{"id":129,"date":"2020-01-14T11:21:29","date_gmt":"2020-01-14T10:21:29","guid":{"rendered":"http:\/\/estatistika.ku.sk\/?page_id=129"},"modified":"2022-05-19T08:08:41","modified_gmt":"2022-05-19T06:08:41","slug":"129-2","status":"publish","type":"page","link":"https:\/\/estatistika.ku.sk\/index.php\/induktivna-statistika\/129-2\/","title":{"rendered":"\u0160tatistick\u00e9 hypot\u00e9zy a hladina v\u00fdznamnosti"},"content":{"rendered":"<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">\u0160tatistick\u00e1 hypot\u00e9za mus\u00ed by\u0165 formulovan\u00e1 tak\u00fdm sp\u00f4sobom, aby ju bolo mo\u017en\u00e9 na z\u00e1klade empirick\u00fdch d\u00e1t podpori\u0165, alebo zamietnu\u0165. Formulujeme ju zmysluplnou, oznamovacou vetou v pr\u00edtomnom \u010dase.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Formul\u00e1cia \u0161tatistick\u00fdch hypot\u00e9z:<\/strong><\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>1.<\/strong> <strong>Formul\u00e1cia nulovej hypot\u00e9zy H0<\/strong> \u2013 hypot\u00e9za o rovnosti, resp. o ch\u00fdban\u00ed rozdielov (napr. deti z \u00fapln\u00fdch rod\u00edn a deti z ne\u00fapln\u00fdch rod\u00edn sa <span style=\"color: #800080;\"><strong><em>nel\u00ed\u0161ia<\/em> <\/strong><\/span>v miere seba\u00facty).<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>2. Formul\u00e1cia alternat\u00edvnej hypot\u00e9zy HA<\/strong> \u2013 je opakom nulovej hypot\u00e9zy a predpoklad\u00e1 rozdiely v istom parametri, resp. rozdiel medzi skupinami (napr. deti z \u00fapln\u00fdch rod\u00edn a deti z ne\u00fapln\u00fdch rod\u00edn sa <span style=\"color: #800080;\"><strong><em>l\u00ed\u0161ia<\/em> <\/strong><\/span>v miere seba\u00facty).<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Alternat\u00edvna hypot\u00e9za<\/strong> m\u00f4\u017ee by\u0165:<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong><em>Jednostrann\u00e1<\/em><\/strong>: deti z \u00fapln\u00fdch rod\u00edn maj\u00fa vy\u0161\u0161iu mieru seba\u00facty v porovnan\u00ed s de\u0165mi z ne\u00fapln\u00fdch rod\u00edn,<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><em><strong>Dvojstrann\u00e1<\/strong><\/em>: deti z \u00fapln\u00fdch rod\u00edn a deti z ne\u00fapln\u00fdch rod\u00edn sa l\u00ed\u0161ia v miere seba\u00facty.<\/span><\/p>\n<blockquote><p><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Hypot\u00e9za by mala by\u0165 podporen\u00e1 te\u00f3riou, resp. v\u00fdsledkami predch\u00e1dzaj\u00facich v\u00fdskumn\u00fdch \u0161t\u00fadi\u00ed.<\/span><\/p><\/blockquote>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>3. Stanovenie hladiny v\u00fdznamnosti<\/strong><\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">hladina v\u00fdznamnosti je pravdepodobnos\u0165 chyby I. stup\u0148a (\u03b1), ktor\u00fa urob\u00edme, ak zamietneme nulov\u00fa hypot\u00e9zu v pr\u00edpade, \u017ee skuto\u010dne plat\u00ed. Teda dospejeme k z\u00e1veru, \u017ee medzi premenn\u00fdmi nie je vz\u0165ah, pri\u010dom medzi nimi vz\u0165ah je.<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">hladina v\u00fdznamnosti sa tradi\u010dne stanovuje na <strong>5 % (p = 0,05)<\/strong>. V\u00fdsledok\/zistenie je vtedy signifikantn\u00e9, ak je p hodnota men\u0161ia ne\u017e 5 % (p &lt; 0,05). P\u00edsmeno \u201ep\u201c znamen\u00e1 pravdepodobnos\u0165 (prakticky ka\u017ed\u00fd \u0161tatistick\u00fd test, ktor\u00fd sa pou\u017e\u00edva, vygeneruje \u201ep\u201c), ktor\u00e9 m\u00f4\u017ee nadob\u00fada\u0165 rozli\u010dn\u00fa hodnotu:<\/span>\n<ul>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>p &lt; 0,05 (tj. \u03b1 = 5 %), signifikantn\u00e9<\/strong><\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>p &lt; 0,01 (tj. \u03b1 = 1 %), signifikantn\u00e9<\/strong><\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>p &lt; 0,001 (tj. \u03b1 = 0,1 %), signifikantn\u00e9<\/strong><\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>p &gt; 0,05 &#8211; nesignifikantn\u00e9<\/strong><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>4. Pou\u017eitie \u0161tatistick\u00e9ho testu a v\u00fdpo\u010det p-hodnoty<\/strong><\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Spr\u00e1vny \u0161tatistick\u00fd test zvol\u00edme na z\u00e1klade pos\u00fadenia viacer\u00fdch krit\u00e9ri\u00ed \u2013 pod\u013ea toho, o ak\u00fa <a href=\"http:\/\/estatistika.ku.sk\/index.php\/druhy-premennych\/\">premenn\u00fa<\/a> sa jedn\u00e1, pod\u013ea toho, \u010di chceme nie\u010do porovn\u00e1va\u0165 (<a href=\"http:\/\/estatistika.ku.sk\/index.php\/induktivna-statistika\/komparacna-analyza\/\">komparova\u0165<\/a>), alebo h\u013eada\u0165 vz\u0165ahy (<a href=\"http:\/\/estatistika.ku.sk\/index.php\/induktivna-statistika\/korelacna-analyza\/\">korelacia<\/a>) a pri kardin\u00e1lnych (spojit\u00fdch) premenn\u00fdch mus\u00edme bra\u0165 do \u00favahy <a href=\"http:\/\/estatistika.ku.sk\/index.php\/induktivna-statistika\/parametricke-vs-neparametricke-statisticke-testy\/\">podmienky pre parametrick\u00fd test.<\/a><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-132\" src=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka-1.jpg\" alt=\"\" width=\"615\" height=\"200\" srcset=\"https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka-1.jpg 615w, https:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka-1-300x98.jpg 300w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Pr\u00edklad:<\/strong><\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">H0 (nulov\u00e1 hypot\u00e9za): \u00damrtnos\u0165 mu\u017eov a \u017eien vzh\u013eadom na vek je rovnak\u00e1.<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">HA (alternat\u00edvna hypot\u00e9za): \u00damrtnos\u0165 mu\u017eov a \u017eien vzh\u013eadom na vek nie je rovnak\u00e1.<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Z v\u00fdberov\u00fdch s\u00faborov sme zistili, \u017ee:<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Priemern\u00fd vek \u00famrtia mu\u017ea je 68 rokov.<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Priemern\u00fd vek \u00famrtia \u017eeny je 75 rokov.<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Pou\u017eijeme pr\u00edslu\u0161n\u00fd \u0161tatistick\u00fd test s v\u00fdsledkom p = 0,031.<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Ktor\u00fa hypot\u00e9zu zavrhneme, resp. pre ktor\u00fa hypot\u00e9zu sa rozhodneme?<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>5. Rie\u0161enie<\/strong><\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">ak je p &lt; 0,05, zisten\u00e9 rozdiely s vysokou pravdepodobnos\u0165ou nevznikli na z\u00e1klade n\u00e1hody, pr\u00edp. chybou v\u00fdberu (prij\u00edmame alternat\u00edvnu hypot\u00e9zu o existencii rozdielov),<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">ak je p &gt; 0,05, zisten\u00e9 rozdiely mohli vznikn\u00fa\u0165 na z\u00e1klade n\u00e1hody, pr\u00edp. chybou v\u00fdberu (prij\u00edmame nulov\u00fa hypot\u00e9zu o neexistencii rozdielov).<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Rie\u0161enie vy\u0161\u0161ie uveden\u00e9ho pr\u00edkladu: ke\u010f\u017ee p &lt; 0,05 (0,031) zavrhujeme nulov\u00fa hypot\u00e9zu a prij\u00edmame alternat\u00edvnu hypot\u00e9zu o rozdieloch. Teda medzi vekom \u00famrtnosti mu\u017eov a \u017eien je signifikantn\u00fd rozdiel.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Postup v\u00fdberu \u0161tatistick\u00e9ho testu<\/strong> n\u00e1jdeme v \u010dasti <a href=\"http:\/\/estatistika.ku.sk\/index.php\/induktivna-statistika\/parametricke-vs-neparametricke-statisticke-testy\/\">&#8222;Parametrick\u00e9 vs. neparametrick\u00e9 testy&#8220;.<\/a><\/span><\/p>\n<blockquote>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><em>Ritomsk\u00fd (2015) upozor\u0148uje, \u017ee \u0161tatistick\u00e1 signifikancia je &#8222;len&#8220; o tom, s ak\u00fdm rizikom (pravdepodobnos\u0165ou) zamietame nulov\u00fa hypot\u00e9zu v situ\u00e1cii, ke\u010f je pravdiv\u00e1. V\u00fdskumn\u00edka, pochopite\u013ene &#8211; v pr\u00edpade, \u017ee prijal alternat\u00edvnu hypot\u00e9zu, ktor\u00e1 hovor\u00ed o existencii popula\u010dn\u00e9ho rozdielu, zauj\u00edma aj z\u00e1va\u017enos\u0165 tohto rozdielu. O nej \u0161tatistick\u00e1 signifikancia nevypoved\u00e1. <\/em><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><em>O ve\u013ekosti popula\u010dnej diferencie poskytuje d\u00f4le\u017eit\u00fa inform\u00e1ciu intervalov\u00fd odhad, i rozdiely v priemeroch, \u0161tandardnej odch\u00fdlke i priemern\u00fdch poradiach v porovn\u00e1van\u00fdch skupin\u00e1ch.<\/em><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><em>Okrem toho v\u00fdznamnou pom\u00f4ckou je ukazovate\u013e <strong>vecnej signifikancie<\/strong> (&#8222;<strong>effect size<\/strong>&#8222;, Cohen\u00b4s d &#8211; viac <a href=\"http:\/\/estatistika.ku.sk\/index.php\/pouzita-a-odporucana-literatura\/\">Rabu\u0161ic, Soukup, Mare\u0161 (2019)<\/a>, s. 226-228).\u00a0<\/em><\/span><\/p>\n<\/blockquote>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Pri formul\u00e1cii \u0161tatistick\u00fdch hypot\u00e9z je d\u00f4le\u017eit\u00e9 dodr\u017eiava\u0165:<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">hypot\u00e9za mus\u00ed ma\u0165 v sebe zahrnut\u00fd potenci\u00e1lny rozdiel alebo vz\u0165ah medzi\u00a0<strong>dvoma<\/strong>\u00a0premenn\u00fdmi.<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">mus\u00ed by\u0165 jednozna\u010dn\u00e1, tzn., \u017ee na hypot\u00e9zu mus\u00ed by\u0165 jednozna\u010dn\u00e1 odpove\u010f (nem\u00f4\u017eeme poveda\u0165, \u017ee hypot\u00e9za sa \u201e\u010diasto\u010dne\u201c ne\/potvrdila).<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Pr\u00edklad nespr\u00e1vne formulovanej hypot\u00e9zy: Predpoklad\u00e1me rozdiel v n\u00e1zoroch mu\u017eov a \u017eien na interrupciu a eutan\u00e1ziu. Hypot\u00e9za je nespr\u00e1vne formulovan\u00e1 preto, lebo neposkytuje jednozna\u010dn\u00fa odpove\u010f v pr\u00edpade, ak sa mu\u017ei a \u017eeny bud\u00fa odli\u0161ova\u0165 v n\u00e1zoroch na eutan\u00e1ziu, ale bud\u00fa sa zhodova\u0165 v n\u00e1zoroch na interrupciu. V pr\u00edpade, ak by sme chceli \u0161tatisticky overova\u0165 vy\u0161\u0161ie uveden\u00e9, spr\u00e1vne by bolo formulova\u0165 dve hypot\u00e9zy:<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Predpoklad\u00e1me rozdiel v n\u00e1zoroch mu\u017eov a \u017eien na interrupciu.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Predpoklad\u00e1me rozdiel v n\u00e1zoroch mu\u017eov a \u017eien na eutan\u00e1ziu.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><!--more--><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt; font-family: helvetica, arial, sans-serif;\">* K vy\u0161\u0161ie uvedenej problematike je vhodn\u00e9 na\u0161tudova\u0165 si e\u0161te t\u00e9mu o chybe prv\u00e9ho a druh\u00e9ho druhu &#8211; odpor\u00fa\u010dame monografiu <a href=\"http:\/\/estatistika.ku.sk\/index.php\/pouzita-a-odporucana-literatura\/\">Rabu\u0161ic, Soukup, Mare\u0161 (2019)<\/a>, s. 245, pr\u00edp. monografiu <a href=\"http:\/\/estatistika.ku.sk\/index.php\/pouzita-a-odporucana-literatura\/\">Walker (2013)<\/a>.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0160tatistick\u00e1 hypot\u00e9za mus\u00ed by\u0165 formulovan\u00e1 tak\u00fdm sp\u00f4sobom, aby ju bolo mo\u017en\u00e9 na z\u00e1klade empirick\u00fdch d\u00e1t podpori\u0165, alebo zamietnu\u0165. Formulujeme ju zmysluplnou, oznamovacou vetou v pr\u00edtomnom \u010dase. Formul\u00e1cia \u0161tatistick\u00fdch hypot\u00e9z: 1. Formul\u00e1cia nulovej hypot\u00e9zy H0 \u2013 hypot\u00e9za o rovnosti, resp. o ch\u00fdban\u00ed rozdielov (napr. deti z \u00fapln\u00fdch rod\u00edn a deti z ne\u00fapln\u00fdch rod\u00edn sa nel\u00ed\u0161ia v [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":17,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"footnotes":""},"class_list":["post-129","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/129","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=129"}],"version-history":[{"count":27,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/129\/revisions"}],"predecessor-version":[{"id":2276,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/129\/revisions\/2276"}],"up":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/17"}],"wp:attachment":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/media?parent=129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}