Bvunzo yeChi-Square muStatistics: Kunzwisisa uye Kushandisa
Muzviverengero, bvunzo dzakasiyana-siyana dzinoshandiswa kuongorora data uye kuwana mhedziso dzesainzi dzakarurama. Imwe yebvunzo dzakakosha muzviverengero iChi-Square test. Bvunzo iyi ine mashandisirwo akasiyana-siyana, kunyanya mukuongorora data remapoka . Chinyorwa chino chichakurukura zvakadzama bvunzo yeChi-Square, kusanganisira pfungwa dzayo dzekutanga , mhando dzebvunzo dzeChi-Square, maitiro ekushandisa, uye mashandisirwo muminda yakasiyana-siyana.
Pfungwa Dzekutanga dzeChi-Square Test
Chi-Square Test ibvunzo isiri yeparametric inoshandiswa kuona kana paine musiyano mukuru pakati pekugoverwa kwemafrequency anotarisirwa uye anoonekwa mune chimwe chikamu kana kupfuura. Bvunzo iyi yakaunzwa naKarl Pearson muna 1900 uye inowanzoshandiswa muzvidzidzo zvakasiyana-siyana zvesainzi zvinosanganisira data remapoka.
Chiratidzo cheChi-Square chinowanzo nyorwa nebhii rechiGiriki rekuti χ², uye fomura yekutanga yebvunzo iyi ndeiyi:
\[ χ² = Σ \frac{(O_i - E_i)^2}{E_i} \]
ne,
– \(O_i\) ndiyo frequency inoonekwa,
– \(E_i\) ndiyo frequency inotarisirwa.
Mhando dzeChi-Square Tests
1. Chi-Square Goodness of Fit Test: Bvunzo iyi inoshandiswa kuona kana seti yezvakaonekwa inoenderana nekugoverwa kunotarisirwa. Semuenzaniso, munhu angada kuona kana dhayisi rakatenderera rakarurama nekuenzanisa kugoverwa kwemhedzisiro yakaonekwa nekugoverwa kunotarisirwa (rutivi rumwe nerumwe runoratidzika chikamu chimwe muzvitanhatu chenguva).
2. Bvunzo yeChi-Square yeKuzvimiririra: Bvunzo iyi inoshandiswa kuona kana zvinhu zviviri zveboka zvakazvimiririra. Semuenzaniso, bvunzo iyi inogona kushandiswa kuferefeta hukama huripo pakati pemurume nemukadzi nerudzi rwemavara.
3. Chi-Square Test yeHomogeneity: Bvunzo iyi yakafanana nebvunzo yekuzvimirira, asi inoshandiswa kuona kana kugoverwa kwechinhu chinoshanduka pakati pevanhu kana mapoka akasiyana kwakafanana. Boka rega rega rinotarisirwa kuve nekugoverwa kwakafanana kwechinhu chinoshanduka chiri kuyedzwa.
Maitiro Ekuita Bvunzo yeChi-Square
Maitiro ekutanga ekuita bvunzo yeChi-Square anosanganisira matanho akati wandei akakosha:
1. Sarudza Fungidziro: Gadzira fungidziro isina basa (H0) inotaura kuti hapana musiyano pakati pekugoverwa kwakaonekwa nekutarisirwa. Fungidziro yeimwe nzira (H1) inotaura kuti pane musiyano mukuru.
2. Gadzira Tafura Yezviitiko Zvinoitika: Gadzira tafura yezviitiko zvinoitika ine kugoverwa kwehuwandu hwezviitiko zvekucherechedza kwezvikamu zvese zvedata.
3. Kuverenga Mafambiro Anotarisirwa: Pasero rega rega riri mutafura, verenga mafrequency anotarisirwa (E_i). Mafambiro anotarisirwa anobva pakugoverwa kwedzidziso kana pahuwandu hwemuenzaniso wese.
4. Kuverenga Nhamba dzeChi-Square: Shandisa fomura ye χ² kuverenga kukosha kwenhamba dzeChi-Square.
5. Kuziva Dhigirii dzeRusununguko: Dhigirii dzeRusununguko (df) dzeChi-Square test dzinoenderana nerudzi rwebvunzo inoshandiswa. Kuti bvunzo ikwane, df = (nhamba yezvikamu - 1). Kuti bvunzo yerusununguko ishande, df = (nhamba yemitsara - 1) (nhamba yemakoramu - 1).
6. Enzanisa neCritical Value: Enzanisa kukosha kwakaverengerwa kweχ² necritical value yeχ² muChi-Square distribution table zvichibva padanho rekukosha rakatarwa (α).
7. Mhedziso: Kana kukosha kweχ² kwakaverengerwa kwakakura kupfuura kukosha kwakakosha, fungidziro isina basa inorambwa, zvinoreva kuti pane musiyano mukuru pakati pekugoverwa kwakaonekwa nekutarisirwa.
Kushandiswa kweChi-Square Bvunzo
Bvunzo ye chi-square ine mashandisirwo akasiyana-siyana mumabasa akasiyana-siyana ekutsvagisa uye emaindasitiri. Mamwe mashandisirwo anoshanda ebvunzo iyi anosanganisira:
1. Zvemagariro evanhu uye zvepfungwa: Tsvagiridzo pamusoro pemaitiro evanhu inowanzo shandiswa bvunzo yeChi-Square kuona kana paine hukama pakati pezvimiro zvevanhu zvakaita sezera, murume kana mukadzi, dzidzo nemaitiro, zvakaita setsika dzekudya kana tsika dzevaraidzo.
2. Bhizinesi neKushambadzira: Mubasa rebhizinesi, bvunzo yeChi-Square inoshandiswa kutarisa kana paine hukama pakati pezvikamu zviviri zvakaita serudzi rwechigadzirwa nezvinodiwa nevatengi, kana pakati penzvimbo yechitoro nehuwandu hwekutengesa.
3. Hutano Nezvekurapa: Mukutsvaga kwezvekurapa, ongororo yeChi-Square inogona kushandiswa kuongorora ruzivo rwekiriniki, semuenzaniso kuona hukama huripo pakati pemamwe mararamiro uye kuwanda kwezvirwere zvakasiyana.
4. Dzidzo: Kuongororwa kwedata mudzidzo kunowanzo shandiswa bvunzo yeChi-Square kuongorora hukama huripo pakati pezvinhu zvakaita senzira dzekudzidzisa nekubudirira kwevadzidzi, kana pakati peruzivo rwevadzidzi nekubudirira kwedzidzo.
Muenzaniso weChi-Square Test
Ngatitii tinoda kuona kana paine musiyano mukuru pakati pezvinwiwa zvatinofarira (kofi, tii, muto) zvichibva pabasa (mushandi wenguva yakazara, mushandi wenguva pfupi, mudzidzi). Data rakaunganidzwa kubva muongororo yevanhu mazana matatu, uye zvinotevera ndizvo zvakaonekwa patafura yezviitiko:
| | Kofi | Tii | Muto | Zvose |
|————————|——-|—–|——–|——-|
| Mushandi Wenguva Yakazara | 50 | 30 | 20 | 100 |
| Mushandi weNguva Isina Kukwana | 30 | 40 | 30 | 100 |
| Mudzidzi | 20 | 10 | 70 | 100 |
| Huwandu | 100 | 80 | 120 | 300 |
Nekuverenga mafrequency anotarisirwa uye tobva taverenga kukosha kweChi-Square statistical, tinogona kuona kana zvido zvezvinwiwa zvine chekuita nemamiriro ebasa.
Penutup
Bvunzo ye chi-square chishandiso chine simba chekuongorora data rezvikamu. Nekunzwisisa pfungwa huru, mhando dzebvunzo, uye maitiro ekushandisa, vaongorori vanogona kushandisa bvunzo iyi kuongorora fungidziro dzavo munzvimbo dzakasiyana-siyana. Kururama kwebvunzo ye chi-square kunoenderana nekusangana nefungidziro dzakati, dzakadai sehukuru hwakakwana hwemuenzaniso uye kuzvimiririra pakati pezvikamu. Kuburikidza nekunzwisisa kwakakodzera uye kushandiswa, bvunzo ye chi-square inogona kupa ruzivo rwakakosha runotsigira kuita sarudzo dzinotungamirirwa nedata.
