Musoro: Muenzaniso weMibvunzo yeKukurukurirana paKubvunzurudza
Bvunzo yechi-square (χ² test) inzira inoshandiswa kuyedza fungidziro pamusoro pekugoverwa kwezviyero zvechikamu. Bvunzo iyi inobatsira zvikuru pakuona kana paine hukama hwakakosha pakati pezviyero zviviri zvechikamu zvakazvimiririra. Chinyorwa chino chichakurukura pfungwa huru yebvunzo yechi-square uye chichapa mienzaniso yakati wandei yemibvunzo nehurukuro yavo.
Pendauluan
Bvunzo yeChi-Square ndeimwe yebvunzo dzisiri dzeparametric dzinoshandiswa zvakanyanya pakuongorora data remapoka. Chinangwa chayo chikuru ndechekuedza musiyano uripo pakati pekugoverwa kwakaonekwa nekugoverwa kunotarisirwa zvichibva pane fungidziro isina basa.
Pfungwa isina chinhu (H0) mubvunzo yekubatanidza mativi inowanzo taura kuti hapana hukama pakati pezvinhu zviviri zveboka, nepo imwe pfungwa (H1) ichiti pane hukama pakati pezvinhu zviviri izvi.
Pfungwa Dzekutanga dzeChi-Square Test
Kutanga, ngatinzwisisei dzimwe pfungwa huru mubvunzo yeChi-Square:
1. Kuwanda kweKucherechedza (O): Iyi ndiyo nhamba yezvaunoona muchikamu chakati chedata.
2. Kuwanda Kwenguva Inotarisirwa (E): Iyi ndiyo nhamba yezvaunotarisira muchikamu chakati zvichibva pakugoverwa kwedzidziso kana kuti null hypothesis.
3. Fomura Yekuyedza yeChi-Square:
\[
\chi² = \sum \frac{(O_i - E_i)²}{E_i}
\]
Apo \(O_i\) iri frequency inoonekwa uye \(E_i\) iri frequency inotarisirwa yechikamu che i-th.
4. Dhigirii reRusununguko (df): Izvi zvinoverengerwa se (nhamba yemitsara - 1) (nhamba yemakoramu - 1) yetafura yezviitiko zvinotarisirwa.
5. Nhanho yeKukosha (\(\alpha\)): Muganho unoshandiswa kuona kana mhedzisiro yebvunzo yehuwandu hwehuwandu yakakosha. Kazhinji, 0,05 kana 5% inoshandiswa senhanho yekukosha.
Mibvunzo yemuenzaniso nekukurukurirana
Ngatitarisei chidzidzo chemuenzaniso kuti tinzwisise kushandiswa kwebvunzo yeChi-Square.
Muenzaniso Mubvunzo 1:
Ongororo yakaitwa kuti ione kana paine hukama pakati pezvinodiwa nenziyo dzemimhanzi nedanho redzidzo. Data rinotevera rakaunganidzwa kubva kuvanhu mazana maviri vakapindura.
| Pop | Rock | Jazz | Zvose |
|—————— |—–|——|——-|——-|
| Chikoro Chesekondari | 20 | 30 | 50 | 100 |
| Vadzidzi veUndergraduate | 35 | 25 | 40 | 100 |
| Huwandu | 55 | 55 | 90 | 200 |
Mubvunzo: Pane hukama here pakati pemhando yemimhanzi yaunofarira nedanho redzidzo?
Matanho Ekukurukurirana:
1. Tsvaga Fungidziro:
– H0: Hapana hukama huripo pakati pemhando yemimhanzi inofarirwa nedanho redzidzo.
– H1: Pane hukama huripo pakati pezvinodiwa nerudzi rwemimhanzi nedanho redzidzo.
2. Verenga Nguva Inotarisirwa (E):
Verenga frequency inotarisirwa yesero rega rega retafura yezviitiko zvinongoitika. Fomura yekuverenga E ndeiyi:
\[
E_{ij} = \frac{(\text{Total Row}_i \times \text{Total Column}_j)}{\text{Grand Total}}
\]
Semuenzaniso, kangani inotarisirwa kuvadzidzi vechikoro chesekondari vanoda Pop ndeiyi:
\[
E_{SMA, Pop} = \frac{(100 \kawa 55)}{200} = 27.5
\]
Nenzira imwecheteyo, tinoverenga masero ese:
| Pop | Rock | Jazz |
|—————— |—–|——|———-|
| Chikoro Chesekondari | 27.5 | 27.5 | 45 |
| Dhigirii reBachelor | 27.5 | 27.5 | 45 |
3. Verenga Chi-Square (χ²):
Kushandisa fomura:
\[
\chi² = \sum \frac{(O - E)²}{E}
\]
Verenga mupiro wesero rega rega uye huwandu hwese:
- Yechikoro chesekondari nePop:
\[
\chi²_{SMA, Pop} = \frac{(20 – 27.5)²}{27.5} \inenge 2.04
\]
- Kuverengera kwakafanana kunoitwa pamusanganiswa wega wega:
\[
\chi² = 2.04 + 0.23 + 0.56 + 0.23 + 0.23 + 0 + 1.96 = 5.25
\]
4. Verenga Dhigirii reRusununguko:
\[
df = (3-1) \nguva (3-1) = 4
\]
5. Sarudza Maitiro Akakosha uye Zvisarudzo:
Tichishandisa tafura yekugovera yeChi-Square ine \(\alpha = 0.05\) uye df = 4, kukosha kwakakosha i9.488. Kubva pa5.25 < 9.488, tinokundikana kuramba H0. Mhedziso: Hapana hukama hwakakosha pakati pezvinodiwa zvemhando yemimhanzi nedanho redzidzo padanho rekukosha kwe0.05. Mhedziso Bvunzo yeChi-Square chishandiso chinobatsira zvikuru pakuongorora data muzvikamu zvakasiyana-siyana zvekutsvagisa. Nekunzwisisa maitiro ekuverenga nekuongorora mhedzisiro yebvunzo yeChi-Square, vaongorori vanogona kuita mhedziso dziri nani nezve data ravo. Chidzidzo chemuenzaniso chakakurukurwa chinopa muenzaniso unoshanda wekuti bvunzo yeChi-Square inoshanda sei uye kuti ingadudzira sei mhedzisiro. Kuwedzera pakuongorora nemaoko, kushandiswa kwesoftware yenhamba dzakadai seSPSS kana R kwakajairikawo mukuita kuti kuve nyore kuverenga nekuongorora kumwe. Mumashandisirwo chaiwo, pamusoro pekuteerera mhedzisiro yenhamba, zvakakosha kufunga nezvemamiriro ekudzidza uye kududzira nhamba nekuchenjera.
