{"id":29176,"date":"2023-08-28T08:29:01","date_gmt":"2023-08-28T11:29:01","guid":{"rendered":"https:\/\/mindthegraph.com\/blog\/hypothesis-testing-copy\/"},"modified":"2024-12-05T15:51:53","modified_gmt":"2024-12-05T18:51:53","slug":"one-way-anova","status":"publish","type":"post","link":"https:\/\/mindthegraph.com\/blog\/lt\/vienakrypte-anova\/","title":{"rendered":"Vienpus\u0117 ANOVA: supratimas, atlikimas ir pristatymas"},"content":{"rendered":"<p>Skirtum\u0173 analiz\u0117 (ANOVA) - tai statistinis metodas, naudojamas dviej\u0173 ar daugiau grupi\u0173 vidurkiams palyginti. Vienpus\u0117 ANOVA yra da\u017eniausiai naudojamas metodas, skirtas vieno i\u0161tisinio kintamojo dispersijai analizuoti dviejose ar daugiau kategorini\u0173 grupi\u0173. \u0160is metodas pla\u010diai taikomas \u012fvairiose srityse, \u012fskaitant versl\u0105, socialinius ir gamtos mokslus, tikrinant hipotezes ir darant i\u0161vadas apie grupi\u0173 skirtumus. Supratimas apie vienpus\u0117s ANOVA pagrindus gali pad\u0117ti tyr\u0117jams ir duomen\u0173 analitikams priimti pagr\u012fstus sprendimus, paremtus statistiniais \u012frodymais. \u0160iame straipsnyje i\u0161samiai paai\u0161kinsime vienakrypt\u0117s ANOVA metod\u0105, aptarsime jo taikym\u0105, prielaidas ir kt.<\/p>\n\n\n\n<h2 id=\"h-what-is-one-way-anova\"><strong>Kas yra vienpus\u0117 ANOVA?<\/strong><\/h2>\n\n\n\n<p>Vienpus\u0117 ANOVA (variacijos analiz\u0117) - tai statistinis metodas, naudojamas reik\u0161mingiems skirtumams tarp duomen\u0173 grupi\u0173 vidurki\u0173 nustatyti. Jis da\u017eniausiai naudojamas eksperimentiniuose tyrimuose, kai norima palyginti skirting\u0173 gydymo b\u016bd\u0173 ar intervencij\u0173 poveik\u012f tam tikram rezultatui.<\/p>\n\n\n\n<p>Pagrindin\u0117 ANOVA id\u0117ja - padalyti bendr\u0105 duomen\u0173 kintamum\u0105 \u012f dvi dalis: kintamum\u0105 tarp grupi\u0173 (d\u0117l gydymo) ir kintamum\u0105 kiekvienoje grup\u0117je (d\u0117l atsitiktinio kintamumo ir individuali\u0173 skirtum\u0173). Atliekant ANOVA test\u0105 apskai\u010diuojama F-statistika, kuri yra kintamumo tarp grupi\u0173 ir kintamumo grup\u0117s viduje santykis.<\/p>\n\n\n\n<p>Jei F-statistika yra pakankamai didel\u0117 ir susijusi p reik\u0161m\u0117 yra ma\u017eesn\u0117 u\u017e i\u0161 anksto nustatyt\u0105 reik\u0161mingumo lygmen\u012f (pvz., 0,05), tai rei\u0161kia, kad yra tvirt\u0173 \u012frodym\u0173, jog bent vienos grup\u0117s vidurkis reik\u0161mingai skiriasi nuo kit\u0173. Tokiu atveju galima naudoti tolesnius post hoc testus, siekiant nustatyti, kurios konkre\u010dios grup\u0117s skiriasi viena nuo kitos. Daugiau apie post hoc testus galite paskaityti m\u016bs\u0173 turinyje \"<a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\" target=\"_blank\" rel=\"noreferrer noopener\">Post Hoc analiz\u0117: Procesas ir test\u0173 tipai<\/a>&#8220;.<\/p>\n\n\n\n<p>Vienakrypt\u0117 ANOVA daro prielaid\u0105, kad duomenys pasiskirst\u0119 normaliai ir kad grupi\u0173 dispersijos yra lygios. Jei \u0161i\u0173 prielaid\u0173 nesilaikoma, galima naudoti alternatyvius neparametrinius testus.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/researcher.life\/all-access-pricing?utm_source=mtg&amp;utm_campaign=all-access-promotion&amp;utm_medium=blog\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"410\" src=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-1024x410.png\" alt=\"\" class=\"wp-image-55425\" srcset=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-1024x410.png 1024w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-300x120.png 300w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-768x307.png 768w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-1536x615.png 1536w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-2048x820.png 2048w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-18x7.png 18w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-100x40.png 100w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<h2 id=\"h-how-is-one-way-anova-used\"><strong>Kaip naudojama vienakrypt\u0117 ANOVA?<\/strong><\/h2>\n\n\n\n<p>Vienpus\u0117 ANOVA - tai statistinis testas, naudojamas nustatyti, ar yra reik\u0161ming\u0173 skirtum\u0173 tarp dviej\u0173 ar daugiau nepriklausom\u0173 grupi\u0173 vidurki\u0173. Jis naudojamas nulinei hipotezei, kad vis\u0173 grupi\u0173 vidurkiai yra vienodi, patikrinti prie\u0161 alternatyvi\u0105 hipotez\u0119, kad bent vienas vidurkis skiriasi nuo kit\u0173.<\/p>\n\n\n\n<h2 id=\"h-assumptions-of-anova\"><strong>ANOVA prielaidos<\/strong><\/h2>\n\n\n\n<p>Kad rezultatai b\u016bt\u0173 pagr\u012fsti ir patikimi, ANOVA turi atitikti kelias prielaidas. \u0160ios prielaidos yra tokios:<\/p>\n\n\n\n<ul>\n<li><strong>Normalumas:<\/strong> Priklausomas kintamasis tur\u0117t\u0173 b\u016bti normaliai pasiskirst\u0119s kiekvienoje grup\u0117je. Tai galima patikrinti naudojant histogramas, normaliosios tikimyb\u0117s diagramas arba statistinius testus, pavyzd\u017eiui, Shapiro-Wilk test\u0105.<\/li>\n\n\n\n<li><strong>Dispersijos homogeni\u0161kumas: <\/strong>Priklausomo kintamojo dispersija visose grup\u0117se tur\u0117t\u0173 b\u016bti ma\u017edaug vienoda. Tai galima patikrinti naudojant statistinius testus, pavyzd\u017eiui, Leveno test\u0105 arba Bartleto test\u0105.<\/li>\n\n\n\n<li><strong>Nepriklausomyb\u0117: <\/strong>Kiekvienos grup\u0117s steb\u0117jimai tur\u0117t\u0173 b\u016bti nepriklausomi vienas nuo kito. Tai rei\u0161kia, kad vienos grup\u0117s reik\u0161m\u0117s netur\u0117t\u0173 b\u016bti susijusios su kitos grup\u0117s reik\u0161m\u0117mis ar nuo j\u0173 priklausyti.<\/li>\n\n\n\n<li><strong>Atsitiktin\u0117 atranka:<\/strong> Grup\u0117s tur\u0117t\u0173 b\u016bti sudaromos atsitiktin\u0117s atrankos b\u016bdu. Taip u\u017etikrinama, kad rezultatus b\u016bt\u0173 galima apibendrinti didesnei populiacijai.<\/li>\n<\/ul>\n\n\n\n<p>Prie\u0161 atliekant ANOVA svarbu patikrinti \u0161ias prielaidas, nes j\u0173 pa\u017eeidimas gali lemti netikslius rezultatus ir neteisingas i\u0161vadas. Jei pa\u017eeid\u017eiama viena ar kelios prielaidos, vietoj j\u0173 galima naudoti alternatyvius testus, pavyzd\u017eiui, neparametrinius testus.<\/p>\n\n\n\n<h2 id=\"h-performing-a-one-way-anova\"><strong>Vienpus\u0117s ANOVA atlikimas<\/strong><\/h2>\n\n\n\n<p>Nor\u0117dami atlikti vienakrypt\u0119 ANOVA, galite atlikti \u0161iuos veiksmus:<\/p>\n\n\n\n<p><strong>1 \u017eingsnis:<\/strong> Nurodykite hipotezes<\/p>\n\n\n\n<p>Apibr\u0117\u017ekite nulin\u0119 hipotez\u0119 ir alternatyvi\u0105j\u0105 hipotez\u0119. Nulin\u0117 hipotez\u0117 teigia, kad n\u0117ra reik\u0161ming\u0173 skirtum\u0173 tarp grupi\u0173 vidurki\u0173. Alternatyvioji hipotez\u0117 yra ta, kad bent vienos grup\u0117s vidurkis reik\u0161mingai skiriasi nuo kit\u0173.<\/p>\n\n\n\n<p><strong>2 \u017eingsnis:<\/strong> Rinkti duomenis<\/p>\n\n\n\n<p>Surinkite kiekvienos grup\u0117s, kuri\u0105 norite palyginti, duomenis. Kiekviena grup\u0117 tur\u0117t\u0173 b\u016bti nepriklausoma ir tur\u0117ti pana\u0161aus dyd\u017eio imt\u012f.<\/p>\n\n\n\n<p><strong>3 veiksmas:<\/strong> Apskai\u010diuokite kiekvienos grup\u0117s vidurk\u012f ir dispersij\u0105<\/p>\n\n\n\n<p>Pagal surinktus duomenis apskai\u010diuokite kiekvienos grup\u0117s vidurk\u012f ir dispersij\u0105.<\/p>\n\n\n\n<p><strong>4 veiksmas:<\/strong> Apskai\u010diuokite bendr\u0105 vidurk\u012f ir dispersij\u0105<\/p>\n\n\n\n<p>Apskai\u010diuokite bendr\u0105 vidurk\u012f ir dispersij\u0105, i\u0161vesdami kiekvienos grup\u0117s vidurk\u012f ir dispersij\u0105.<\/p>\n\n\n\n<p><strong>5 veiksmas:<\/strong> Apskai\u010diuokite kvadrat\u0173 tarp grupi\u0173 sum\u0105 (SSB)<\/p>\n\n\n\n<p>Apskai\u010diuokite kvadrat\u0173 tarp grupi\u0173 sum\u0105 (SSB) pagal formul\u0119:<\/p>\n\n\n\n<p>SSB = \u03a3ni (x\u0304i - x\u0304)^2<\/p>\n\n\n\n<p>kur ni - i-osios grup\u0117s imties dydis, x\u0304i - i-osios grup\u0117s vidurkis, o x\u0304 - bendras vidurkis.<\/p>\n\n\n\n<p><strong>6 veiksmas:<\/strong> Apskai\u010diuokite kvadrat\u0173 sum\u0105 grup\u0117se (SSW)<\/p>\n\n\n\n<p>Apskai\u010diuokite kvadrat\u0173 sum\u0105 grup\u0117se (SSW) pagal formul\u0119:<\/p>\n\n\n\n<p>SSW = \u03a3\u03a3(xi - x\u0304i)^2<\/p>\n\n\n\n<p>kur xi yra i-tas steb\u0117jimas j-oje grup\u0117je, x\u0304i yra j-tosios grup\u0117s vidurkis, o j yra nuo 1 iki k grupi\u0173.<\/p>\n\n\n\n<p><strong>7 veiksmas: <\/strong>Apskai\u010diuokite F-statistik\u0105<\/p>\n\n\n\n<p>Apskai\u010diuokite F-statistik\u0105 padalydami dispersij\u0105 tarp grupi\u0173 (SSB) i\u0161 dispersijos grup\u0117s viduje (SSW):<\/p>\n\n\n\n<p>F = (SSB \/ (k - 1)) \/ (SSW \/ (n - k))<\/p>\n\n\n\n<p>kur k - grupi\u0173 skai\u010dius, o n - bendras imties dydis.<\/p>\n\n\n\n<p><strong>8 veiksmas:<\/strong> Nustatykite kritin\u0119 F reik\u0161m\u0119 ir p reik\u0161m\u0119<\/p>\n\n\n\n<p>Nustatykite kritin\u0119 F reik\u0161m\u0119 ir atitinkam\u0105 p reik\u0161m\u0119, remdamiesi norimu reik\u0161mingumo lygmeniu ir laisv\u0117s laipsniais.<\/p>\n\n\n\n<p><strong>9 veiksmas:<\/strong> Palyginkite apskai\u010diuot\u0105 F-statistik\u0105 su kritine verte F<\/p>\n\n\n\n<p>Jei apskai\u010diuota F-statistika yra didesn\u0117 u\u017e kritin\u0119 F reik\u0161m\u0119, atmeskite nulin\u0119 hipotez\u0119 ir padarykite i\u0161vad\u0105, kad bent dviej\u0173 grupi\u0173 vidurkiai reik\u0161mingai skiriasi. Jei apskai\u010diuota F-statistika yra ma\u017eesn\u0117 arba lygi kritinei F reik\u0161mei, nulin\u0117s hipotez\u0117s neatmeskite ir darykite i\u0161vad\u0105, kad reik\u0161mingo skirtumo tarp grupi\u0173 vidurki\u0173 n\u0117ra.<\/p>\n\n\n\n<p><strong>10 veiksmas:<\/strong> post hoc analiz\u0117 (jei reikia).<\/p>\n\n\n\n<p>Jei nulin\u0117 hipotez\u0117 atmetama, atlikite post hoc analiz\u0119, kad nustatytum\u0117te, kurios grup\u0117s reik\u0161mingai skiriasi viena nuo kitos. \u012eprasti post hoc testai: Tukey's HSD testas, Bonferroni korekcija ir Scheffe's testas.<\/p>\n\n\n\n<h2 id=\"h-interpreting-the-results\"><strong>Rezultat\u0173 ai\u0161kinimas<\/strong><\/h2>\n\n\n\n<p>Atlikus vienpus\u0119 ANOVA analiz\u0119, rezultatus galima interpretuoti taip:<\/p>\n\n\n\n<p><strong>F-statistika ir p-vert\u0117: <\/strong>F-statistika parodo dispersijos tarp grupi\u0173 ir dispersijos grup\u0117s viduje santyk\u012f. P reik\u0161m\u0117 rodo tikimyb\u0119 gauti toki\u0105 pat ekstremali\u0105 F statistik\u0105, kaip ir steb\u0117toji, jei nulin\u0117 hipotez\u0117 yra teisinga. Ma\u017ea p reik\u0161m\u0117 (ma\u017eesn\u0117 u\u017e pasirinkt\u0105 reik\u0161mingumo lygmen\u012f, da\u017eniausiai 0,05) rodo, kad yra svari\u0173 \u012frodym\u0173, paneigian\u010di\u0173 nulin\u0119 hipotez\u0119, t. y. kad bent dviej\u0173 grupi\u0173 vidurkiai reik\u0161mingai skiriasi.<\/p>\n\n\n\n<p><strong>Laisv\u0117s laipsniai: <\/strong>Tarpgrupini\u0173 ir vidini\u0173 grupi\u0173 veiksni\u0173 laisv\u0117s laipsniai yra atitinkamai k-1 ir N-k, kur k - grupi\u0173 skai\u010dius, o N - bendras imties dydis.<\/p>\n\n\n\n<p><strong>Vidutin\u0117 kvadratin\u0117 paklaida:<\/strong><em> <\/em>Vidutin\u0117 kvadratin\u0117 paklaida (MSE) - tai grup\u0117s viduje esan\u010dios kvadrat\u0173 sumos ir grup\u0117s viduje esan\u010di\u0173 laisv\u0117s laipsni\u0173 santykis. Tai parodo apskai\u010diuot\u0105 dispersij\u0105 kiekvienoje grup\u0117je, atsi\u017evelgus \u012f skirtumus tarp grupi\u0173.<\/p>\n\n\n\n<p><strong>Poveikio dydis:<\/strong> Poveikio dyd\u012f galima i\u0161matuoti naudojant etakvadrat\u0105 (\u03b7\u00b2), kuris parodo, koki\u0105 dal\u012f viso priklausomo kintamojo variacijos kiekio sudaro grupi\u0173 skirtumai. \u012eprastai eta kvadrato reik\u0161m\u0117s interpretuojamos taip:<\/p>\n\n\n\n<p>Ma\u017eas poveikis: \u03b7\u00b2 &lt; 0,01<\/p>\n\n\n\n<p>Vidutinis poveikis: 0,01 \u2264 \u03b7 \u03b7\u00b2 &lt; 0,06<\/p>\n\n\n\n<p>Didelis poveikis: \u03b7\u00b2 \u2265 0,06<\/p>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\"><strong>Post hoc analiz\u0117:<\/strong><\/a> Jei nulin\u0117 hipotez\u0117 atmetama, galima atlikti post hoc analiz\u0119 ir nustatyti, kurios grup\u0117s reik\u0161mingai skiriasi viena nuo kitos. Tai galima atlikti naudojant \u012fvairius testus, pavyzd\u017eiui, Tukey'o HSD test\u0105, Bonferroni patais\u0105 arba Scheffe's test\u0105.<\/p>\n\n\n\n<p>Rezultatai tur\u0117t\u0173 b\u016bti interpretuojami atsi\u017evelgiant \u012f tyrimo klausim\u0105 ir analiz\u0117s prielaidas. Jei prielaid\u0173 nesilaikoma arba rezultat\u0173 ne\u012fmanoma interpretuoti, gali prireikti alternatyvi\u0173 tyrim\u0173 arba analiz\u0117s pakeitim\u0173.<\/p>\n\n\n\n<h2 id=\"h-post-hoc-testing\"><strong>Post hoc testavimas<\/strong><\/h2>\n\n\n\n<p>Statistikoje vienakrypt\u0117 ANOVA yra metodas, naudojamas trij\u0173 ar daugiau grupi\u0173 vidurkiams palyginti. Atlikus ANOVA test\u0105 ir atmetus nulin\u0119 hipotez\u0119, o tai rei\u0161kia, kad yra reik\u0161ming\u0173 \u012frodym\u0173, leid\u017eian\u010di\u0173 teigti, jog bent vienos grup\u0117s vidurkis skiriasi nuo kit\u0173 grupi\u0173 vidurki\u0173, galima atlikti post hoc testavim\u0105, siekiant nustatyti, kurios grup\u0117s reik\u0161mingai skiriasi viena nuo kitos.<\/p>\n\n\n\n<p>Post hoc testai naudojami konkretiems skirtumams tarp grupi\u0173 vidurki\u0173 nustatyti. Kai kurie \u012fprasti post hoc testai: Tukey'aus s\u0105\u017einingai reik\u0161mingo skirtumo (HSD), Bonferroni pataisa, Scheffe's metodas ir Dunnett'o testas. Kiekvienas i\u0161 \u0161i\u0173 test\u0173 turi savo prielaidas, privalumus ir apribojimus, tod\u0117l pasirinkimas, kur\u012f test\u0105 naudoti, priklauso nuo konkretaus tyrimo klausimo ir duomen\u0173 savybi\u0173.<\/p>\n\n\n\n<p>Apskritai, post hoc testai yra naudingi, nes suteikia i\u0161samesn\u0117s informacijos apie konkre\u010dius grupi\u0173 skirtumus vienakrypt\u0117je ANOVA analiz\u0117je. Ta\u010diau svarbu \u0161iuos testus naudoti atsargiai ir rezultatus interpretuoti atsi\u017evelgiant \u012f tyrimo klausim\u0105 ir konkre\u010dias duomen\u0173 charakteristikas.<\/p>\n\n\n\n<p>Su\u017einokite daugiau apie \"Post Hoc\" analiz\u0119 i\u0161 m\u016bs\u0173 turinio \"<a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\">Post Hoc analiz\u0117: Procesas ir test\u0173 tipai<\/a>&#8220;.<\/p>\n\n\n\n<h2 id=\"h-reporting-the-results-of-anova\"><strong>ANOVA rezultat\u0173 pateikimas<\/strong><\/h2>\n\n\n\n<p>Pateikiant ANOVA analiz\u0117s rezultatus, reik\u0117t\u0173 nurodyti kelet\u0105 informacijos element\u0173:<\/p>\n\n\n\n<p><strong>F statistika: <\/strong>Tai ANOVA testo statistika, kuri parodo dispersijos tarp grupi\u0173 ir dispersijos grup\u0117s viduje santyk\u012f.<\/p>\n\n\n\n<p><strong>F statistikos laisv\u0117s laipsniai:<\/strong> Tai apima laisv\u0117s laipsnius skaitikliui (skirtumai tarp grupi\u0173) ir vardikliui (skirtumai grup\u0117s viduje).<\/p>\n\n\n\n<p><strong>p reik\u0161m\u0117: <\/strong>Tai rodo tikimyb\u0119 gauti stebim\u0105 F statistik\u0105 (arba ekstremalesn\u0119 reik\u0161m\u0119) vien d\u0117l atsitiktinumo, darant prielaid\u0105, kad nulin\u0117 hipotez\u0117 yra teisinga.<\/p>\n\n\n\n<p><strong>Parei\u0161kimas, ar nulin\u0117 hipotez\u0117 buvo atmesta, ar ne:<\/strong> Tai tur\u0117t\u0173 b\u016bti pagr\u012fsta p reik\u0161me ir pasirinktu reik\u0161mingumo lygiu (pvz., alfa = 0,05).<\/p>\n\n\n\n<p><strong>Post hoc testavimas:<\/strong> Jei nulin\u0117 hipotez\u0117 atmetama, reikia pateikti post hoc testavimo rezultatus, kad b\u016bt\u0173 galima nustatyti, kurios grup\u0117s reik\u0161mingai skiriasi viena nuo kitos.<\/p>\n\n\n\n<p>Pavyzd\u017eiui, ataskaitos pavyzdys gal\u0117t\u0173 b\u016bti toks:<\/p>\n\n\n\n<p>Siekiant palyginti trij\u0173 grupi\u0173 (A grup\u0117s, B grup\u0117s ir C grup\u0117s) atminties i\u0161laikymo testo vidutinius rezultatus, buvo atlikta vienpus\u0117 ANOVA. F statistika buvo 4,58, laisv\u0117s laipsniai - 2, 87, o p reik\u0161m\u0117 - 0,01. Nulin\u0117 hipotez\u0117 buvo atmesta, o tai rei\u0161kia, kad bent vienos grup\u0117s atminties i\u0161laikymo rezultatai reik\u0161mingai skiriasi. post hoc testavimas naudojant Tukey's HSD parod\u0117, kad A grup\u0117s (M = 83,4, SD = 4,2) rezultat\u0173 vidurkis buvo reik\u0161mingai didesnis nei B grup\u0117s (M = 76,9, SD = 5,5) ir C grup\u0117s (M = 77,6, SD = 5,3), kurios tarpusavyje reik\u0161mingai nesiskyr\u0117.<\/p>\n\n\n\n<h2 id=\"h-find-the-perfect-infographic-template-for-you\"><strong>Raskite tobul\u0105 infografikos \u0161ablon\u0105<\/strong><\/h2>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a> tai platforma, kurioje pateikiama daugyb\u0117 i\u0161 anksto parengt\u0173 infografik\u0173 \u0161ablon\u0173, padedan\u010di\u0173 mokslininkams ir tyr\u0117jams kurti vaizdines priemones, kuriomis veiksmingai perteikiamos mokslin\u0117s koncepcijos. Platforma suteikia prieig\u0105 prie didel\u0117s mokslini\u0173 iliustracij\u0173 bibliotekos, tod\u0117l mokslininkai ir tyr\u0117jai gali lengvai rasti tobul\u0105 infografikos \u0161ablon\u0105, skirt\u0105 vizualiai perteikti savo tyrim\u0173 rezultatus.<\/p>\n\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/mindthegraph.com\/offer-trial\"><img decoding=\"async\" loading=\"lazy\" width=\"651\" height=\"174\" src=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04.jpg\" alt=\"\" class=\"wp-image-26792\" srcset=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04.jpg 651w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04-300x80.jpg 300w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04-18x5.jpg 18w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04-100x27.jpg 100w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/a><\/figure><\/div>\n\n\n<div style=\"height:44px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>","protected":false},"excerpt":{"rendered":"<p>Su\u017einokite apie vienpus\u0119 ANOVA - statistin\u012f metod\u0105, naudojam\u0105 keli\u0173 grupi\u0173 vidurkiams palyginti duomen\u0173 analiz\u0117je, ir kaip j\u012f taikyti.<\/p>","protected":false},"author":35,"featured_media":29180,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[959,28],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>One-Way ANOVA: Understanding, Conducting, and Presenting - Mind the Graph Blog<\/title>\n<meta name=\"description\" content=\"Learn about the one-way ANOVA, a statistical method used to compare means among multiple groups in data analysis, and how to apply it.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mindthegraph.com\/blog\/lt\/vienakrypte-anova\/\" \/>\n<meta property=\"og:locale\" content=\"lt_LT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"One-Way ANOVA: Understanding, Conducting, and Presenting\" \/>\n<meta property=\"og:description\" content=\"Learn about the one-way ANOVA, a statistical method used to compare means among multiple groups in data analysis, and how to apply it.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mindthegraph.com\/blog\/lt\/vienakrypte-anova\/\" \/>\n<meta property=\"og:site_name\" content=\"Mind the Graph Blog\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-28T11:29:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-12-05T18:51:53+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/08\/one-way-anova-blog.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1123\" \/>\n\t<meta property=\"og:image:height\" content=\"612\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Ang\u00e9lica Salom\u00e3o\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"One-Way ANOVA: Understanding, Conducting, and Presenting\" \/>\n<meta name=\"twitter:description\" content=\"Learn about the one-way ANOVA, a statistical method used to compare means among multiple groups in data analysis, and how to apply it.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/08\/one-way-anova-blog.jpg\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Ang\u00e9lica Salom\u00e3o\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"One-Way ANOVA: Understanding, Conducting, and Presenting - 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