Bvunzo reChi-Square reKuzvimirira
Bvunzo ye chi-square (χ²) yekuzvimirira inzira isingashandisirwe pakuverenga nhamba iyo inowanzoshandiswa kuona kana zvinhu zviviri zvechikamu (chikero chemazita kana chenguva dzose) zvine hukama kana kuti zvisina hukama. Muzvidzidzo zvakawanda zvemagariro evanhu, hutano, dzidzo, kushambadzira, uye kuongorora mitemo, vaongorori vanowanzosangana neruzivo rwechikamu senge murume kana mukadzi (murume/mukadzi), mamiriro ekusvuta (hongu/kwete), nhanho yedzidzo (dhigirii rechikoro chesekondari/dhigirii redhigirii/dhigirii rebachelor), zvinofarirwa nebrand (A/B/C), nezvimwewo. Bvunzo ye chi-square yekuzvimirira inobatsira kupindura mubvunzo mukuru: kugoverwa kwechinhu chimwe chete chakasiyana zvakanyanya here pane zvimwe zvikamu zvekuchinja?
Pfungwa Dzekutanga: Chii chinonzi Kuzvimirira?
Zvikamu zviviri zvinonzi zvakazvimiririra kana ruzivo nezvezvikamu zviri muchimiro chekutanga rusingabatsire kufanotaura zvikamu zviri muchimiro chechipiri. Semuenzaniso, kana "murume kana mukadzi" uye "chido chezvinwiwa" zvakazvimiririra, saka huwandu hwezvido zvezvinwiwa huchafanana mumapoka ese ari maviri evarume nevakadzi. Kusiyana neizvi, kana zviyero zvakasiyana zvakanyanya, zvinoreva kuti zviviri izvi hazvina kuzvimiririra (zvine chekuita nazvo).
Kuedza kwechi-square kwekuzvimirira kunoshanda nekuenzanisa mafrequency akacherechedzwa (data chairo ratinoona) nemafrequencies anotarisirwa (mafrequencies "anofanira kuitika" kana mavariable maviri aya akazvimiririra zvechokwadi). Musiyano uripo pakati pemakoshero akacherechedzwa neanotarisirwa, kukosha kwenhamba ye χ² kunowedzera, uye humbowo hwehukama hwakasimba.
Tafura yeZvingangoitika
Data rebvunzo iyi rakarongwa kuita tafura yezviitiko zvinokonzeresa njodzi, inoratidza mafrequency ekusanganiswa kwezvikamu zviviri. Semuenzaniso, ngationgororei hukama huripo pakati pekusvuta (Hongu/Kwete) uye kuwanda kwekukosora kusingaperi (Hongu/Kwete). Tichagadzira tafura ye2x2 ine huwandu hwevanhu vakapindura musanganiswa wega wega.
Kazhinji, matafura anogona kuva 2×2, 2×3, 3×4, zvichingodaro, zvichienderana nehuwandu hwezvikamu mune chimwe nechimwe chinoshanduka. Chiyedzo che chi-square chekuzvimirira chinogona kushandiswa pamatafura ehukuru hupi zvahwo, chero bedzi mamwe mamiriro ezvinhu akazadzikiswa.
Kuedzwa kweFungidziro
Mubvunzo wechi-square wekuzvimirira, fungidziro ndeiyi:
– H0 (fungidziro isina basa): Zvose zviri zviviri zvakazvimiririra (hapana hukama/hukama).
– H1 (imwe pfungwa): Zvinhu zviviri izvi hazvina kuzvimiririra (kune hukama/hukama).
Chinangwa chebvunzo ndechekuona kana data racho richipa humbowo hwakakwana hwekuramba H0.
Fomura yeChi-Square Statistical
Nhamba yekuedza chi-square inoverengwa uchishandisa fomura:
\[
\chi^2 = \huwandu \frac{(O_{ij} - E_{ij})^2}{E_{ij}}
\]
Information:
– \(O_{ij}\) ndiyo nguva yekucherechedza mumutsara-i wesero uye mukoramu-j.
– \(E_{ij}\) ndiyo frequency inotarisirwa musero re row-i ne column-j.
Mafambiro anotarisirwa anoverengerwa kubva pahuwandu hwemutsara uye huwandu hwekoramu:
\[
E_{ij} = \frac{(\text{Total row i}) \times (\text{Total column j})}{\text{Grand total}}
\]
Fomura iyi inoratidza zvinotarisirwa kuitika kana kugoverwa kwemutsara wega wega nekoramu kusina kukanganisana (kwaive kwakazvimirira).
Dhigirii reRusununguko
Madhigirii erusununguko (df) ebvunzo iyi anotemerwa nehukuru hwetafura:
\[
df = (r – 1)(c – 1)
\]
ne:
– \(r\) = nhamba yemitsara (chikamu chekutanga chinoshanduka)
– \(c\) = nhamba yemakoramu (chikamu chechipiri chinoshanduka)
Madhigirii erusununguko anokanganisa chimiro chekugoverwa kwechi-square chinoshandiswa kuona p-value.
Matanho Ekuita Bvunzo reChi-Square Independence
Zvinotevera ndizvo zvinotevedzana zvekuita bvunzo iyi:
1. Ronga data racho mufurafura yezviitiko zvinongoitika.
Iva nechokwadi chekuti data iri muchimiro chemafrequencies, kwete mapercentages.
2. Verenga frequency inotarisirwa yesero rega rega uchishandisa fomura \(E_{ij}\).
3. Verenga kukosha kweχ² nekupfupisa zvikamu zve \((OE)^2/E\) zvemasero ese.
4. Sarudza df uchishandisa \((r-1)(c-1)\).
5. Verenga p-value zvichibva pakugoverwa kwechi-square ne df (kana enzanisa χ² yakaverengerwa netafura χ² padanho rekukosha α, semuenzaniso 0,05).
6. Sarudza zvaunoda kuita.
– Kana p-value ≤ α → kuramba H0 → pane hukama/kuvimbana.
– Kana p-value > α → ikatadza kuramba H0 → hapana humbowo hwehukama.
7. Dudziro yechokwadi.
Tsanangura zvinorehwa nehukama uhwu muongororo iyi, kwete kungoti "zvakakosha" kana kuti "zvisina kukosha."
Muenzaniso weKududzira (Pasina Kuverenga Kwakadzama)
Ngatitii muongorori ari kuongorora hukama huripo pakati pe "nzira yekudzidza" (yakazvimiririra/boka) uye "kupedza kudzidza" (kupasa/kukundikana). Mushure mekuita bvunzo ye chi-square, p-value i0,02. Ne α = 0,05, mhedziso ndeyekuramba H0, zvichiratidza hukama huripo pakati penzira yekudzidza nekupedza kudzidza. Muongorori anofanira kuona kuti ndeapi masero anopa mutsauko mukuru (semuenzaniso, kana kudzidza kweboka kuchiwedzera huwandu hwevapedza kudzidza). Mukuita, ongororo inogona kuwedzerwa nekuongorora ma residues akajairwa kana saizi dzemhedzisiro.
Mitemo Nemafungiro Akakosha
Kunyange zvazvo chi-square isiri parametric, bvunzo iyi ine zvinodiwa zvakakosha zvakati wandei:
1. Data riri muchimiro chekuverengwa (frequency) uye chidzidzo chimwe nechimwe chinongowira muchikamu chimwe chete (chisingabatanidzwi).
2. Kuongororwa kwakazvimirira, zvichireva kuti munhu mumwe chete anopindura haafanirwe kuverengwa kanopfuura kamwe chete, uye hapana hukama huripo pakati pekuongorora.
3. Mafambiro anotarisirwa akakura zvakakwana. Mutemo wakajairika: huwandu hwakawanda hwe \(E_{ij}\) hunofanira kunge huri ≥ 5. Kana paine masero akawanda ane madiki anotarisirwa, mhinduro dzebvunzo dze chi-square dzinogona kunge dzisiri dzechokwadi.
Pamatafura e2×2 ane mafrequency madiki, imwe nzira inowanzo shandiswa ndeyeFisher's Exact Test. Padata rakabatana (semuenzaniso, risati rasvika pane mumwe munhu ari kupindura), imwe nzira ndeye McNemar's test.
Saizi Yemhedzisiro: Haisi Yekukosha Chete
Mhedzisiro yakakosha hazvirevi hazvo kuti hukama "hwakasimba". Nokudaro, zvinowanzokurudzirwa kutaura nezvehukuru hwemhedzisiro, semuenzaniso:
– Phi (φ) yetafura ye 2×2
- Cramér's V yematafura akakura
V yaCramér inotangira pa0 kusvika pa1, ine kukosha kukuru kunoratidza hukama hwakasimba. Saizi dzemhedzisiro yemishumo inobatsira vaverengi kunzwisisa kusimba kwehukama, kwete kungovapo kwahwo chete.
Zvakanakira uye Zvisina Kukwana
Zvakawandisa:
- Zviri nyore kushandisa paruzivo rwezvikamu.
- Hazvidi kuti munhu afungidzire kuti zvinhu zvakajairika.
- Yakakodzera nzvimbo dzakawanda dzekutsvaga.
Keterbatasan:
- Inonzwisisa saizi yemuenzaniso: mienzaniso mikuru inogona kuita kuti mutsauko mudiki uve "wakakosha".
– Hazviratidzi divi rehukama zvakananga, asi chete kuvapo/kusavapo kwehukama.
– Zvinonetsa kana masero mazhinji aine ma frequency madiki anotarisirwa.
– Dudziro inofanira kutsigirwa nekuongorora kwakawedzerwa (semuenzaniso kutarisa huwandu kana zvasara).
Penutup
Kuyedzwa kwechi-square kwekuzvimirira chishandiso chakakosha chekuongorora kuvapo kana kusavapo kwehukama pakati pezvinhu zviviri zvechikamu. Nekugadzira tafura yezviitiko zvinotarisirwa, kuverenga mafrequency anotarisirwa, uye kuenzanisa nemafrequencies akaonekwa uchishandisa nhamba ye χ², vaongorori vanogona kuyedza fungidziro yekuzvimirira nenzira isina kujeka. Zvisinei, kuti vagadzire ongororo yakasimba, vaongorori vanofanira kupfuura kuona kana paine mhedzisiro yakakosha iripo here kana kwete; vanofanirawo kutaura saizi yemhedzisiro, kuongorora zvinodiwa zvefrequency inotarisirwa, uye kubatanidza zvakawanikwa nemamiriro ezvinhu echidzidzo. Saka, bvunzo yechi-square inova inopfuura kungova maitiro emasvomhu, asi chikamu chekufunga kwesainzi kunobatsira kunzwisisa mapatani ehukama mudata rechikamu.
