Imibuzo Yezibonelo kanye Nengxoxo Yokuhlaziywa Kobudlelwano
Ukuhlaziywa kobudlelwano kuyindlela yezibalo esetshenziselwa ukunquma izinga lobudlelwano phakathi kwezinto ezimbili eziguquguqukayo. Lokhu kuhlaziywa kuvame ukusetshenziswa emikhakheni ehlukahlukene, okuhlanganisa ezomnotho, ezengqondo, ezokwelapha, kanye nezenhlalo, ukuqonda ukuthi izinto ezimbili eziguquguqukayo zihlobene kangakanani. Kulesi sihloko, sizoxoxa ngezinkinga eziningana zezibonelo kanye nezingxoxo ukusiza ukuqonda umqondo wokuhlaziywa kobudlelwano.
Ukuqonda Ukuhlaziywa Kobudlelwano
Ukuhlaziywa kobudlelwano kusetshenziselwa ukukala amandla kanye nesiqondiso sobudlelwano phakathi kwezinguquko ezimbili zezinombolo. Leli nani lobudlelwano livame ukuvezwa kusetshenziswa i-coefficient yobudlelwano, engasukela ku--1 kuya ku-1. Lawa manani angahunyushwa kanje:
– +1 : Ukuxhumana okuhle okuphelele. Zombili iziguquguquko zihamba ngendlela efanayo.
– 0 : Akukho ukuhlobana. Lezi ziguquguquko ezimbili azinabo ubudlelwano obucacile obuqondile.
– -1 : Ukuxhumana okungalungile okuphelele. Zombili iziguquguquko zihamba ngezindlela eziphambene.
I-coefficient yokuxhumana esetshenziswa kakhulu yi-Pearson correlation. Kodwa-ke, kunezinye izindlela zokuxhumana, njenge-Spearman ne-Kendall, ezifaneleka kakhulu kudatha ye-ordinal noma ye-nonlinear.
Izinyathelo Zokuhlaziya Ubudlelwano
1. Ukuqoqwa Kwedatha: Qoqa idatha yeziguquguquko ezimbili ezizohlaziywa.
2. Ukubona Idatha: Dala icebo lokuhlakaza ukuze ubone iphethini yobudlelwano phakathi kweziguquguquko ezimbili.
3. Ukubalwa kwe-Correlation Coefficient: Bala i-Pearson, i-Spearman, noma i-Kendall coefficient yokuxhumana.
4. Ukuchazwa Kwemiphumela: Phetha amandla kanye nesiqondiso sobudlelwano ngokusekelwe enanini le-coefficient yokuxhumana.
5. Ukuhlolwa Kokubaluleka: Thola ukuthi ukuhlangana okutholiwe kubalulekile yini ngokwezibalo.
Imibuzo Eyisibonelo Nengxoxo
Umbuzo 1: Ubudlelwano bukaPearson
Kunikezwe idatha ngokuphakama (cm) kanye nesisindo (kg) sabantu aba-5 kanje:
| Umuntu | Ukuphakama (cm) | Isisindo (kg) |
|——-|————-|———|
| A | 160 | 55 |
| B | 165 | 60 |
| C | 170 | 65 |
| D | 175 | 70 |
| E | 180 | 75 |
Bala i-coefficient yokuxhumana kwe-Pearson yedatha.
Ingxoxo:
1. Ukubala Isilinganiso:
– Ukuphakama okumaphakathi (X̄) = (160 + 165 + 170 + 175 + 180) / 5 = 170
– Isisindo esimaphakathi (Ȳ) = (55 + 60 + 65 + 70 + 75) / 5 = 65
2. Ukubala Ukuphambuka Kusuka Ku-Mean:
– Ukuphambuka okuphezulu: (160 – 170), (165 – 170), (170 – 170), (175 – 170), (180 – 170)
– Ukuphambuka okukhulu: (55 – 65), (60 – 65), (65 – 65), (70 – 65), (75 – 65)
3. Ukubala Umkhiqizo Wokuphambuka:
– (160-170)(55-65) = 10 10 = 100
– (165-170)(60-65) = 5 5 = 25
– (170-170)(65-65) = 0 0 = 0
– (175-170)(70-65) = 5 5 = 25
– (180-170)(75-65) = 10 10 = 100
Isamba = 100 + 25 + 0 + 25 + 100 = 250
4. Ukubala Isikwele Sokuphambuka:
– Ukuphakama: (160-170)², (165-170)², (170-170)², (175-170)², (180-170)²
– Isisindo: (55-65)², (60-65)², (65-65)², (70-65)², (75-65)²
Ukuphakama:
– (160-170)² = 100
– (165-170)² = 25
– (170-170)² = 0
– (175-170)² = 25
– (180-170)² = 100
Isamba = 100 + 25 + 0 + 25 + 100 = 250
Ngesisindo:
– (55-65)² = 100
– (60-65)² = 25
– (65-65)² = 0
– (70-65)² = 25
– (75-65)² = 100
Isamba = 100 + 25 + 0 + 25 + 100 = 250
5. Ukubala i-Pearson Correlation Coefficient:
\[
r = \frac{\sum ((X – X̄)(Y – Ȳ))}{\sqrt{\sum (X – X̄)² \sum (Y – Ȳ)²}}
\]
\[
r = \frac{250}{\sqrt{250 \izikhathi ezingu-250}} = \frac{250}{250} = 1
\]
Incazelo: Inani le-Pearson correlation coefficient elingu-1 libonisa ubudlelwano obuhle obuphelele phakathi kokuphakama nesisindo.
Umbuzo 2: Ubudlelwano be-Spearman
Njengoba kunikezwe idatha yezinga leziguquguquko ezimbili kanje:
| Umuntu | Oguquguqukayo X | Oguquguqukayo Y |
|——-|————|———|
| A | 1 | 3 |
| B | 2 | 1 |
| C | 3 | 4 |
| D | 4 | 2 |
| E | 5 | 5 |
Bala i-coefficient yokuxhumana kwe-Spearman ngokusekelwe kudatha.
Ingxoxo:
1. Ukubalwa Komehluko Wezinga (d):
- Ukuze uthole izinga X kanye no-Y:
– A: 1 – 3 = -2
– B: 2 – 1 = 1
– C: 3 – 4 = -1
– D: 4 – 2 = 2
– E: 5 – 5 = 0
2. Ukubalwa Kwesikwele Somehluko Ekubekweni (d²):
– (-2)² = 4
– (1)² = 1
– (-1)² = 1
– (2)² = 4
– (0)² = 0
Isamba (Σd²) = 4 + 1 + 1 + 4 + 0 = 10
3. Ukubala i-Spearman Correlation Coefficient:
\[
r_s = 1 – \frac{6 \sum d^2}{n(n^2 – 1)}
\]
\[
r_s = 1 – \frac{6 \izikhathi 10}{5(5^2 – 1)} = 1 – \frac{60}{120} = 1 – 0.5 = 0.5
\]
Incazelo: Inani le-coefficient yokuxhumana likaSpearman elingu-0.5 libonisa ubudlelwano obuhle obuphakathi kweziguquguquko u-X no-Y.
Isiphetho
Kusukela ezibonelweni ezingenhla, sibona indlela ukuhlaziywa kobudlelwano okungasetshenziswa ngayo ukunquma amandla kanye nesiqondiso sobudlelwano phakathi kweziguquguquko ezimbili. I-Pearson correlation coefficient isetshenziselwa idatha yezinombolo enobudlelwano obuqondile, kuyilapho i-Spearman correlation coefficient isetshenziselwa idatha ye-ordinal noma engeyona eqondile. Ngokuqonda nangokuqonda lawa masu, singahlaziya kangcono idatha futhi senze iziphetho ezinembile emikhakheni ehlukahlukene yokufunda.
