Isihloko: Isibonelo Semibuzo Yengxoxo Yokuhlola Okuphambene
Ukuhlolwa kwesikwele se-chi (ukuhlolwa kwe-χ²) kuyindlela yezibalo esetshenziselwa ukuhlola imibono mayelana nokusatshalaliswa kwemvamisa kwezinguquko zesigaba. Lokhu kuhlolwa kuwusizo kakhulu ekunqumeni ukuthi kukhona yini ubudlelwano obubalulekile phakathi kwezinguquko ezimbili ezizimele zesigaba. Lesi sihloko sizoxoxa ngomqondo oyisisekelo wokuhlolwa kwesikwele se-chi futhi sinikeze imibuzo eminingana yezibonelo kanye nengxoxo yazo.
I-Pendahuluan
Ukuhlolwa kwe-Chi-Square kungenye yezivivinyo ezingezona eze-parametric ezisetshenziswa kakhulu ekuhlaziyweni kwedatha yezigaba. Inhloso yayo eyinhloko ukuhlola ubukhulu bomehluko phakathi kokusatshalaliswa okubonwayo kanye nokusatshalaliswa okulindelekile ngokusekelwe ku-null hypothesis.
I-null hypothesis (H0) ekuhlolweni kwe-cross-reference ivame ukuthi akukho buhlobo phakathi kwezinguquko ezimbili zesigaba, kuyilapho i-alternative hypothesis (H1) ithi kukhona ubudlelwano phakathi kwezinguquko ezimbili.
Imiqondo Eyisisekelo Yokuhlolwa Kwe-Chi-Square
Okokuqala, ake siqonde imiqondo eyisisekelo esivivinyweni se-Chi-Square:
1. Imvamisa Yokubuka (O): Lena inani lokubuka okubonayo esigabeni esithile sedatha.
2. Imvamisa Elindelekile (E): Lena inani lokubonwa okulindele esigabeni esithile ngokusekelwe ekusatshalalisweni kwethiyori noma i-null hypothesis.
3. Ifomula Yokuhlola Ye-Chi-Square:
\[
\chi² = \ isamba \frac{(O_i – E_i)²}{E_i}
\]
Lapho i-\(O_i\) ingumvamisa obonwayo kanye ne-\(E_i\) ingumvamisa olindelekile wesigaba se-i-th.
4. Amadigri Enkululeko (df): Lokhu kubalwa njenge (inani lemigqa - 1) (inani lamakholomu - 1) yethebula le-contingency.
5. Izinga Lokubaluleka (\(\alpha\)): Umkhawulo osetshenziswa ukunquma ukuthi imiphumela yokuhlolwa kwezibalo ibalulekile yini. Ngokuvamile, u-0,05 noma u-5% usetshenziswa njengezinga lokubaluleka.
Imibuzo Eyisibonelo Nengxoxo
Ake sibheke isifundo secala ukuze siqonde ukusetshenziswa kokuhlolwa kwe-Chi-Square.
Isibonelo Sombuzo 1:
Kwenziwe ucwaningo ukuze kutholakale ukuthi kukhona yini ubudlelwano phakathi kwezintandokazi zohlobo lomculo kanye nezinga lemfundo. Idatha elandelayo yaqoqwa kwabaphenduli abangu-200.
| I-Pop | I-Rock | I-Jazz | Ingqikithi |
|——————— |—–|——|——-|——-|
| Isikole Samabanga Aphezulu | 20 | 30 | 50 | 100 |
| Abafundi abaphothule iziqu | 35 | 25 | 40 | 100 |
| Isiyonke | 55 | 55 | 90 | 200 |
Umbuzo: Ingabe kukhona ubudlelwano phakathi kohlobo lomculo oluthandayo kanye nezinga lemfundo?
Izinyathelo Zokuxoxisana:
1. Thola i-Hypothesis:
– H0: Akukho buhlobo phakathi kokukhethwa kohlobo lomculo kanye nezinga lemfundo.
– H1: Kukhona ubudlelwano phakathi kwezintandokazi zohlobo lomculo kanye nezinga lemfundo.
2. Bala Imvamisa Elindelekile (E):
Bala imvamisa elindelekile yeseli ngayinye yethebula le-contingency. Ifomula yokubala u-E ithi:
\[
E_{ij} = \frac{(\text{Total Row}_i \times \text{Total Column}_j)}{\text{Grand Total}}
\]
Isibonelo, imvamisa elindelekile yabafundi besikole samabanga aphezulu abathanda i-Pop yile:
\[
E_{SMA, Pop} = \frac{(100 \izikhathi ezingu-55)}{200} = 27.5
\]
Ngendlela efanayo, sibala wonke amaseli:
| I-Pop | I-Rock | I-Jazz |
|—————— |—–|——|——-|
| Isikole Samabanga Aphezulu | 27.5 | 27.5 | 45 |
| Isiqu | 27.5 | 27.5 | 45 |
3. Bala i-Chi-Square (χ²):
Ukusebenzisa ifomula:
\[
\chi² = \samba \frac{(O – E)²}{E}
\]
Bala umnikelo weseli ngayinye kanye nesamba:
– Kwesikole Samabanga Aphezulu kanye ne-Pop:
\[
\chi²_{SMA, Pop} = \frac{(20 – 27.5)²}{27.5} \cishe kube ngu-2.04
\]
– Izibalo ezifanayo zenziwa ngenhlanganisela ngayinye:
\[
\chi² = 2.04 + 0.23 + 0.56 + 0.23 + 0.23 + 0 + 1.96 = 5.25
\]
4. Bala amazinga enkululeko:
\[
df = (3-1) \izikhathi (3-1) = 4
\]
5. Thola Izindinganiso Ezibalulekile Nezinqumo:
Sisebenzisa ithebula lokusabalalisa le-Chi-Square eline-\(\alpha = 0.05\) kanye ne-df = 4, inani elibalulekile lingu-9.488. Kusukela ku-5.25 < 9.488, sehluleka ukwenqaba i-H0. Isiphetho: Akukho buhlobo obubalulekile ngokwezibalo phakathi kokukhethwa kohlobo lomculo kanye nezinga lemfundo ezingeni lokubaluleka elingu-0.05. Isiphetho Isivivinyo se-Chi-Square siyithuluzi eliwusizo kakhulu lokuhlaziywa kwedatha ngokwezigaba emikhakheni eyahlukene yocwaningo. Ngokuqonda ukuthi ungabala kanjani futhi uhlole imiphumela yesivivinyo se-Chi-Square, abacwaningi bangenza iziphetho ezingcono mayelana nedatha yabo. Ucwaningo lwecala oluxoxwe ngalo lunikeza umfanekiso osebenzayo wokuthi isivivinyo se-Chi-Square sisebenza kanjani nokuthi singahumusha kanjani imiphumela. Ngaphezu kokuhlaziywa ngesandla, ukusetshenziswa kwesofthiwe yezibalo njenge-SPSS noma i-R nakho kuvamile ekusebenzeni ukuze kube lula ukubala nokuhlaziya okwengeziwe. Ezisetshenzisweni zangempela, ngaphezu kokunaka imiphumela yezibalo, kubalulekile ukucabangela umongo wesifundo nokuhumusha izibalo ngokuhlakanipha.
