection":[{"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/comments?post=955"}],"version-history":[{"count":4,"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/posts\/955\/revisions"}],"predecessor-version":[{"id":2125,"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/posts\/955\/revisions\/2125"}],"wp:attachment":[{"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/media?parent=955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/categories?post=955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/biostatistics.med.uoa.gr\/en\/wp-json\/wp\/v2\/tags?post=955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}