Kulingelo lwenzululwazi, kukho izinto ezimbini ezibalulekileyo ezibizwa ngokuba ziinguqu ezizimeleyo nezixhomekeke kuzo. Kweli nqaku, siza kujonga ukuba zeziphi iinguqu ezizimeleyo nezixhomekeke kuzo, kubandakanywa iintlobo kunye nemizekelo.
Ukuguquguquka okuzimeleyo koko izazinzulu zitshintsha okanye zilawula kuvavanyo. Benza oku ukubona ukuba kwenzeka ntoni kuguquguquko oluxhomekeke.
I-variable variable yinto izazinzulu ezivavanyayo kunye nokulinganisa kuvavanyo. Kuxhomekeke kwinto eyenziwa zizazinzulu ngenguqu ezimeleyo. Xa izazinzulu zitshintsha ukuguquguquka okuzimeleyo, zibukele kwaye zibhale phantsi okwenzekayo kuguquguquko oluxhomekeke.
Ngoko ke, ngamagama alula, umahluko ozimeleyo ngulowo utshintshayo, kwaye umahluko oxhomekeke kulowo ubonisa umphumo wolo tshintsho. Izazinzulu zijonga indlela uguquguquko oluxhomekeke kuyo olusabela ngayo xa lusenza izinto kuguquguquko oluzimeleyo.
Yintoni i-Independent Variable?
Ukuguquguquka okuzimeleyo yinto ethi izazinzulu zitshintshe ngenjongo kumfuniselo wokubona okwenzekayo. Kufana nokutshintsha ukuba bavule okanye bacime ukuze babone iziphumo. Izazinzulu ngamanye amaxesha zinokuseta olu tshintsho kumaxabiso ahlukeneyo ukuze ufunde ngakumbi ngalo. Kodwa, kwezinye iimeko, abanako ukuyilawula ngokuthe ngqo, kodwa basajonge ukuba isichaphazela njani isiphumo sovavanyo.
Oosonzululwazi banokusebenzisa amagama ahlukeneyo ukuthetha ngezinto ezizimeleyo. Umzekelo, xa besenza into ebizwa ngokuba yi-linear regression, banokubiza ii-variables ezizimeleyo "i-right-side variables" kuba zibonakala kwicala lasekunene letshathi. Basenokuzibiza ngokuba ziguquguqukayo zokuxela kwangaphambili kuba zinceda izazinzulu ukuba zenze uqikelelo malunga nokuya kwenzeka kuvavanyo.
Elinye igama ziinguqu ezichazayo kuba zinceda ekuchazeni iziphumo zokugqibela. Ke, ukuguquguquka okuzimeleyo kufana neyona nto iphambili izazinzulu zitshintsha okanye ziqwalasele ukuqonda ukuba ziluchaphazela njani umfuniselo.
Iintlobo ezimbini zeeNguqulelo ezizimeleyo
- Izinto eziguquguqukayo zovavanyo: Ezi zikwabizwa ngokuba ziinguqu ezilawulwayo kuba abaphandi banokutshintsha okanye balawule ngexesha lovavanyo ukuze babone indlela ezichaphazela ngayo iziphumo. Ngokomzekelo, ukuba izazinzulu zifuna ukuvavanya indlela izixa ezahlukeneyo zokukhanya kwelanga ezichaphazela ngayo ukukhula kwezityalo, zinokulawula umlinganiselo wokukhanya kwelanga ezifunyanwa zizityalo.
- Izinto eziguquguqukayo zesihloko: Ngokungafaniyo nezinto eziguquguqukayo zokulinga, abaphandi abakwazi ukulawula iinguqu zezifundo. Ngaphandle koku, zisenexabiso kwiimvavanyo njengoko zinokunceda ukuphendula imibuzo yophando. Umzekelo, ukuba abaphandi bafunda amanqaku ovavanyo asemgangathweni abafundi bezikolo eziphakamileyo abavela kwimimandla eyahlukeneyo, abanako ukulawula okanye ukutshintsha imimandla aphuma kuyo umfundi ngamnye. Nangona kunjalo, basenokusebenzisa umahluko wengingqi ukwenza amaqela abafundi ekuqaleni kwesifundo sabo.
Imizekelo yeeNguqulelo eziZimeleyo
Makhe sijonge eminye imizekelo ukuqonda iinguqu ezizimeleyo ngcono.
Okokuqala, khawufane ucinge ukuba oosonzululwazi banomdla malunga nokuba izixa ezahlukeneyo zesichumiso zikuchaphazela njani ukukhula kwezityalo. Kuphononongo, bagqiba ekubeni banike iidosi ezahlukeneyo zesichumiso kwizityalo ezahlukeneyo. Isixa sesichumiso esinikwa isityalo ngasinye sitshintsha-tshintsha esizimeleyo. Oku kuguquguquka yinto izazinzulu ezinokutshintsha ngenjongo. Bafuna ukubona ukuba oku kunokuchaphazela njani ukukhula kwesityalo ngasinye. Ukukhula kwezityalo sisiphumo, okanye ukuguquguquka okuxhomekeke ekubeni kuxhomekeke kwisixa sesichumiso.
Ngoku, makhe siqwalasele isifundo malunga neziphumo zovavanyo lwezibalo. Abaphandi banomdla wokuthelekisa amanqaku abafundi abathathe iihonours-level algebra nabo bathathe ialgebra eqhelekileyo. Ukhetho lwabafundi kwiiklasi zizinto ezahlukeneyo ezizimeleyo kwesi sifundo. Abaphandi abakwazi ukulawula okanye ukutshintsha ukuba yeyiphi iklasi ekhethwe ngumfundi ngamnye. Nangona kunjalo, basenokufunda ukuba ukhetho lweklasi lubangela nawuphi na umahluko kumanqaku ovavanyo amiselweyo abafundi. Kule meko, amanqaku ovavanyo olusemgangathweni ahluka ngokuxhomekeke kuba axhomekeke kukhetho lweklasi lwabafundi.
Ngoko ke, kuyo yomibini imizekelo, izazinzulu zijonge indlela enye ezinokuthi zilawule ngayo (inguqu ezimeleyo) inokukhokelela kutshintsho kwenye into abayijongileyo (inguqu exhomekeke kuyo). Oku kubanceda baqonde ubudlelwane kunye neepateni kwihlabathi lezenzululwazi.
Yintoni Uguquguquko oluxhomekeke?
Ukuguquguquka okuxhomekekayo yinto eguqukayo xa usenza utshintsho kwenye into ebizwa ngokuba luguquko oluzimeleyo kumfuniselo wenzululwazi. Abanye abantu bakwayibiza ngokuthi "isiphumo esiguquguqukayo" okanye "impendulo eguquguqukayo" kuba ixhomekeke kwinto eyenzekayo kuguquguquko oluzimeleyo.
Xa izazinzulu zisenza imifuniselo, zilandela umgaqo obizwa ngokuba yindlela yenzululwazi. Umgaqo omnye obalulekileyo kukutshintsha kuphela into enye ngexesha kuvavanyo. Yonke enye into kufuneka ihlale ifana. Oku kunceda izazinzulu zibone indlela utshintsho kwinto enye, ukuguquguquka okuzimeleyo, okuchaphazela ezinye izinto, njengokuguquguquka okuxhomekeke.
Izazinzulu azilawuli ngokuthe ngqo okanye zitshintshe ukuguquguquka okuxhomekeke kuyo. Endaweni yoko, batshintsha ukuguquguquka okuzimeleyo kwaye babone ukuba kwenzeka ntoni kuguquguquko oluxhomekeke. Kufana nobudlelwane besizathu kunye nesiphumo. Izazinzulu zilindele ukuba ukuguquguquka okuxhomekeke kuye kunyuke okanye kuhle ngokusekelwe kwinto abayenzayo kuguquko oluzimeleyo.
Ke, ngamagama alula, ukuguquguquka okuxhomekeke kwinto eguqukayo ngenxa yento oyenzayo kwenye into kumfuniselo wesayensi. Izazinzulu zifuna ukubona indlela izinto ezinxibelelana ngayo nendlela enye into enokuyenza ngayo enye into itshintshe.
Imizekelo yeZiguquguquko ezixhomekeke
Makhe sihlolisise izinto ezixhomekeke kuzo ngamagama alula sisebenzisa imizekelo emibini yokwenyani:
- Isifundo sokuKhula kweZityalo: Khawufane ucinge ukuba sisenza umfuniselo wokuzenzisa ukubona ukuba izixa ezahlukeneyo zesichumiso zikuchaphazela njani ukukhula kwezityalo. Ukutshintsha okuzimeleyo, into esiyitshintsha ngenjongo, sisixa sesichumiso esinikwa isityalo ngasinye. Ngoku, ukuguquguquka okuxhomekeke koko silinganisa kwaye siqwalasele - kule meko, kukukhula okurekhodiweyo kwesityalo ngasinye. Ukuba sigcina yonke enye into iyafana, njengobungakanani bamanzi, ubukhulu besitya, ukukhanya kwelanga, kunye nexesha lokukhula, sinokuthi ngokufanelekileyo ukukhula kwesityalo kuchaphazeleka ngokuthe ngqo kukuguquguquka okuzimeleyo, okusisichumiso.
- Uhlalutyo lwezibalo: Masithi sinomdla kwindlela iindidi ezahlukeneyo zeeklasi zealjebra eziwaphembelela ngayo amanqaku ovavanyo amiselweyo abafundi. Ukutshintsha okuzimeleyo apha yimvelaphi yomsebenzi wekhosi yabafundi - nokuba bathathe iklasi yealjebra eqhelekileyo okanye iklasi ye-honours algebra. Ukuguquguquka okuxhomekeke kwelinye icala, ngamanqaku abafundi abawafumanayo kuvavanyo olusemgangathweni. Thina, njengabaphandi, asikwazi ukulawula okanye ukutshintsha la manqaku ovavanyo; sinokuzijonga kuphela kwaye sizithelekise emva kokukhetha amaqela abafundi abaneemvelaphi ezahlukeneyo zekhosi.
Kuyo yomibini imizekelo, ukuguquguquka okuxhomekeke koko sibukeleyo kwaye silinganisa, kwaye kuyatshintsha ngokusekwe kuguquko oluzimeleyo esilusebenzisayo ngabom. Isinceda siqonde unobangela-kunye-nesiphumo ubudlelwane phakathi kweenguqu esizenzayo kunye neziphumo esizibonayo.
Iiguquguquki ezizimeleyo nezixhomekeke kwimizekelo
Kumalinge enzululwazi, kukho izinto ezilawulwa zizazinzulu kunye nezinto ezizibonayo. Masiyicazulule ngeminye imizekelo.
Umzekelo 1: Amanundu kunye nokukhanya
Yiba nomfanekiso wenzululwazi efunda amanundu kunye nokukhanya. Bafuna ukwazi ukuba ukukhanya kokukhanya kuyayichaphazela indlela amanundu atsalwa ngayo kuko. Inzululwazi ilungisa ukukhanya kokukhanya (inguqu ezimeleyo) kwaye ijonge indlela amanundu asabela ngayo (i-dependent variable).
Umzekelo 2: Isidlo sakusasa kunye namanqaku ovavanyo
Ngoku, cinga ngabafundi kunye nesidlo sakusasa. Umntu uyazibuza ukuba ukutya kwasekuseni kwenza umahluko kumanqaku ovavanyo. Umfunisi ulawula isidlo sakusasa (ukuguquguquka okuzimeleyo) kwaye ujonge ukuba amanqaku ovavanyo atshintsha njani (ukuguquguquka okuxhomekeke). Nokuba akukho nxibelelwano phakathi kwesidlo sakusasa kunye namanqaku, iziphumo zovavanyo zisaxhomekeke kwisidlo sakusasa.
Umzekelo 3: Iziyobisi Noxinzelelo Lwegazi
Kolunye ulingo, isazinzulu sijonga ukuba ichiza elithile libhetele na ekulawuleni uxinzelelo lwegazi oluphezulu kunelinye. Uhlobo lwechiza luyi-variable ezimeleyo, kwaye i-variable variable yi-blood pressure yesigulane. Ukwenza uvavanyo luchaneke ngakumbi, i-variable variable (i-placebo engenazo izithako ezisebenzayo) yongezwa. Oku kunceda ekufumaniseni ukuba ngaba eliphi ichiza liyaluchaphazela ngokwenene uxinzelelo lwegazi.
Iinguqu ezizimeleyo nezixhomekeke kuPhando
Kuphando, sihlala sisebenzisa izinto ezizimeleyo nezixhomekeke kuzo, ngakumbi kwizifundo zovavanyo kunye novavanyo olulinganayo. Makhe sijonge imizekelo yemibuzo yophando kunye nezinto ezihambelanayo ezizimeleyo nezixhomekeke.
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- Ukuzila ukutya okwethutyana kuyichaphazela njani iSwekile yegazi?
- Ukuguquguquka okuzimeleyo: Ubukho okanye ukungabikho kokuzila okuphakathi
- Ukuguquguquka okuxhomekekayo: Amanqanaba eswekile yegazi
- Ngaba i-Marijuana yoNyango iyakunciphisa iintlungu ezingapheliyo?
- Ukuhluka okuzimeleyo: Ubukho okanye ukungabikho kokusetyenziswa kwentsangu kwezonyango
- Iinguqu ezixhomekeke: Ukuphindaphinda kunye nokuqina kweentlungu
- Ngaba uMsebenzi okwiNdawo ekude uchaphazela uKwaneliseka koMsebenzi?
- Umehluko ozimeleyo: Uhlobo lwendawo yokusebenza (ekude okanye eofisini)
- Ukwahluka okuxhomekekayo: Ukwaneliseka komsebenzi-u-self-reports
Xa ujongana nedatha yovavanyo, uhlalutyo lubandakanya ukuvelisa izibalo ezichazayo kunye nokubona iziphumo. Ukukhethwa kovavanyo lwamanani kuxhomekeke kwiindidi eziguquguqukayo, inqanaba lokulinganisa, kunye nenani lamanqanaba ahlukeneyo azimeleyo.
Ngokuqhelekileyo, iimvavanyo or Ii-ANOVAs baqeshelwe ukuhlalutya idatha kunye nokujongana nemibuzo yophando. Ezi mvavanyo zinceda ekwenzeni izigqibo kunye nokuqonda ubudlelwane phakathi kwezinto ezizimeleyo nezixhomekeke kuzo.
Funda Ukwahlula Iiguquguquki ezizimeleyo nezixhomekeke
Ukwahlula phakathi kwezinto ezizimeleyo nezixhomekeke kuzo, landela esi sikhokelo silula:
- Ijongiwe okanye ijongiwe: Okokuqala, qwalasela ukuba ukuguquguquka kungatshintshwa okanye kukhethwe ngabaphandi (kusetyenziswe) okanye ukuba kujongwe kwaye kulinganiswe ngexesha lovavanyo (luqwalaselwe). Izinto eziguquguqukayo ezilawulwa ngabaphandi zihlala zizimeleyo. Izinto eziguquguqukayo ezijongwayo nezirekhodwayo zixhomekeke. Nokuba abaphandi abanako ukulawula ukuguquguquka kwezifundo, basaphathwa njengabazimeleyo kuba baphembelela izinto ezixhomekeke kuzo.
- Umzobo: Yiba nomfanekiso-ngqondweni uceba izinto eziguquguqukayo kwigrafu ene-X-Y yokulungelelanisa inqwelo-moya. Iinguqu ezizimeleyo, ezo onokuzitshintsha, zihlala zihamba kwi-X-axis (horizontal). Iinguqu ezixhomekeke, iziphumo ezichaphazelekayo ngotshintsho, hamba kwi-Y-axis (ethe nkqo).
- Udidi Lwesithathu-Iiguquguquko ezibhidayo: Ngamanye amaxesha kukho uhlobo lwesithathu lokuguquguquka olungazimeleyo okanye oluxhomekeke kodwa lusenokuphazamisana neziphumo - ezi zibizwa ngokuba ziguquguqukayo eziphazamisayo. Banefuthe kuvavanyo ngeendlela abaphandi abanokuthi bangazilindelanga, njengokuguquguquka okuzimeleyo okungalindelekanga. Ukuhlela izinto eziguquguqukayo akusoloko kukhetha ngokucacileyo phakathi kokuzimela kunye nokuxhomekeka; ezinye iinguqu, njengeenguqu ezibhidayo, azingeni kakuhle kwezo ndidi.
Shiya iMpendulo