{"id":55803,"date":"2024-12-12T09:00:00","date_gmt":"2024-12-12T12:00:00","guid":{"rendered":"https:\/\/mindthegraph.com\/blog\/?p=55803"},"modified":"2024-12-09T14:05:01","modified_gmt":"2024-12-09T17:05:01","slug":"chi-square-test","status":"publish","type":"post","link":"https:\/\/mindthegraph.com\/blog\/lv\/chi-square-test\/","title":{"rendered":"Chi-kvadr\u0101ta tests: \u0160\u012b statistikas r\u012bka izpratne un pielieto\u0161ana"},"content":{"rendered":"<p>Chi-kvadr\u0101ts tests ir sp\u0113c\u012bgs instruments statistik\u0101, jo \u012bpa\u0161i da\u017e\u0101du veidu un discipl\u012bnu kategorisku datu anal\u012bzei. Da\u017e\u0101s datu kop\u0101s datus reprezent\u0113 nep\u0101rtraukti skait\u013ci, bet cit\u0101s kategoriskie dati reprezent\u0113 datus, kas sagrup\u0113ti p\u0113c dzimuma, v\u0113lm\u0113m vai izgl\u012bt\u012bbas l\u012bme\u0146a. Analiz\u0113jot kategoriskus datus, chi-kvadr\u0101ta tests ir pla\u0161i izmantots statistikas r\u012bks, lai izp\u0113t\u012btu sakar\u012bbas un g\u016btu noz\u012bm\u012bgas atzi\u0146as. \u0160aj\u0101 rakst\u0101 apl\u016bkots, k\u0101 darbojas chi-kvadr\u0101ta tests, k\u0101di ir t\u0101 lietojumi un k\u0101p\u0113c tas ir b\u016btisks p\u0113tniekiem un datu anal\u012bti\u0137iem.<\/p>\n\n\n\n<p>\u0160aj\u0101 blog\u0101 m\u0113s apl\u016bkosim, k\u0101 darbojas Chi-kvadr\u0101ts tests, k\u0101 to veic un k\u0101 to var interpret\u0113t. J\u016bs varat izmantot Chi-kvadr\u0101ta testu, lai lab\u0101k izprastu datu anal\u012bzi neatkar\u012bgi no t\u0101, vai esat students, p\u0113tnieks vai interes\u0113jaties par datu anal\u012bzi kopum\u0101.<\/p>\n\n\n\n<h2>Izpratne par to, cik svar\u012bgs ir Chi-kvadr\u0101ts tests<\/h2>\n\n\n\n<p>Chi-kvadr\u0101ts tests ir fundament\u0101la statistikas metode, ko izmanto, lai p\u0101rbaud\u012btu attiec\u012bbas starp kategoriskiem main\u012bgajiem un p\u0101rbaud\u012btu hipot\u0113zes da\u017e\u0101d\u0101s jom\u0101s. Izpratne par to, k\u0101 piem\u0113rot chi-kvadr\u0101ts testu, var pal\u012bdz\u0113t p\u0113tniekiem noteikt noz\u012bm\u012bgus mode\u013cus un asoci\u0101cijas savos datos. Saska\u0146\u0101 ar nulles hipot\u0113zi tas sal\u012bdzina nov\u0113rotos datus ar to, ko m\u0113s sagaid\u012btu, ja starp main\u012bgajiem neb\u016btu nek\u0101das saist\u012bbas. T\u0101d\u0101s jom\u0101s k\u0101 biolo\u0123ija, m\u0101rketings un soci\u0101l\u0101s zin\u0101tnes \u0161is tests ir \u012bpa\u0161i noder\u012bgs, lai p\u0101rbaud\u012btu hipot\u0113zes par popul\u0101cijas sadal\u012bjumu.<\/p>\n\n\n\n<p>P\u0113c b\u016bt\u012bbas Chi-kvadr\u0101ta tests m\u0113ra neatbilst\u012bbu starp nov\u0113rotaj\u0101m un sagaid\u0101maj\u0101m frekvenc\u0113m kategoriskos datos. Izmantojot to, m\u0113s varam atbild\u0113t uz \u0161\u0101diem jaut\u0101jumiem: \"Vai nov\u0113rotie datu mode\u013ci at\u0161\u0137iras no sagaid\u0101m\u0101 nejau\u0161\u012bbas gad\u012bjum\u0101?\" vai \"Vai divi kategoriskie main\u012bgie ir viens no otra neatkar\u012bgi?\".<\/p>\n\n\n\n<h3>Chi-kvadr\u0101ts testu veidi<\/h3>\n\n\n\n<p>Chi-kvadr\u0101ta tests ir divos galvenajos veidos - atbilst\u012bbas atbilst\u012bbas tests un neatkar\u012bbas tests - katrs no tiem ir piel\u0101gots konkr\u0113tiem statistiskiem p\u0113t\u012bjumiem.<\/p>\n\n\n\n<p><strong>1. Chi-kvadr\u0101ta atbilst\u012bbas tests<\/strong><\/p>\n\n\n\n<p>Test\u0113 atsevi\u0161\u0137u kategorisku main\u012bgo, lai noteiktu, vai tas atbilst noteiktam sadal\u012bjumam. Lai p\u0101rbaud\u012btu, vai nov\u0113rotie dati atbilst sagaid\u0101majam sadal\u012bjumam, bie\u017ei izmanto modeli vai v\u0113sturiskos datus.<\/p>\n\n\n\n<figure class=\"wp-block-image alignwide size-full\"><a href=\"https:\/\/mindthegraph.com\/science-figures\/?utm_source=blog&amp;utm_medium=cta-final&amp;utm_campaign=conversion\"><img decoding=\"async\" loading=\"lazy\" width=\"651\" height=\"174\" src=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/06\/mind-the-graph-1.png\" alt=\"Mind the Graph logotips - platforma zin\u0101tnisko ilustr\u0101ciju un vizu\u0101lo materi\u0101lu izveidei p\u0113tniekiem un pasniedz\u0113jiem.\" class=\"wp-image-54660\" srcset=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/06\/mind-the-graph-1.png 651w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/06\/mind-the-graph-1-300x80.png 300w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/06\/mind-the-graph-1-18x5.png 18w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/06\/mind-the-graph-1-100x27.png 100w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/a><figcaption class=\"wp-element-caption\">Mind the Graph - <a href=\"https:\/\/mindthegraph.com\/science-figures\/?utm_source=blog&amp;utm_medium=cta-final&amp;utm_campaign=conversion\">Izveidojiet saisto\u0161as zin\u0101tnisk\u0101s ilustr\u0101cijas.<\/a><\/figcaption><\/figure>\n\n\n\n<p>Padom\u0101jiet par kauli\u0146a ripin\u0101\u0161anu 60 reizes. T\u0101 k\u0101 kauli\u0146\u0161 ir taisn\u012bgs, var sagaid\u012bt, ka katra puse par\u0101d\u012bsies desmit reizes, bet faktiskie rezult\u0101ti nedaudz at\u0161\u0137iras. Lai noteiktu, vai \u0161\u012b novirze ir noz\u012bm\u012bga vai tikai nejau\u0161\u012bbas rezult\u0101ts, varat veikt atbilst\u012bbas labuma testu.<\/p>\n\n\n\n<p><strong>Iesaist\u012btie so\u013ci:<\/strong><\/p>\n\n\n\n<ol>\n<li>Pamatojoties uz teor\u0113tisko sadal\u012bjumu, nosakiet sagaid\u0101m\u0101s frekvences.<\/li>\n\n\n\n<li>P\u0113c tam sal\u012bdziniet t\u0101s ar nov\u0113rotaj\u0101m frekvenc\u0113m.<\/li>\n\n\n\n<li>Apr\u0113\u0137iniet Chi-kvadr\u0101ta statistiku, lai kvantitat\u012bvi noteiktu novirzi.<\/li>\n<\/ol>\n\n\n\n<p>P\u0113tnieki bie\u017ei izmanto \u0161o testu kvalit\u0101tes kontrol\u0113, \u0123en\u0113tik\u0101 un cit\u0101s jom\u0101s, kur vi\u0146i v\u0113las sal\u012bdzin\u0101t nov\u0113rotos datus ar teor\u0113tisko sadal\u012bjumu.<\/p>\n\n\n\n<p><strong>2. Neatkar\u012bbas p\u0101rbaude p\u0113c Chi-kvadr\u0101ta<\/strong><\/p>\n\n\n\n<p>\u0160aj\u0101 test\u0101 tiek nov\u0113rt\u0113ta divu kategorisku main\u012bgo neatkar\u012bba. Ar \u0161o testu p\u0101rbauda, vai viena main\u012bg\u0101 lieluma sadal\u012bjums main\u0101s da\u017e\u0101dos otr\u0101 main\u012bg\u0101 lieluma l\u012bme\u0146os. Neizb\u0113gam\u012bbas tabul\u0101s, kur\u0101s par\u0101d\u012bti main\u012bgo lielumu bie\u017eumu sadal\u012bjumi, neatkar\u012bbu parasti p\u0101rbauda, izmantojot Chi-kvadr\u0101ta testu.<\/p>\n\n\n\n<p>Pie\u0146emsim, ka j\u016bs veicat aptauju, jaut\u0101jot dal\u012bbniekiem par vi\u0146u dzimumu un v\u0113lamo filmu veidu (darb\u012bba, dr\u0101ma, kom\u0113dija). Lai noteiktu, vai dzimums ietekm\u0113 filmu izv\u0113li vai ar\u012b tie ir neatkar\u012bgi, var izmantot neatkar\u012bbas Chi-kvadr\u0101ta testu.<\/p>\n\n\n\n<p><strong>Iesaist\u012btie so\u013ci:<\/strong><\/p>\n\n\n\n<ol>\n<li>Izveidojiet divu main\u012bgo kontingences tabulu.<\/li>\n\n\n\n<li>Pamatojoties uz pie\u0146\u0113mumu, ka main\u012bgie ir neatkar\u012bgi, apr\u0113\u0137iniet sagaid\u0101m\u0101s frekvences.<\/li>\n\n\n\n<li>Izmantojot Chi-kvadr\u0101ta statistiku, sal\u012bdziniet nov\u0113rot\u0101s frekvences ar sagaid\u0101maj\u0101m frekvenc\u0113m.<\/li>\n<\/ol>\n\n\n\n<p>Tirgus izp\u0113t\u0113, vesel\u012bbas apr\u016bp\u0113 un izgl\u012bt\u012bb\u0101 \u0161o testu pla\u0161i izmanto, lai p\u0113t\u012btu saikni starp demogr\u0101fiskiem main\u012bgajiem lielumiem un rezult\u0101tiem, piem\u0113ram, saikni starp izgl\u012bt\u012bbas l\u012bmeni un v\u0113lm\u0113m balsot.<\/p>\n\n\n\n<h2>Chi-kvadr\u0101ta testa pielietojums re\u0101l\u0101s dz\u012bves scen\u0101rijos<\/h2>\n\n\n\n<p>Chi-kvadr\u0101ts tests ir \u012bpa\u0161i noder\u012bgs, ja str\u0101d\u0101jat ar kategoriskiem datiem, piem\u0113ram, dzimuma, preferen\u010du vai politisk\u0101s pieder\u012bbas datiem, lai p\u0101rbaud\u012btu sakar\u012bbas un mode\u013cus. Neatkar\u012bbas un atbilst\u012bbas atbilst\u012bbas testus izmanto, lai noteiktu, vai starp diviem main\u012bgajiem past\u0101v noz\u012bm\u012bga saist\u012bba (neatkar\u012bbas tests).<\/p>\n\n\n\n<p>P\u0113tnieki var p\u0101rbaud\u012bt hipot\u0113zes un noteikt likumsakar\u012bbas, izmantojot Chi-kvadr\u0101ta testu kategoriskiem datiem. Ir vair\u0101ki iemesli, k\u0101p\u0113c tas ir pla\u0161i izplat\u012bts:<\/p>\n\n\n\n<ul>\n<li>At\u0161\u0137ir\u012bb\u0101 no parametriskiem testiem tam nav nepiecie\u0161ami pie\u0146\u0113mumi par datu sadal\u012bjumu.<\/li>\n\n\n\n<li>To var izmantot da\u017e\u0101d\u0101s discipl\u012bn\u0101s, t\u0101p\u0113c t\u0101 ir daudzpus\u012bga.<\/li>\n\n\n\n<li>Pamatojoties uz nov\u0113rotajiem mode\u013ciem, tas pal\u012bdz pie\u0146emt pamatotus l\u0113mumus.<\/li>\n<\/ul>\n\n\n\n<h2>Chi-kvadr\u0101ta testa pie\u0146\u0113mumi<\/h2>\n\n\n\n<p>Lai nodro\u0161in\u0101tu Chi-kvadr\u0101ts testa rezult\u0101tu der\u012bgumu, ir j\u0101iev\u0113ro da\u017ei pie\u0146\u0113mumi. \u0160ie pie\u0146\u0113mumi pal\u012bdz saglab\u0101t testa precizit\u0101ti un atbilst\u012bbu, jo \u012bpa\u0161i str\u0101d\u0101jot ar kategoriskiem datiem. Ir j\u0101\u0146em v\u0113r\u0101 tr\u012bs galvenie pie\u0146\u0113mumi: nejau\u0161\u012bbas izlase, kategoriskie main\u012bgie un sagaid\u0101mie bie\u017eumu skait\u013ci.<\/p>\n\n\n\n<p><strong>1. Izlases veido\u0161ana p\u0113c nejau\u0161\u012bbas principa<\/strong><\/p>\n\n\n\n<p>Pirmais un pats svar\u012bg\u0101kais pie\u0146\u0113mums ir, ka dati j\u0101v\u0101c, izmantojot nejau\u0161\u0101s izlases metodi. Rezult\u0101t\u0101 izlas\u0113 vienl\u012bdz liel\u0101 m\u0113r\u0101 tiek iek\u013cauts katrs indiv\u012bds vai elements. Nejau\u0161\u012bbas izlase samazina novirzi, t\u0101p\u0113c rezult\u0101tus var visp\u0101rin\u0101t uz liel\u0101ku popul\u0101ciju.<\/p>\n\n\n\n<p>Ja izlase nav nejau\u0161a, rezult\u0101ti var b\u016bt izkrop\u013coti, kas var novest pie nepareiziem secin\u0101jumiem. Aptaujas rezult\u0101ti, kas izplat\u012bti tikai noteiktai iedz\u012bvot\u0101ju grupai, var neatspogu\u013cot visas organiz\u0101cijas viedokli, t\u0101d\u0113j\u0101di p\u0101rk\u0101pjot nejau\u0161as izlases principa pie\u0146\u0113mumu.<\/p>\n\n\n\n<p><strong>2. Kategoriskie main\u012bgie<\/strong><\/p>\n\n\n\n<p>\u0136ipkvadr\u0101ta testa m\u0113r\u0137is ir analiz\u0113t kategoriskus main\u012bgos lielumus - datus, kurus var iedal\u012bt atsevi\u0161\u0137\u0101s kategorij\u0101s. Main\u012bgajiem lielumiem nav j\u0101b\u016bt skaitliski izteiktiem (lai gan \u0113rt\u012bbas labad tos var kod\u0113t skaitliski), un tie j\u0101sadala skaidri defin\u0113t\u0101s grup\u0101s.<\/p>\n\n\n\n<p>Kategori\u0101lo main\u012bgo piem\u0113ri ir \u0161\u0101di:<\/p>\n\n\n\n<ul>\n<li>Dzimums (v\u012brietis, sieviete, ne-bin\u0101rs)<\/li>\n\n\n\n<li>\u0122imenes st\u0101voklis (neprec\u0113jies, prec\u0113jies, \u0161\u0137\u012bries)<\/li>\n\n\n\n<li>Acu kr\u0101sa (zila, br\u016bna, za\u013ca)<\/li>\n<\/ul>\n\n\n\n<p>Chi-kvadr\u0101ts testu nevar tie\u0161i izmantot ar nep\u0101rtrauktiem datiem, piem\u0113ram, augumu vai svaru, ja vien tie nav p\u0101rv\u0113rsti kategorij\u0101s. Lai Chi-kvadr\u0101ta tests b\u016btu j\u0113gpilns, datiem j\u0101b\u016bt kategoriskiem, piem\u0113ram, \"zems\", \"vid\u0113js\" vai \"augsts\".<\/p>\n\n\n\n<p><strong>3. Paredzamais bie\u017euma skaits<\/strong><\/p>\n\n\n\n<p>V\u0113l viens kritisks Chi-kvadr\u0101ta testa pie\u0146\u0113mums ir paredzamais kategoriju vai \u0161\u016bnu bie\u017eums neparedz\u0113to gad\u012bjumu tabul\u0101. Pie\u0146emot, ka nulles hipot\u0113ze ir patiesa (t. i., ka main\u012bgie nav saist\u012bti), sagaid\u0101mais bie\u017eums ir teor\u0113tiskais bie\u017eums, kas past\u0101v katr\u0101 kategorij\u0101.&nbsp;<\/p>\n\n\n\n<p>Pamatnoteikums ir \u0161\u0101ds: Paredzamajam bie\u017eumam katr\u0101 \u0161\u016bn\u0101 j\u0101b\u016bt vismaz 5. Zems sagaid\u0101mais bie\u017eums var novest pie neuzticamiem rezult\u0101tiem, ja testa statistika ir izkrop\u013cota. Fi\u0161era eksaktais tests j\u0101apsver, ja paredzam\u0101 bie\u017euma v\u0113rt\u012bba ir zem\u0101ka par 5, jo \u012bpa\u0161i maz\u0101s izlas\u0113s.<\/p>\n\n\n\n<h2>Soli pa solim, k\u0101 veikt Chi-kvadr\u0101ts testu<\/h2>\n\n\n\n<ol>\n<li>Hipot\u0113\u017eu (nulles un alternat\u012bv\u0101s) noteik\u0161ana<\/li>\n<\/ol>\n\n\n\n<ul>\n<li>Nulles hipot\u0113ze (H0): Starp ab\u0101m sal\u012bdzin\u0101maj\u0101m liet\u0101m nav nek\u0101das saist\u012bbas. Jebkuras nov\u0113rot\u0101s at\u0161\u0137ir\u012bbas ir nejau\u0161as.<\/li>\n\n\n\n<li>Alternat\u012bv\u0101 hipot\u0113ze (H\u2081): Tas noz\u012bm\u0113, ka starp ab\u0101m liet\u0101m past\u0101v re\u0101ls sakars. At\u0161\u0137ir\u012bbas nav nejau\u0161as, bet gan noz\u012bm\u012bgas.<\/li>\n<\/ul>\n\n\n\n<h3>2. Neparedz\u0113to gad\u012bjumu tabulas izveide<\/h3>\n\n\n\n<p>Nepiecie\u0161am\u012bbas tabulas par\u0101da, cik bie\u017ei noteiktas lietas notiek kop\u0101. Piem\u0113ram, tabul\u0101 ir par\u0101d\u012btas da\u017e\u0101das grupas (piem\u0113ram, v\u012brie\u0161i un sievietes) un da\u017e\u0101das izv\u0113les (piem\u0113ram, k\u0101dam produktam vi\u0146i dod priek\u0161roku). Apl\u016bkojot tabulu, j\u016bs redz\u0113siet, cik daudz cilv\u0113ku ietilpst katr\u0101 no grup\u0101m un izv\u0113l\u0113m.<\/p>\n\n\n\n<h3>3. Paredzamo bie\u017eumu apr\u0113\u0137in\u0101\u0161ana<\/h3>\n\n\n\n<p>Ja starp sal\u012bdzin\u0101maj\u0101m liet\u0101m neb\u016btu nek\u0101da re\u0101la sakara, sagaid\u0101m\u0101s frekvences b\u016btu t\u0101das, k\u0101das j\u016bs sagaid\u012btu. To apr\u0113\u0137in\u0101\u0161anai var izmantot vienk\u0101r\u0161u formulu:<\/p>\n\n\n\n<p>Paredzamais bie\u017eums = (rindu kopsumma \u00d7 kolonnu kopsumma) \/ kopsumma kop\u0101<\/p>\n\n\n\n<p>Tas tikai par\u0101da, k\u0101diem b\u016btu j\u0101b\u016bt skait\u013ciem, ja viss notiktu nejau\u0161i.<\/p>\n\n\n\n<h3>4. Chi-kvadr\u0101ta statistikas apr\u0113\u0137in\u0101\u0161ana<\/h3>\n\n\n\n<p>Kvadr\u0101tsvarianta tests \u013cauj noteikt, cik \u013coti nov\u0113rotie dati at\u0161\u0137iras no sagaid\u0101majiem rezult\u0101tiem, pal\u012bdzot noteikt, vai past\u0101v sakar\u012bbas. Tas izskat\u0101s sare\u017e\u0123\u012bti, bet tas sal\u012bdzina re\u0101los skait\u013cus ar sagaid\u0101majiem:<\/p>\n\n\n\n<p>\ud835\udf122=\u2211(Nov\u0113rots- Paredzams)2\/ Paredzams<\/p>\n\n\n\n<p>To veiciet katram tabulas laukam un p\u0113c tam tos visus saskaitiet kop\u0101, lai ieg\u016btu vienu skaitli, kas ir j\u016bsu Chi-kvadr\u0101ta statistika.<\/p>\n\n\n\n<h3>5. Br\u012bv\u012bbas pak\u0101pju noteik\u0161ana<\/h3>\n\n\n\n<p>Lai interpret\u0113tu rezult\u0101tus, ir j\u0101zina br\u012bv\u012bbas pak\u0101pes. Pamatojoties uz tabulas lielumu, j\u016bs t\u0101s apr\u0113\u0137in\u0101t. \u0160eit ir formula:<\/p>\n\n\n\n<p>Br\u012bv\u012bbas gr\u0101di = ( rindu skaits -1)\u00d7(kolonnu skaits-1)<\/p>\n\n\n\n<p>Tas ir tikai izdom\u0101ts veids, k\u0101 \u0146emt v\u0113r\u0101 datu lielumu.<\/p>\n\n\n\n<h3>6. Chi-kvadr\u0101ta sadal\u012bjuma izmanto\u0161ana, lai atrastu p-v\u0113rt\u012bbu<\/h3>\n\n\n\n<p>P-v\u0113rt\u012bbu var apr\u0113\u0137in\u0101t, izmantojot Chi-kvadr\u0101ta statistiku un br\u012bv\u012bbas pak\u0101pes. Apl\u016bkojot p-v\u0113rt\u012bbu, var noteikt, vai nov\u0113rot\u0101s at\u0161\u0137ir\u012bbas, visticam\u0101k, radu\u0161\u0101s nejau\u0161\u012bbas d\u0113\u013c, vai ar\u012b t\u0101s ir noz\u012bm\u012bgas.<\/p>\n\n\n\n<p>P-v\u0113rt\u012bbas interpret\u0101cija:<\/p>\n\n\n\n<ul>\n<li>Parasti maza p v\u0113rt\u012bba nor\u0101da, ka konstat\u0113t\u0101s at\u0161\u0137ir\u012bbas nav nejau\u0161as, t\u0101p\u0113c nulles hipot\u0113zi noraidiet. J\u016bs varat redz\u0113t re\u0101lu saikni starp to, ko j\u016bs p\u0113t\u0101t, un to, ko j\u016bs dar\u0101t.<\/li>\n\n\n\n<li>Ja p v\u0113rt\u012bba ir liel\u0101ka par 0,05, tas nor\u0101da, ka at\u0161\u0137ir\u012bbas, visticam\u0101k, ir nejau\u0161as, t\u0101p\u0113c jums b\u016btu j\u0101saglab\u0101 nulles hipot\u0113ze. T\u0101p\u0113c starp ab\u0101m hipot\u0113z\u0113m nav re\u0101las saiknes.<\/li>\n<\/ul>\n\n\n\n<p>Ja divas lietas notiek nejau\u0161i vai ir saist\u012btas, varat izmantot \u0161o vienk\u0101r\u0161oto procesu, lai noteiktu, vai t\u0101s ir saist\u012btas!<\/p>\n\n\n\n<h2>Chi-kvadr\u0101ta testa rezult\u0101tu interpret\u0113\u0161ana<\/h2>\n\n\n\n<p>Chi-kvadr\u0101ta statistika par\u0101da, cik \u013coti faktiskie dati (tas, ko j\u016bs nov\u0113roj\u0101t) at\u0161\u0137iras no t\u0101, ko m\u0113s sagaid\u012btu, ja starp kategorij\u0101m neb\u016btu nek\u0101das saist\u012bbas. B\u016bt\u012bb\u0101 t\u0101 m\u0113ra, cik \u013coti m\u016bsu nov\u0113rotie rezult\u0101ti at\u0161\u0137iras no t\u0101, ko m\u0113s prognoz\u0113j\u0101m p\u0113c nejau\u0161\u012bbas.<\/p>\n\n\n\n<ul>\n<li>Liela Chi-kvadr\u0101ta v\u0113rt\u012bba: Starp\u012bba starp j\u016bsu gaid\u0101m un realit\u0101ti ir liela. Tas var\u0113tu liecin\u0101t, ka datos notiek kaut kas interesants.<\/li>\n\n\n\n<li>Maza Chi-kvadr\u0101ta v\u0113rt\u012bba: Tas noz\u012bm\u0113, ka nov\u0113rotie dati ir diezgan tuvi gaid\u012btajam, un, iesp\u0113jams, nekas neparasts nenotiek.<\/li>\n<\/ul>\n\n\n\n<p>Lai gan t\u0101 ir taisn\u012bba, Chi-kvadr\u0101ta v\u0113rt\u012bba vien nesniedz visu nepiecie\u0161amo inform\u0101ciju. Izmantojot p-v\u0113rt\u012bbu, j\u016bs varat noteikt, vai at\u0161\u0137ir\u012bba ir b\u016btiska vai tikai nejau\u0161\u012bba.<\/p>\n\n\n\n<h3>Ko noz\u012bm\u0113 p v\u0113rt\u012bba<\/h3>\n\n\n\n<p>P-v\u0113rt\u012bbas pal\u012bdz noteikt, vai at\u0161\u0137ir\u012bbas starp j\u016bsu datiem ir noz\u012bm\u012bgas. Citiem v\u0101rdiem sakot, t\u0101 jums nor\u0101da, k\u0101da ir varb\u016bt\u012bba, ka nov\u0113rot\u0101s at\u0161\u0137ir\u012bbas ir nejau\u0161\u012bbas rezult\u0101ts.<\/p>\n\n\n\n<ul>\n<li>Zema p v\u0113rt\u012bba (parasti 0,05 vai maz\u0101ka): Tas noz\u012bm\u0113, ka at\u0161\u0137ir\u012bba, visticam\u0101k, nav nejau\u0161a. Tas noz\u012bm\u0113, ka at\u0161\u0137ir\u012bba, visticam\u0101k, ir re\u0101la un notiek kaut kas interesants. Rezult\u0101t\u0101 j\u016bs noraid\u012btu pie\u0146\u0113mumu, ka nav nek\u0101das saist\u012bbas (\"nulles hipot\u0113ze\").<\/li>\n<\/ul>\n\n\n\n<ul>\n<li>Augsta p v\u0113rt\u012bba (liel\u0101ka par 0,05): Tas liecina, ka at\u0161\u0137ir\u012bba var\u0113tu b\u016bt nejau\u0161\u012bba. Rezult\u0101t\u0101 nav p\u0101rliecino\u0161as nor\u0101des, ka j\u016bsu datos notiek kaut kas neparasts. Ja starp kategorij\u0101m nav nek\u0101das saist\u012bbas, j\u016bs nenoraid\u012btu nulles hipot\u0113zi.<\/li>\n<\/ul>\n\n\n\n<h3>K\u0101 izdar\u012bt secin\u0101jumus<\/h3>\n\n\n\n<p>Kad ir zin\u0101ma gan Chi-kvadr\u0101ta statistika, gan p-v\u0113rt\u012bba, var izdar\u012bt secin\u0101jumus:<\/p>\n\n\n\n<p>Apl\u016bkojiet p-v\u0113rt\u012bbu:<\/p>\n\n\n\n<ul>\n<li>J\u016bs noraid\u0101t domu, ka starp div\u0101m kategorij\u0101m nav saist\u012bbas, ja p-v\u0113rt\u012bba ir 0,05 vai maz\u0101ka. Piem\u0113ram, ja j\u016bs p\u0101rbaud\u0101t, vai dzimums ietekm\u0113 produktu izv\u0113li, un p-v\u0113rt\u012bba ir zema (0,05 vai maz\u0101ka), j\u016bs varat teikt: \"\u0160\u0137iet, ka dzimums ietekm\u0113 cilv\u0113ku izv\u0113li.\".<\/li>\n<\/ul>\n\n\n\n<ul>\n<li>Ja p-v\u0113rt\u012bba ir liel\u0101ka par 0,05, dati neuzr\u0101da b\u016btisku at\u0161\u0137ir\u012bbu, t\u0101p\u0113c j\u016bs secin\u0101t, ka kategorijas, visticam\u0101k, nav saist\u012btas. Izmantojot lielu p-v\u0113rt\u012bbu (liel\u0101ku par 0,05), j\u016bs var\u0113tu teikt: \"Nav p\u0101rliecino\u0161u pier\u0101d\u012bjumu tam, ka dzimums ietekm\u0113 produktu izv\u0113li.<\/li>\n<\/ul>\n\n\n\n<h3>Atcerieties re\u0101l\u0101s pasaules noz\u012bmi<\/h3>\n\n\n\n<p>Jums j\u0101apsver, vai statistiski noz\u012bm\u012bgajai at\u0161\u0137ir\u012bbai ir noz\u012bme re\u0101laj\u0101 dz\u012bv\u0113, pat ja t\u0101 liecina par statistiski noz\u012bm\u012bgu at\u0161\u0137ir\u012bbu. Var uzskat\u012bt, ka pat nelielas at\u0161\u0137ir\u012bbas ir svar\u012bgas, ja datu kopa ir \u013coti liela, ta\u010du re\u0101laj\u0101 dz\u012bv\u0113 t\u0101m var neb\u016bt b\u016bt b\u016btiska ietekme. T\u0101 viet\u0101, lai skat\u012btos tikai uz skait\u013ciem, vienm\u0113r apsveriet, ko rezult\u0101ts noz\u012bm\u0113 praks\u0113.<\/p>\n\n\n\n<p>Izmantojot Chi-kvadr\u0101ta statistiku, t\u0101 par\u0101da, vai starp\u012bba starp gaid\u012bto un ieg\u016bto rezult\u0101tu ir re\u0101la vai tikai nejau\u0161\u012bba. J\u016bs varat noteikt, vai j\u016bsu datiem ir noz\u012bm\u012bga saist\u012bba, kad tos apvienojat.<\/p>\n\n\n\n<h2>Chi-kvadr\u0101ts testa rezult\u0101tu vizualiz\u0113\u0161ana ar Mind the Graph<\/h2>\n\n\n\n<p>Chi-kvadr\u0101ta tests pal\u012bdz atkl\u0101t datu likumsakar\u012bbas, ta\u010du, lai \u0161\u012bs atzi\u0146as efekt\u012bvi atspogu\u013cotu, ir nepiecie\u0161ami saisto\u0161i vizu\u0101li materi\u0101li. <a href=\"https:\/\/mindthegraph.com\/science-figures\/?utm_source=blog&amp;utm_medium=cta-final&amp;utm_campaign=conversion\">Mind the Graph<\/a> nodro\u0161ina intuit\u012bvus r\u012bkus, lai rad\u012btu satrieco\u0161us vizu\u0101lus chi-kvadr\u0101ta testu rezult\u0101tus, padarot sare\u017e\u0123\u012btus datus viegl\u0101k saprotamus. Neatkar\u012bgi no t\u0101, vai tas paredz\u0113ts akad\u0113miskiem zi\u0146ojumiem, prezent\u0101cij\u0101m vai publik\u0101cij\u0101m, Mind the Graph pal\u012bdz jums skaidri un p\u0101rliecino\u0161i atspogu\u013cot statistikas atzi\u0146as. Izp\u0113tiet m\u016bsu platformu jau \u0161odien, lai p\u0101rveidotu savus datus p\u0101rliecino\u0161os vizu\u0101los st\u0101stos.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/09\/mtg-80-plus-fields.gif\" alt=\"&quot;Anim\u0113ts GIF, kas par\u0101da vair\u0101k nek\u0101 80 zin\u0101tnisko jomu, kuras pieejamas Mind the Graph, tostarp biolo\u0123iju, \u0137\u012bmiju, fiziku un medic\u012bnu, un ilustr\u0113 platformas daudzpus\u012bbu p\u0113tniekiem.&quot;\" class=\"wp-image-29586\" width=\"840\" height=\"555\"\/><figcaption class=\"wp-element-caption\">Anim\u0113ts GIF, kas demonstr\u0113 pla\u0161u zin\u0101tnes jomu kl\u0101stu, ko aptver <a href=\"https:\/\/mindthegraph.com\/science-figures\/?utm_source=blog&amp;utm_medium=cta-final&amp;utm_campaign=conversion\">Mind the Graph<\/a>.<\/figcaption><\/figure>\n\n\n\n<div class=\"is-content-justification-center is-layout-flex wp-container-1 wp-block-buttons\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/mindthegraph.com\/science-figures\/?utm_source=blog&amp;utm_medium=cta-final&amp;utm_campaign=conversion\" style=\"background-color:#7833ff\"><strong>Izveidojiet skaistus grafikus ar Mind the Graph<\/strong><\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>Uzziniet, k\u0101 izmantot chi-kvadr\u0101ts testu kategorisku datu anal\u012bzei, hipot\u0113\u017eu p\u0101rbaudei un attiec\u012bbu izp\u0113tei starp main\u012bgajiem.<\/p>","protected":false},"author":27,"featured_media":55804,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[961,977],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.9 - 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She is currently pursuing a master's degree in Bioentrepreneurship from Karolinska Institute. She is interested in health and diseases, global health, socioeconomic development, and women's health. As a science enthusiast, she is keen in learning more about the scientific world and wants to play a part in making a difference.","sameAs":["http:\/\/linkedin.com\/in\/aayushizaveri"],"url":"https:\/\/mindthegraph.com\/blog\/lv\/author\/aayuyshi\/"}]}},"_links":{"self":[{"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/posts\/55803"}],"collection":[{"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/users\/27"}],"replies":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/comments?post=55803"}],"version-history":[{"count":1,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/posts\/55803\/revisions"}],"predecessor-version":[{"id":55805,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/posts\/55803\/revisions\/55805"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/media\/55804"}],"wp:attachment":[{"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/media?parent=55803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/categories?post=55803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/tags?post=55803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}