{"id":11438,"date":"2025-10-25T15:23:23","date_gmt":"2025-10-25T13:23:23","guid":{"rendered":"https:\/\/e-ucebnice.ff.ucm.sk\/?page_id=11438"},"modified":"2025-11-25T14:14:20","modified_gmt":"2025-11-25T13:14:20","slug":"statistika-prakticky-8","status":"publish","type":"page","link":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/statistika-prakticky-8\/","title":{"rendered":"Statistika-prakticky-8"},"content":{"rendered":"\t\t
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\u0160TATISTIKA PRAKTICKY (NIELEN) V Z\u00c1VERE\u010cN\u00ddCH PR\u00c1CACH<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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8. TESTOVANIE S\u00daVISLOST\u00cd MEDZI DVOMA KATEGORICK\u00ddMI PREMENN\u00ddMI<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Kategorick\u00e9 premenn\u00e9 m\u00f4\u017eu by\u0165 nomin\u00e1lne, ale i ordin\u00e1lne, je mo\u017en\u00e9 pod\u013ea nich rozdeli\u0165 s\u00fabor do podskup\u00edn. \u0160pecifick\u00e9 je, \u017ee dok\u00e1\u017eeme v podskupin\u00e1ch po\u010d\u00edta\u0165 po\u010detnosti zast\u00fapenia kateg\u00f3ri\u00ed in\u00e9ho javu. Po\u010detnosti je mo\u017en\u00e9 zobrazi\u0165 v bivaria\u010dnej tabu\u013eke, ktor\u00fa naz\u00fdvame KR\u00cd\u017dOV\u00c1, kontingen\u010dn\u00e1 alebo po anglicky\n(a v SPSS) CROSSTABS (Tabu\u013eka 8, prv\u00e1 \u010das\u0165), kde v st\u013apcoch s\u00fa kateg\u00f3rie jednej premennej a v riadkoch kateg\u00f3rie druhej premennej. S\u00favislosti medzi takto ur\u010den\u00fdmi\npremenn\u00fdmi sa po\u010d\u00edtaj\u00fa na z\u00e1klade po\u010detnost\u00ed, pri\u010dom hypot\u00e9zy m\u00f4\u017eeme formulova\u0165 kompara\u010dne, pokia\u013e je to mo\u017en\u00e9 a logick\u00e9 (Napr. rozdiel v politickej orient\u00e1cii medzi mu\u017emi a \u017eenami.), alebo asocia\u010dne (Napr. Predpoklad\u00e1me, \u017ee existuje vz\u0165ah medzi politickou orient\u00e1ciou a profesijnou orient\u00e1ciou.). Princ\u00edp vyhodnotenia v\u0161ak v\u017edy pracuje s kon\u0161truktom o\u010dak\u00e1van\u00fdch po\u010detnost\u00ed, ktor\u00e9 porovn\u00e1va s re\u00e1lnymi (nameran\u00fdmi po\u010detnos\u0165ami), z rozdielu generuje hodnotu pr\u00edslu\u0161n\u00e9ho testu a \u0161tatistick\u00fa v\u00fdznamnos\u0165 v\u00fdsledku (Tabu\u013eka 8, druh\u00e1 \u010das\u0165), ktor\u00e1 je potrebn\u00e1 pre prijatie \u010di zamietnutie nulovej hypot\u00e9zy. Pri r\u00f4zne stanoven\u00fdch hypot\u00e9zach (rozdiel, vz\u0165ah) je teda postup podobn\u00fd, av\u0161ak interpretuj\u00fa sa v\u00fdsledky in\u00e9ho testu. V SPSS n\u00e1jdeme v sekcii CROSSTABS viacero testov (pod\u013ea typu premenn\u00fdch), my si uvedieme iba najpou\u017e\u00edvanej\u0161ie: Ch\u00ed-kvadr\u00e1t a Ph\u00ed\/ Cramerovo V.<\/p>\n

Na tomto mieste sa prv\u00fdkr\u00e1t uv\u00e1dzaj\u00fa v\u00fdsledky \u0161tatistick\u00e9ho testovania, preto ozrejm\u00edme, ako sa zobrazuj\u00fa v\u00fdsledky \u0161tatistick\u00fdch testov v tabu\u013ek\u00e1ch. V\u00fdsledn\u00e9 hodnoty z testov a \u0161tatistick\u00e1 v\u00fdznamnos\u0165 sa spravidla zaokr\u00fah\u013euje na 3 desatinn\u00e9 miesta (\u03c72 , F, U, Z, r, p\/Sig. a pod.). V odbornej literat\u00fare sa, navy\u0161e, zvykn\u00fa vynech\u00e1va\u0165 nuly pred desatinnou \u010diarkou, pokia\u013e parameter dosahuje hodnoty od -1 do +1 (korela\u010dn\u00e9 koeficienty, regresn\u00e9 koeficienty, p\/Sig. hodnota).13<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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8.1 Rozdiel v kategorickej premennej medzi skupinami (Ch\u00ed-kvadr\u00e1t test)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Rozdiely v kategorickej premennej (tzn. nomin\u00e1lnej \u010di ordin\u00e1lnej, ktor\u00e1 m\u00e1 max. 3 \u00farovne) medzi skupinami respondentov (rozdelen\u00e9 pod\u013ea inej kategorickej premennej), m\u00f4\u017eeme testova\u0165 Ch\u00ed-kvadr\u00e1t testom. Formulujeme hypot\u00e9zu o rozdiele.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Pr\u00edklad 1:<\/strong>
\nH1: Predpoklad\u00e1me, \u017ee medzi mu\u017emi a \u017eenami existuje rozdiel v o v\u00fdskyte experimentovania s marihuanou (dvojsmern\u00e1).
\nEkvivalenty hypot\u00e9zy:<\/strong>
\nH1a (dvojsmern\u00e1): Predpoklad\u00e1me, \u017ee existuje rozdiel v tom, \u010di jednotlivec experimentoval s marihuanou vzh\u013eadom na pohlavie.
\nH1b (jednosmern\u00e1 hypot\u00e9za): Predpoklad\u00e1me, \u017ee diev\u010dat\u00e1 menej \u010dasto experimentovali s marihuanou ne\u017e chlapci.
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  • Experimentovanie s marihuanou je dichotomick\u00e1 premenn\u00e1, m\u00e1\nkateg\u00f3rie NIE a \u00c1NO.<\/li><\/ul><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    V pr\u00edpade takto kompara\u010dne postaven\u00fdch hypot\u00e9z v<\/p>

    • ANALYZE\/ DESCRIPTIVE STATISTICS\/ CROSSTABS je dobr\u00e9 zada\u0165 premenn\u00fa skup\u00edn (v tomto pr\u00edklade Pohlavie) do riadkov ( ROWS<\/strong>) a t\u00fa, ktor\u00fa porovn\u00e1vame (Experimentovanie s marihuanou) do st\u013apcov (COLUMNS<\/strong>), potom v sekcii \/ ELLS za\u0161krtn\u00fa\u0165 OBSERVED, EXPECTED, ROWS<\/strong> percent\u00e1 (aby sme v tabu\u013eke mali len riadkov\u00e9 percent\u00e1, ktor\u00e9 sa jednoduch\u0161ie interpretuj\u00fa ako porovnanie skup\u00edn, vi\u010f ni\u017e\u0161ie). V sekcii \/STATISTIC mus\u00edme e\u0161te za\u0161krtn\u00fa\u0165 CHI-SQUARE<\/strong><\/u>, aby bolo \u0161tatistick\u00e9 testovanie v\u00f4bec aplikovan\u00e9, \/CONTINUE a \/OK.<\/li><\/ul>

      \u00a0<\/p>

      Interpret\u00e1cia v\u00fdsledku testovania<\/strong>:<\/em><\/p>

      Predpoklad bol overovan\u00fd Ch\u00ed-kvadr\u00e1t testom s v\u00fdsledkom \u03c72 = 16,190; Sig. < 0,001, na z\u00e1klade ktor\u00e9ho interpretujeme rozdiely v po\u010detnostiach v bunk\u00e1ch kr\u00ed\u017eovej tabu\u013eky za v\u00fdznamn\u00e9 (Tabu\u013eka 8). Medzi mu\u017emi a \u017eenami je \u0161tatisticky v\u00fdznamn\u00fd rozdiel v zast\u00fapen\u00ed kateg\u00f3ri\u00ed experimentovania s marihuanou. Hypot\u00e9zu H1 (rovnako H1a) prij\u00edmame.<\/em> (Tak\u00e1to interpret\u00e1cia posta\u010duje, ak je hypot\u00e9za dvojsmern\u00e1.)
      Ak je jednosmern\u00e1, sledujeme \u010falej aj percentu\u00e1lne hodnoty a ich rozdiely medzi prv\u00fdm a druh\u00fdm riadkom:
      Vzh\u013eadom k percentu\u00e1lnym hodnot\u00e1m v bunk\u00e1ch kr\u00ed\u017eovej tabu\u013eky kon\u0161tatujeme, \u017ee experimentovanie s marihuanou sa vyskytlo u 30,9% chlapcov, a u 23,5% diev\u010dat a naopak, 69,1% chlapcov a 76,5% diev\u010dat e\u0161te neexperimentovalo s marihuanou. Z uveden\u00e9ho vypl\u00fdva, \u017ee mu\u017ei (chlapci) \u010dastej\u0161ie experimentovali s marihuanou ne\u017e \u017eeny (diev\u010dat\u00e1). Hypot\u00e9zu H1b preto prij\u00edmame.\u00a0<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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      Tabu\u013eka 8 Kr\u00ed\u017eov\u00e1 tabu\u013eka a v\u00fdsledok k H1: Ch\u00ed-kvadr\u00e1t test<\/em><\/p>\n\n

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      <\/td>\nExperimentovanie s marihuanou<\/strong><\/td>\n<\/tr>\n
      Pohlavie <\/strong><\/td>\nNie<\/td>\n\u00c1no<\/td>\nSpolu<\/td>\n<\/tr>\n
      Mu\u017ei<\/strong><\/td>\nPo\u010det<\/em><\/td>\n663<\/td>\n296<\/td>\n959<\/td>\n<\/tr>\n
      O\u010dak\u00e1van\u00fd po\u010det<\/em><\/td>\n706,0<\/td>\n253,0<\/td>\n959<\/td>\n<\/tr>\n
      %<\/em><\/td>\n69,1%<\/td>\n30,9%<\/strong><\/td>\n100,0%<\/td>\n<\/tr>\n
      \u017deny<\/strong><\/td>\nPo\u010det<\/em><\/td>\n1156<\/td>\n356<\/td>\n1512<\/td>\n<\/tr>\n
      O\u010dak\u00e1van\u00fd po\u010det<\/em><\/td>\n1113,0<\/td>\n399,0<\/td>\n1512<\/td>\n<\/tr>\n
      %<\/em><\/td>\n76,5%<\/strong><\/td>\n23,5%<\/td>\n100,0%<\/td>\n<\/tr>\n
      <\/td>\nHodnota<\/em><\/td>\ndf<\/em><\/td>\nSig.<\/em><\/td>\n<\/tr>\n
      <\/td>\nCh\u00ed-kvadr\u00e1t<\/strong><\/td>\n16,190<\/td>\n1<\/td>\n,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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      Pre zobrazenie by bol vhodn\u00fd zlo\u017een\u00fd st\u013apcov\u00fd graf,<\/u>., kde na osi x s\u00fa umiestnen\u00e9 skupiny (pohlavie) a porovn\u00e1van\u00e1 premenn\u00e1 je zobrazen\u00e1 r\u00f4znofarebn\u00fdmi st\u013apcami (Graf 8).<\/p>\n\"\"\n

      Graf 8 Percentu\u00e1lne zast\u00fapenie kateg\u00f3ri\u00ed premennej Podpora od u\u010dite\u013ea vzh\u013eadom na pohlavie<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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      8.2 Vz\u0165ah (asoci\u00e1cia) medzi dvoma kategorick\u00fdmi premenn\u00fdmi (Cramerovo V)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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      Hoci aj asoci\u00e1cie medzi kvalitat\u00edvnymi premenn\u00fdmi sa po\u010d\u00edtaj\u00fa na b\u00e1ze kr\u00ed\u017eovej tabu\u013eky a rozdielu medzi re\u00e1lnymi a o\u010dak\u00e1van\u00fdmi po\u010detnos\u0165ami, v\u00fdsledok n\u00e1m poskytuje i hodnotu v intervale 0 \u2013 1 vyjadruj\u00facu tesnos\u0165 vz\u0165ahu, ktor\u00e1 \u010d\u00edm je vy\u0161\u0161ia, t\u00fdm je vz\u0165ah tesnej\u0161\u00ed. Ide o test v\u00fdpo\u010dtu Crameovho V koeficientu (koeficientu kontingencie).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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      Pr\u00edklad 2:<\/strong>
      \nH2: Predpoklad\u00e1me, \u017ee existuje s\u00favislos\u0165 medzi experimentovan\u00edm\ns alkoholom a experimentovan\u00edm s faj\u010den\u00edm (dvojsmern\u00e1).
      \nEkvivalenty hypot\u00e9zy:<\/strong>
      \nH2a (dvojsmern\u00e1): Predpoklad\u00e1me, \u017ee experimentovanie s faj\u010den\u00edm s\u00favis\u00ed s experimentovan\u00edm s alkoholom.
      \nH2b (dvojsmern\u00e1): Predpoklad\u00e1me, \u017ee medzi experimentovan\u00edm s alkoholom a experimentovan\u00edm s faj\u010den\u00edm existuje tesn\u00fd vz\u0165ah<\/p>\n\n

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      • Experimentovanie s alkoholom i Experimentovanie s faj\u010den\u00edm s\u00fa\ndichotomick\u00e9 premenn\u00e9, kateg\u00f3rie v oboch s\u00fa \u00c1NO a NIE.<\/li>\n<\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        M\u00f4\u017eeme si v\u0161imn\u00fa\u0165, \u017ee medzi ekvivalentn\u00fdmi hypot\u00e9zami nen\u00e1jdeme jednosmern\u00fa verziu. Interpret\u00e1cia asoci\u00e1cie medzi kvalitat\u00edvnymi kategorick\u00fdmi premenn\u00fdmi neumo\u017e\u0148uje formulova\u0165 smerovanie, preto\u017ee koeficient asoci\u00e1cie nadob\u00fada len kladn\u00e9 hodnoty a interpret\u00e1cie konkr\u00e9tnych s\u00favislost\u00ed sa realizuje cez sledovanie percent v kr\u00ed\u017eovej tabu\u013eke, rovnako ako sme to prezentovali pri kompar\u00e1cii (Ch\u00ed – kvadr\u00e1t).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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        Ak by sme sa pok\u00fasili formulova\u0165, v ktorej bunke kr\u00ed\u017eovej tabu\u013eky o\u010dak\u00e1vame vy\u0161\u0161ie percento, u\u017e by sme sk\u013azli k porovn\u00e1vaniu tejto bunky s inou a i\u0161lo by o kompar\u00e1ciu.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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        Postup:<\/p>

        • ANALYZE\/ DESCRIPTIVE STATISTICS\/ CROSSTABS, jednu premenn\u00fa presunieme do riadkov (ROWS)<\/strong> druh\u00fa premenn\u00fa do st\u013apcov (COLUMNS)<\/strong>, potom v sekcii \/CELLS za\u0161krtneme OBSERVED, EXPECTED, TOTAL<\/strong> percent\u00e1 a m\u00f4\u017eeme aj ROW<\/strong> a COLUMN<\/strong> percent\u00e1.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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          Je to rozdiel oproti kompar\u00e1cii, tu s\u00fa premenn\u00e9 rovnocenn\u00e9, preto nez\u00e1le\u017e\u00ed, ktor\u00e1 bude v riadkoch a ktor\u00e1 v st\u013apcoch a taktie\u017e s\u00fa relevantn\u00e9 percent\u00e1 aj v r\u00e1mci riadkov aj v r\u00e1mci st\u013apcov.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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          V sekcii \/STATISTIC mus\u00edme e\u0161te za\u0161krtn\u00fa\u0165 PHI and CRAMER`S V<\/strong> (v sekcii Nominal), aby n\u00e1m test v\u00f4bec aplikovalo, \/CONTINUE a \/OK.<\/p>

          \u00a0<\/p>

          Interpret\u00e1cia v\u00fdsledku testovania<\/strong>:<\/em><\/p>

          Predpoklad bol overovan\u00fd v\u00fdpo\u010dtom Cramerovho V koeficientu s v\u00fdsledkom V = 0,383; Sig. < 0,001, na z\u00e1klade ktor\u00e9ho interpretujeme vz\u0165ah ako v\u00fdznamn\u00fd (Tabu\u013eka 10). Medzi experimentovan\u00edm s alkoholom a experimentovan\u00edm s faj\u010den\u00edm existuje v\u00fdznamn\u00fd vz\u0165ah, strednej tesnosti14<\/span>. Hypot\u00e9zu H2 (rovnako H2a a H2b) prij\u00edmame.<\/em><\/p>

          M\u00f4\u017eeme v interpret\u00e1cii pokra\u010dova\u0165 d\u00f4slednou anal\u00fdzou kr\u00ed\u017eovej tabu\u013eky, kde vid\u00edme percentu\u00e1lne zast\u00fapenia kombin\u00e1ci\u00ed kateg\u00f3ri\u00ed v celom s\u00fabore, alebo v r\u00e1mci riadkov a st\u013apcov.<\/p>

          M\u00f4\u017eeme vidie\u0165, \u017ee 56,7% z cel\u00e9ho s\u00faboru u\u017e experimentovalo aj s alkoholom aj s faj\u010den\u00edm, 13,1% nem\u00e1 sk\u00fasenos\u0165 s ani jednou uvedenou formou experimentovania (celkov\u00e9 percent\u00e1). Z t\u00fdch, ktor\u00ed experimentovali s alkoholom 66,9% experimentovalo aj s faj\u010den\u00edm a z t\u00fdch, ktor\u00ed neexperimentovali s alkoholom iba 14,6% m\u00e1 sk\u00fasenos\u0165 s faj\u010den\u00edm (riadkov\u00e9 percent\u00e1). Z respondentov, ktor\u00ed maj\u00fa sk\u00fasenos\u0165 s faj\u010den\u00edm, iba 3,8% nem\u00e1 sk\u00fasenos\u0165 s pit\u00edm alkoholu a z t\u00fdch, ktor\u00ed neexperimentovali s faj\u010den\u00edm, 31,9% nem\u00e1 sk\u00fasenos\u0165 ani s alkoholom (st\u013apcov\u00e9 %). At\u010f.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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          Tabu\u013eka 9 Kr\u00ed\u017eov\u00e1 tabu\u013eka a v\u00fdsledok k H2: Phi a Cramerovo V<\/em><\/p>\n\n

          \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
          Experimentovanie s alkoholom<\/strong><\/td>\n<\/td>\nExperimentovanie s faj\u010den\u00edm<\/strong><\/td>\n<\/tr>\n
          Nie<\/td>\n\u00c1no<\/td>\nSpolu<\/td>\n<\/tr>\n
          NIE<\/strong><\/td>\nPo\u010det<\/em><\/td>\n327<\/td>\n56<\/td>\n383<\/td>\n<\/tr>\n
          O\u010dak\u00e1van\u00fd po\u010det<\/em><\/td>\n157,4<\/td>\n225,6<\/td>\n383<\/td>\n<\/tr>\n
          % v r\u00e1mci riadkov<\/em><\/td>\n85,4%<\/td>\n14,6%<\/strong><\/td>\n100%<\/td>\n<\/tr>\n
          % v r\u00e1mci st\u013apcov<\/em><\/td>\n31,9%<\/strong><\/td>\n3,8%<\/strong><\/td>\n15,3%<\/td>\n<\/tr>\n
          % zo v\u0161etk\u00fdch<\/em><\/td>\n13,1%<\/strong><\/td>\n2,2%<\/strong><\/td>\n15,3%<\/td>\n<\/tr>\n
          \u00c1NO<\/strong><\/td>\nPo\u010det<\/em><\/td>\n699<\/td>\n1414<\/td>\n2113<\/td>\n<\/tr>\n
          O\u010dak\u00e1van\u00fd po\u010det<\/em><\/td>\n868,6<\/td>\n1244,4<\/td>\n2113<\/td>\n<\/tr>\n
          % v r\u00e1mci riadkov<\/em><\/td>\n33,1%<\/td>\n66,9%<\/strong><\/td>\n100%<\/td>\n<\/tr>\n
          % v r\u00e1mci st\u013apcov<\/em><\/td>\n68,1%<\/td>\n96,2%<\/td>\n84,7%<\/td>\n<\/tr>\n
          % zo v\u0161etk\u00fdch<\/em><\/td>\n28,0%<\/strong><\/td>\n56,7%<\/strong><\/td>\n84,7%<\/td>\n<\/tr>\n
          Spolu<\/strong><\/td>\nPo\u010det<\/em><\/td>\n1026<\/td>\n1470<\/td>\n2496<\/td>\n<\/tr>\n
          O\u010dak\u00e1van\u00fd po\u010det<\/em><\/td>\n1026<\/td>\n1470<\/td>\n2496<\/td>\n<\/tr>\n
          % v r\u00e1mci riadkov<\/em><\/td>\n41,1%<\/td>\n58,9%<\/td>\n100%<\/td>\n<\/tr>\n
          % v r\u00e1mci st\u013apcov<\/em><\/td>\n100%<\/td>\n100%<\/td>\n100%<\/td>\n<\/tr>\n
          % zo v\u0161etk\u00fdch<\/em><\/td>\n41,1%<\/td>\n58,9%<\/td>\n100,0%<\/td>\n<\/tr>\n
          <\/td>\n<\/td>\nHodnota<\/em><\/td>\nSig.<\/em><\/td>\n<\/td>\n<\/tr>\n
          <\/td>\nCramer’s V<\/strong><\/td>\n0,383<\/td>\n,000<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

          Rovnako ako pri Ch\u00ed-kvadr\u00e1te m\u00f4\u017eeme na zobrazenie pou\u017ei\u0165 zlo\u017een\u00fd st\u013apcov\u00fd graf<\/u>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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          \u00daLOHY<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
          \n\t\t\t\t
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            \n \t
          1. Vytvorte v Exceli zlo\u017een\u00fd st\u013apcov\u00fd graf pre v\u00fdsledky z Tabu\u013eky 9<\/li>\n \t
          2. Rozm\u00fd\u0161\u013eajte, ak\u00e9 kategorick\u00e9 premenn\u00e9 by bolo mo\u017en\u00e9 porovna\u0165 medzi:\n
              \n \t
            • Mu\u017emi a \u017eenami.<\/li>\n \t
            • Seniormi a dospievaj\u00facimi.<\/li>\n \t
            • Dospel\u00fdmi pracuj\u00facimi v zdravotn\u00edctve, priemysle a v \u0161kolstve.<\/li>\n \t
            • \u0160tudentmi vysok\u00fdch \u0161k\u00f4l s r\u00f4znym vz\u0165ahov\u00fdm statusom.<\/li>\n \t
            • Dospievaj\u00facimi s r\u00f4znym vierovyznan\u00edm.<\/li>\n<\/ul>\n<\/li>\n \t
            • K uveden\u00fdm pr\u00edkladom sformulujte jednosmern\u00e9 hypot\u00e9zy.<\/li>\n \t
            • Uva\u017eujte, s ak\u00fdmi kategorick\u00fdmi premenn\u00fdmi by mohli s\u00favisie\u0165 premenn\u00e9:\n
                \n \t
              • Politick\u00e1 orient\u00e1cia (pravicov\u00e1, \u013eavicov\u00e1, liber\u00e1lna…).<\/li>\n \t
              • Vierovyznanie.<\/li>\n \t
              • Typ preferovanej \u0161portovej aktivity (kardio, fitness, joga, pilates…).<\/li>\n \t
              • Vo\u013eno\u010dasov\u00e9 zameranie (kult\u00fara, \u0161port, manu\u00e1lne zru\u010dnosti, vzdel\u00e1vanie, pr\u00edroda a pod.)<\/li>\n \t
              • Preferencia zna\u010dky supermarketu.<\/li>\n \t
              • Odbor \u0161t\u00fadia na V\u0160.<\/li>\n<\/ul>\n<\/li>\n
              • K uveden\u00fdm pr\u00edkladom sformulujte dvojsmern\u00e9 hypot\u00e9zy v zmysle s\u00favislosti, vz\u0165ahu.<\/li> \t\n
              • Sformulujte jednosmern\u00fa hypot\u00e9zu na kompar\u00e1ciu kategorickej premennej medzi\ndvoma \u010di viacer\u00fdmi skupinami s pou\u017eit\u00edm cvi\u010dnej \u010di vlastnej datab\u00e1zy.\n
                  \n \t
                • Zvo\u013ete \u0161tatistick\u00fd test a aplikujte ho.<\/li>\n \t
                • V\u00fdsledky spracujte do tabu\u013eky a interpretujte.<\/li>\n \t
                • V\u00fdsledok zobrazte pr\u00edslu\u0161n\u00fdm grafom.<\/li>\n<\/ul>\n<\/li>\n \t
                • Sformulujte hypot\u00e9zu na vz\u0165ah medzi kategorick\u00fdmi premenn\u00fdmi z cvi\u010dnej \u010di vlastnej datab\u00e1zy.\n
                    \n \t
                  • Zvo\u013ete \u0161tatistick\u00fd test a aplikujte ho.<\/li>\n \t
                  • V\u00fdsledky spracujte do tabu\u013eky a interpretujte.<\/li>\n \t
                  • V\u00fdsledok zobrazte pr\u00edslu\u0161n\u00fdm grafom.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

                    \u0160TATISTIKA PRAKTICKY (NIELEN) V Z\u00c1VERE\u010cN\u00ddCH PR\u00c1CACH 8. TESTOVANIE S\u00daVISLOST\u00cd MEDZI DVOMA KATEGORICK\u00ddMI PREMENN\u00ddMI Kategorick\u00e9 premenn\u00e9 m\u00f4\u017eu by\u0165 nomin\u00e1lne, ale i ordin\u00e1lne, je mo\u017en\u00e9 pod\u013ea nich rozdeli\u0165 s\u00fabor do podskup\u00edn. \u0160pecifick\u00e9 je, \u017ee dok\u00e1\u017eeme v podskupin\u00e1ch po\u010d\u00edta\u0165 po\u010detnosti zast\u00fapenia kateg\u00f3ri\u00ed in\u00e9ho javu. Po\u010detnosti je mo\u017en\u00e9 zobrazi\u0165 v bivaria\u010dnej tabu\u013eke, ktor\u00fa naz\u00fdvame KR\u00cd\u017dOV\u00c1, kontingen\u010dn\u00e1 alebo po anglicky […]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-11438","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/wp-json\/wp\/v2\/pages\/11438","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/wp-json\/wp\/v2\/comments?post=11438"}],"version-history":[{"count":109,"href":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/wp-json\/wp\/v2\/pages\/11438\/revisions"}],"predecessor-version":[{"id":13577,"href":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/wp-json\/wp\/v2\/pages\/11438\/revisions\/13577"}],"wp:attachment":[{"href":"https:\/\/e-ucebnice.ff.ucm.sk\/index.php\/wp-json\/wp\/v2\/media?parent=11438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}