Ukuhlolwa kwe-Chi-Square kokuzimela
Ukuhlolwa kwe-chi-square (χ²) kokuzimela kuyindlela yezibalo engeyona i-parametric evame ukusetshenziswa ukunquma ukuthi iziguquguquko ezimbili zesigaba (isikali esijwayelekile noma esijwayelekile) zihlobene noma azihlobene. Ezifundweni eziningi zezenhlalo, ezempilo, ezemfundo, ukumaketha, kanye nokuhlaziywa kwenqubomgomo, abacwaningi bavame ukuhlangana nedatha yesigaba njengobulili (owesilisa/owesifazane), isimo sokubhema (yebo/cha), izinga lemfundo (isikole samabanga aphezulu/idiploma/iziqu ze-bachelor), izintandokazi zomkhiqizo (A/B/C), njalo njalo. Ukuhlolwa kwe-chi-square kokuzimela kusiza ukuphendula umbuzo oyinhloko: ingabe ukusatshalaliswa kwesiguquguquko esisodwa kuhluke kakhulu kwezinye izigaba eziguquguqukayo?
Imiqondo Eyisisekelo: Kuyini Ukuzimela?
Kuthiwa iziguquguquko ezimbili zizimele uma ulwazi mayelana nezigaba ezikuguquguquko lokuqala lungasizi ukubikezela izigaba ezikuguquguquko lwesibili. Isibonelo, uma "ubulili" kanye "nokukhethwa kweziphuzo" kuzimele, khona-ke isilinganiso sezintandokazi zeziphuzo sizofana kakhulu emaqenjini abesilisa nabesifazane. Ngokuphambene nalokho, uma izilinganiso zihluka kakhulu, khona-ke lokhu kubonisa ukuthi lezi ziguquguquko ezimbili azizimele (ezihlobene).
Ukuhlolwa kwe-chi-square kokuzimela kusebenza ngokuqhathanisa amaza aqashelwayo (idatha yangempela esiyibonayo) namaza alindelekile (amaza "okufanele avele" uma lezi ziguquguquko ezimbili bezizimele ngempela). Uma umehluko omkhulu phakathi kwamanani aqashelwayo nalawo alindelekile, inani lezibalo ze-χ² liba likhulu, futhi ubufakazi bobuhlobo buqina.
Ithebula Lezinto Ezingalindelekile
Idatha yalolu vivinyo ihlelwe yaba yithebula lezinto ezingenzeka, elibonisa imvamisa yokuhlanganiswa kwezigaba zezinhlobo ezimbili. Isibonelo, ake sihlole ubudlelwano phakathi kwesimo sokubhema (Yebo/Cha) kanye nokukhwehlela okungapheli (Yebo/Cha). Sizokwakha ithebula elingu-2x2 eliqukethe inani labaphenduli kunhlanganisela ngayinye.
Ngokuvamile, amathebula angaba ngu-2×2, 2×3, 3×4, njalo njalo, kuye ngenani lezigaba ku-variable ngayinye. Ukuhlolwa kwe-chi-square kokuzimela kungasetshenziswa kumathebula anoma yiluphi usayizi, inqobo nje uma izimo ezithile zihlangatshezwa.
Ukuhlolwa Kwe-Hypothesis
Ekuhlolweni kwe-chi-square kokuzimela, i-hypothesis ithi:
– H0 (i-null hypothesis): Zombili iziguquguquko zizimele (akukho buhlobo/ukuhlangana).
– H1 (i-hypothesis ehlukile): Lezi ziguquguquko ezimbili azizimele (kukhona ubudlelwano/ukuhlangana).
Inhloso yokuhlolwa ukuthola ukuthi idatha inikeza ubufakazi obanele yini bokwenqaba i-H0.
Ifomula Yezibalo ze-Chi-Square
Isibalo sokuhlolwa kwe-chi-square sibalwa kusetshenziswa ifomula:
\[
\chi^2 = \ isamba \frac{(O_{ij} – E_{ij})^2}{E_{ij}}
\]
Imininingwane:
– \(O_{ij}\) imvamisa yokubuka kumugqa weseli-i kanye nekholomu-j.
– \(E_{ij}\) imvamisa elindelekile kuseli lomugqa-i kanye nekholomu-j.
Imvamisa elindelekile ibalwa kusukela kunani lomugqa kanye nenani lamakholomu:
\[
E_{ij} = \frac{(\text{Total row i}) \times (\text{Total column j})}{\text{Grand total}}
\]
Le fomula ibonisa lokho obekulindeleke ukuthi kwenzeke uma ukusatshalaliswa komugqa ngamunye kanye nekholomu kungazange kuthintane (bekuzimele).
Izinga Lenkululeko
Amadigri enkululeko (df) alolu vivinyo anqunywa ngobukhulu bethebula:
\[
df = (r – 1)(c – 1)
\]
no:
– \(r\) = inani lemigqa (isigaba sokuqala esiguquguqukayo)
– \(c\) = inani lamakholomu (isigaba sesibili esiguquguqukayo)
Amadigri enkululeko athinta ukuma kokusatshalaliswa kwesikwele se-chi okusetshenziselwa ukunquma inani le-p.
Izinyathelo Zokwenza Ukuhlolwa Kokuzimela Kwe-Chi-Square
Okulandelayo ukulandelana okujwayelekile kokwenza lolu vivinyo:
1. Hlela idatha kuthebula lezinto ezingenzeka.
Qiniseka ukuthi idatha isesimweni samafrikhwensi, hhayi amaphesenti.
2. Bala imvamisa elindelekile yeseli ngayinye usebenzisa ifomula \(E_{ij}\).
3. Bala inani le-χ² ngokufingqa izingxenye ze-\((OE)^2/E\) zawo wonke amaseli.
4. Thola i-df usebenzisa i-\((r-1)(c-1)\).
5. Bala inani le-p ngokusekelwe ekusabalalisweni kwesikwele se-chi nge-df (noma qhathanisa i-χ² ebalwe nethebula i-χ² ezingeni lokubaluleka α, isibonelo 0,05).
6. Yenza isinqumo.
– Uma inani le-p ≤ α → lenqaba i-H0 → kukhona ubudlelwano/ukuncika.
– Uma inani le-p > α → lihluleka ukwenqaba i-H0 → abukho ubufakazi bobudlelwano.
7. Ukuhumusha okunesisekelo.
Chaza ukuthi ubudlelwano busho ukuthini kumongo wocwaningo, hhayi nje "okubalulekile" noma "okungabalulekile."
Isibonelo Sokuhumusha (Ngaphandle Kwezibalo Eziningiliziwe)
Ake sithi umcwaningi uhlola ubudlelwano phakathi "kwendlela yokufunda" (ozimele/iqembu) kanye "nokuphothula" (ukuphumelela/ukwehluleka). Ngemva kokwenza isivivinyo se-chi-square, inani le-p lingu-0,02. Nge-α = 0,05, isiphetho siwukwenqaba i-H0, okubonisa ubudlelwano phakathi kwendlela yokufunda kanye nokuphothula. Umcwaningi ube esedinga ukunquma ukuthi yimaphi amaseli anikela ngomehluko omkhulu (isibonelo, ukuthi ngabe isifundo seqembu siyandisa yini isilinganiso sabaphothule). Empeleni, ukuhlaziywa kungandiswa ngokuhlola izinsalela ezijwayelekile noma osayizi bomphumela.
Imigomo Nezicabango Ezibalulekile
Nakuba i-chi-square ingeyona i-parametric, lokhu kuhlolwa kunezidingo eziningana ezibalulekile:
1. Idatha isesimweni sokubalwa (imvamisa) futhi isihloko ngasinye siwela esigabeni esisodwa kuphela (esingabandakanyi oxhumana nabo).
2. Ukuqaphela okuzimele, okusho ukuthi umuntu oyedwa ophendulayo akakwazi ukubalwa ngaphezu kwesisodwa, futhi akukho ubudlelwano obuhambisanayo phakathi kokuqaphela.
3. Imvamisa elindelekile inkulu ngokwanele. Umthetho ojwayelekile: iningi lamanani e-\(E_{ij}\) kufanele libe ngu-≥ 5. Uma kunamaseli amaningi kakhulu anamanani amancane alindelekile, imiphumela yokuhlolwa kwe-chi-square ingase ingavumelekile.
Kumathebula angu-2×2 anemvamisa emincane, okunye okuvamile yi-Fisher's Exact Test. Kudatha ebhangqiwe (isb., ngaphambi nangemva kokuphendula okufanayo), okunye ukuhlolwa kukaMcNemar.
Usayizi Womphumela: Akuyona Into Ebalulekile Nje
Umphumela obalulekile akusho ukuthi ubudlelwano "obuqinile". Ngakho-ke, kuvame ukunconywa ukubika ubukhulu bomphumela, isibonelo:
– I-Phi (φ) yetafula elingu-2×2
– I-Cramér’s V yamatafula amakhulu
U-V kaCramér usukela ku-0 kuya ku-1, kanti amanani amakhulu abonisa ukuhlangana okuqinile. Ubukhulu bomphumela wokubika kusiza abafundi ukuqonda amandla obudlelwano, hhayi nje ukuba khona kwabo.
Izinzuzo kanye nokulinganiselwa
Izinzuzo:
- Kulula ukuyisebenzisa ngemininingwane yezigaba.
– Akudingi ukucabanga ngokujwayelekile.
- Kufanelekela imikhakha eminingi yocwaningo.
Imikhawulo:
– Kuyazwela ngobukhulu besampula: amasampula amakhulu angenza umehluko omncane “ube mkhulu”.
– Akubonisi ngqo indlela yobudlelwano, kodwa kuphela ukuba khona/ukungabikho kobudlelwano.
– Kuyinkinga uma amaseli amaningi enemvamisa emincane elindelekile.
– Ukuchazwa kumele kusekelwe ngokuhlaziywa okwengeziwe (isib. ukubheka izilinganiso noma izinsalela).
I-Penutup
Ukuhlolwa kwe-chi-square kokuzimela kuyithuluzi elibalulekile lokuhlola ukuba khona noma ukungabikho kobudlelwano phakathi kweziguquguquko ezimbili zesigaba. Ngokwakha ithebula le-contingency, ukubala ama-frequency alindelekile, nokuwaqhathanisa nama-frequency abonwe kusetshenziswa izibalo ze-χ², abacwaningi bangahlola ngobuqotho umbono wokuzimela. Kodwa-ke, ukuze bakhiqize ukuhlaziywa okuqinile, abacwaningi kufanele badlule ekunqumeni ukuthi kukhona yini umphumela obalulekile noma cha; kufanele futhi babike osayizi bomphumela, bahlole izidingo zemvamisa ezilindelekile, futhi bahlobanise okutholakele nomongo obalulekile wocwaningo. Ngakho-ke, ukuhlolwa kwe-chi-square kuba ngaphezu nje kwenqubo yezibalo, kodwa kuyingxenye yokucabanga kwesayensi okusiza ukuqonda amaphethini obudlelwano kudatha yesigaba.
