{"id":446,"date":"2020-03-19T12:42:17","date_gmt":"2020-03-19T11:42:17","guid":{"rendered":"http:\/\/estatistika.ku.sk\/?page_id=446"},"modified":"2022-02-27T10:37:21","modified_gmt":"2022-02-27T09:37:21","slug":"vztahy-medzi-kardinalnymi-premennymi","status":"publish","type":"page","link":"https:\/\/estatistika.ku.sk\/index.php\/induktivna-statistika\/korelacna-analyza\/vztahy-medzi-kardinalnymi-premennymi\/","title":{"rendered":"Kardin\u00e1lna premenn\u00e1"},"content":{"rendered":"<ul>\n<li style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Na meranie vz\u0165ahu medzi kardin\u00e1lnymi premenn\u00fdmi pou\u017e\u00edvame Pearsonov korela\u010dn\u00fd koeficient.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>Pr\u00edklad \u010d. 1:<\/strong> Cie\u013eom anal\u00fdzy je vy\u0161etri\u0165 intenzitu z\u00e1vislosti medzi \u0161tyrmi znakmi, ktor\u00e9 sme sledovali na vzorke 44 stredo\u0161kol\u00e1kov. Sledovan\u00e9 znaky s\u00fa:<\/p>\n<ul style=\"text-align: justify;\">\n<li>po\u010det hod\u00edn absencie na hodin\u00e1ch matematiky po\u010das roka,<\/li>\n<li>po\u010det bodov, ktor\u00e9 z\u00edskali\u00a0\u00a0z koncoro\u010dn\u00e9ho testu\u00a0\u00a0z matematiky,<\/li>\n<li>koncoro\u010dn\u00e1 zn\u00e1mka z matematiky<\/li>\n<li>body z Amthauerovho testu vedomost\u00ed.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Zauj\u00edma n\u00e1s, medzi ktor\u00fdmi znakmi je najsilnej\u0161ia line\u00e1rna z\u00e1vislos\u0165.<\/p>\n<p style=\"text-align: justify;\">H<sub>0<\/sub>:\u00a0 Znaky s\u00fa line\u00e1rne nez\u00e1visl\u00e9.<\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 12pt;\">H<sub>0a: <\/sub>Medzi po\u010dtom hod\u00edn absencie na hodin\u00e1ch matematiky a po\u010dtom bodov z koncoro\u010dn\u00e9ho testu neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>0b: <\/sub>Medzi po\u010dtom hod\u00edn absencie na hodin\u00e1ch matematiky a koncoro\u010dnou zn\u00e1mkou z matematiky neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>0c: <\/sub>Medzi po\u010dtom hod\u00edn absencie na hodin\u00e1ch matematiky a testom vedomost\u00ed neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>0d: <\/sub>Medzi po\u010dtom bodov z koncoro\u010dn\u00e9ho testu a testom vedomost\u00ed neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>0e: <\/sub>Medzi po\u010dtom hod\u00edn z koncoro\u010dn\u00e9ho testu a koncoro\u010dnou zn\u00e1mkou z matematiky neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>0f: <\/sub>Medzi koncoro\u010dnou zn\u00e1mkou z matematiky a testom vedomost\u00ed neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">H<sub>A<\/sub>: Znaky s\u00fa liner\u00e1ne z\u00e1visl\u00e9.<\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 12pt;\">H<sub>Aa: <\/sub>Medzi po\u010dtom hod\u00edn absencie na hodin\u00e1ch matematiky a po\u010dtom bodov z koncoro\u010dn\u00e9ho testu existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>Ab: <\/sub>Medzi po\u010dtom hod\u00edn absencie na hodin\u00e1ch matematiky a koncoro\u010dnou zn\u00e1mkou z matematiky existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>Ac: <\/sub>Medzi po\u010dtom hod\u00edn absencie na hodin\u00e1ch matematiky a testom vedomost\u00ed existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>Ad: <\/sub>Medzi po\u010dtom bodov z koncoro\u010dn\u00e9ho testu a testom vedomost\u00ed existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>Ae: <\/sub>Medzi po\u010dtom hod\u00edn z koncoro\u010dn\u00e9ho testu a koncoro\u010dnou zn\u00e1mkou z matematiky existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>Af: <\/sub>Medzi koncoro\u010dnou zn\u00e1mkou z matematiky a testom vedomost\u00ed existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<\/ul>\n<table style=\"border-collapse: collapse; width: 100%; height: 80px;\">\n<tbody>\n<tr style=\"height: 40px;\">\n<td style=\"width: 601px; height: 40px; text-align: center;\"><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>Videon\u00e1vod: SPSS<\/strong><\/span><\/td>\n<td style=\"width: 601px; height: 40px; text-align: center;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">Videon\u00e1vod: EXCEL<\/span><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 40px;\">\n<td style=\"width: 601px; height: 40px;\"><iframe title=\"Pearsonov korela\u010dn\u00fd koeficient - SPSS\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/2yy8Cm07syY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/td>\n<td style=\"width: 601px; height: 40px;\"><iframe title=\"Korela\u010dn\u00e1 anal\u00fdza - Excel\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/VXbth5qwGn8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #800080;\"><span style=\"color: #000000;\"><br \/>\nPr\u00edklad \u010d. 2 si m\u00f4\u017eete sk\u00fasi\u0165 sami vypo\u010d\u00edta\u0165. Ni\u017e\u0161ie n\u00e1jdete pr\u00edslu\u0161n\u00fa d\u00e1tov\u00fa maticu v SPSS i v Exceli, s\u00fabory si m\u00f4\u017eete stiahnu\u0165. To \u010di ste zadanie spr\u00e1vne vypo\u010d\u00edtali si m\u00f4\u017eete overi\u0165, ak v\u00e1\u0161 v\u00fdsledok vlo\u017e\u00edte do v\u00fdsledkov\u00e9ho okna, ktor\u00e9 taktie\u017e n\u00e1jdete ni\u017e\u0161ie pod zadan\u00edm pr\u00edkladu.<\/span><\/span><\/p>\n<p><span style=\"color: #800080;\"><b>Sk\u00fa\u0161obn\u00fd pr\u00edklad:<\/b><\/span><\/p>\n<p style=\"text-align: justify;\"><strong>Pr\u00edklad \u010d. 2: <\/strong>Cie\u013eom anal\u00fdzy je vy\u0161etri\u0165 intenzitu z\u00e1vislosti medzi tromi znakmi, ktor\u00e9 sme sledovali na vzorke 55 pracovn\u00edkov soci\u00e1lnych slu\u017eieb. Sledovan\u00e9 znaky s\u00fa:<\/p>\n<ul style=\"text-align: justify;\">\n<li>po\u010det dn\u00ed absencie v pr\u00e1ci v roku 2021,<\/li>\n<li>vek,<\/li>\n<li>priemern\u00e1 mesa\u010dn\u00e1 mzda po\u010das sledovan\u00e9ho roka.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Ur\u010dte hodnotu korela\u010dn\u00e9ho koeficientu medzi znakmi, u ktor\u00fdch m\u00f4\u017eeme kon\u0161tatova\u0165 najv\u00e4\u010d\u0161iu intenzitu line\u00e1rnej z\u00e1vislosti.<\/p>\n<p style=\"text-align: justify;\">H<sub>0<\/sub>:\u00a0 Znaky s\u00fa line\u00e1rne nez\u00e1visl\u00e9.<\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 12pt;\">H<sub>0a: <\/sub>Medzi po\u010dtom hod\u00edn absencie v pr\u00e1ci a vekom neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>0b: <span style=\"font-size: 12pt;\">Medzi po\u010dtom hod\u00edn absencie v pr\u00e1ci a priemernou mesa\u010dnou mzdou neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/sub><\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>0c: <\/sub>Medzi vekom a priemernou mesa\u010dnou mzdou po\u010das roka neexistuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">H<sub>A<\/sub>: Znaky s\u00fa liner\u00e1ne z\u00e1visl\u00e9.<\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 12pt;\">H<sub>Aa: <\/sub>Medzi po\u010dtom hod\u00edn absencie v pr\u00e1ci a vekom existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<li><span style=\"font-size: 12pt;\">H<sub>Ab: <span style=\"font-size: 12pt;\">Medzi po\u010dtom hod\u00edn absencie v pr\u00e1ci a priemernou mesa\u010dnou mzdou existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/sub><\/span><\/li>\n<li><span style=\"font-size: 12pt;\"><sub><span style=\"font-size: 14pt;\">H<\/span>Ac:: <\/sub>Medzi vekom a priemernou mesa\u010dnou mzdou po\u010das roka existuje \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/span><\/li>\n<\/ul>\n<table style=\"border-collapse: collapse; width: 100%; height: 81px;\">\n<tbody>\n<tr style=\"height: 41px;\">\n<td style=\"width: 50%; height: 41px; text-align: center;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 12pt;\"><strong>D\u00e1tov\u00e1 matica IBM SPSS na stiahnutie<br \/>\n<\/strong><\/span><\/td>\n<td style=\"width: 50%; height: 41px; text-align: center;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 12pt;\"><strong>D\u00e1tov\u00e1 matica MS EXCEL na stiahnutie<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 40px;\">\n<td style=\"width: 50%; height: 40px;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><a href=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2022\/02\/data_kardinalne_skusobny_korelacie.zip\"><img decoding=\"async\" class=\"alignnone wp-image-980\" src=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/cropped-logoIBM-SPSS.png\" alt=\"\" width=\"116\" height=\"94\" \/><\/a><\/span><\/td>\n<td style=\"width: 50%; height: 40px;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><a href=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2022\/02\/data-korelacia-_nove.xlsx\"><img decoding=\"async\" class=\"alignnone wp-image-105\" src=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/782px-Microsoft_Excel_2013_logo.svg_.png\" alt=\"\" width=\"102\" height=\"100\" srcset=\"https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/782px-Microsoft_Excel_2013_logo.svg_.png 782w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/782px-Microsoft_Excel_2013_logo.svg_-300x295.png 300w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/782px-Microsoft_Excel_2013_logo.svg_-768x754.png 768w\" sizes=\"(max-width: 102px) 100vw, 102px\" \/><\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>Overte si \u010di ste pr\u00edklad vypo\u010d\u00edtali spr\u00e1vne<\/strong><\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 12pt;\">(v pr\u00edpade spr\u00e1vneho v\u00fdpo\u010dtu je v\u00fdsledok v zelenom r\u00e1m\u010deku)<\/span><\/p>\n<p style=\"text-align: center;\"><div class = \"hdq_quiz_wrapper\"><a href = \"https:\/\/estatistika.ku.sk\/index.php\/induktivna-statistika\/korelacna-analyza\/vztahy-medzi-kardinalnymi-premennymi\/\" rel=\"noamphtml\" class = \"hdq_quiz_start hdq_button button\" role = \"button\">Otvori\u0165 overenie v\u00fdpo\u010dtu<\/a><\/div><\/p>\n<blockquote><p><strong><span style=\"font-size: 12pt;\">! vpisujte hodnotu korela\u010dn\u00e9ho koeficientu zaokr\u00fahlen\u00fa na 3-desatinn\u00e9 miesta.<\/span><\/strong><\/p>\n<p><span style=\"font-size: 12pt;\">! ak ste po\u010d\u00edtali v SPSS, vpisujte v\u00fdsledok i <strong>s nulou pred \u010diarkou<\/strong>, napr. 0,005 (v SPSS je v\u00fdsledok vo forme z\u00e1pisu .005).<\/span><\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Na meranie vz\u0165ahu medzi kardin\u00e1lnymi premenn\u00fdmi pou\u017e\u00edvame Pearsonov korela\u010dn\u00fd koeficient. Pr\u00edklad \u010d. 1: Cie\u013eom anal\u00fdzy je vy\u0161etri\u0165 intenzitu z\u00e1vislosti medzi \u0161tyrmi znakmi, ktor\u00e9 sme sledovali na vzorke 44 stredo\u0161kol\u00e1kov. Sledovan\u00e9 znaky s\u00fa: po\u010det hod\u00edn absencie na hodin\u00e1ch matematiky po\u010das roka, po\u010det bodov, ktor\u00e9 z\u00edskali\u00a0\u00a0z koncoro\u010dn\u00e9ho testu\u00a0\u00a0z matematiky, koncoro\u010dn\u00e1 zn\u00e1mka z matematiky body z Amthauerovho testu [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":440,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"footnotes":""},"class_list":["post-446","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/comments?post=446"}],"version-history":[{"count":21,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/446\/revisions"}],"predecessor-version":[{"id":2245,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/446\/revisions\/2245"}],"up":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/440"}],"wp:attachment":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/media?parent=446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}