Mehlala ea Lipotso le Puisano ea Tlhahlobo ea Likamano
Tlhahlobo ea kamano ke mokhoa oa lipalo-palo o sebelisoang ho fumana hore na kamano e pakeng tsa mefuta e 'meli e fapana hakae. Tlhahlobo ena e sebelisoa khafetsa mafapheng a fapaneng, ho kenyeletsoa moruo, kelello, bongaka le sosioloji, ho utloisisa hore na mefuta e 'meli e amana haufi hakae. Sehloohong sena, re tla buisana ka mathata a 'maloa a mehlala le lipuisano ho thusa ho utloisisa mohopolo oa tlhahlobo ea kamano.
Ho Utloisisa Tlhahlobo ea Likamano
Tlhahlobo ea kamano e sebelisoa ho lekanya matla le tataiso ea kamano pakeng tsa li-variable tse peli tsa lipalo. Boleng bona ba kamano hangata bo hlahisoa ho sebelisoa coefficient ea kamano, e ka tlohang ho -1 ho isa ho 1. Boleng bona bo ka hlalosoa ka tsela e latelang:
– +1 : Kamano e phethahetseng e ntle. Diphetoho ka bobedi di tsamaya ka lehlakoreng le le leng.
– 0 : Ha ho na kamano. Diphetoho tsena tse pedi ha di na kamano e hlakileng ya mola.
– -1 : Kamano e phethahetseng e fosahetseng. Diphetoho ka bobedi di tsamaya ka mahlakoreng a fapaneng.
Coefficient e sebelisoang haholo ea khokahano ke coefficient ea Pearson. Leha ho le joalo, ho boetse ho na le mekhoa e meng ea khokahano, joalo ka Spearman le Kendall, e loketseng haholoanyane data ea ordinal kapa e seng ea linear.
Mehato ea Tlhahlobo ea Kamano
1. Pokello ea Lintlha: Bokella lintlha bakeng sa mefuta e 'meli e lokelang ho hlahlojoa.
2. Pono ea Lintlha: Etsa moralo oa ho hasanya ho bona mokhoa oa kamano lipakeng tsa li-variable tse peli.
3. Palo ea Coefficient ea Kamano: Bala coefficient ea kamano ea Pearson, Spearman, kapa Kendall.
4. Tlhaloso ea Liphetho: Qetella matla le tataiso ea kamano ho latela boleng ba coefficient ea kamano.
5. Teko ea Bohlokoa: Fumana hore na kamano e fumanoeng e bohlokoa ka lipalo-palo.
Lipotso tsa Mehlala le Puisano
Potso ea 1: Kamano ea Pearson
Ho fanoe ka lintlha tse mabapi le bolelele (cm) le boima (kg) ba batho ba 5 ka tsela e latelang:
| Motho | Bolelele (cm) | Boima (kg) |
|——-|———--|————|
| A | 160 | 55 |
| B | 165 | 60 |
| C | 170 | 65 |
| D | 175 | 70 |
| E | 180 | 75 |
Bala coefficient ea kamano ea Pearson bakeng sa data.
Puisano:
1. Ho Bala Karolelano:
– Bolelele bo tloaelehileng (X̄) = (160 + 165 + 170 + 175 + 180) / 5 = 170
– Boima bo tloaelehileng (Ȳ) = (55 + 60 + 65 + 70 + 75) / 5 = 65
2. Ho Bala Phapang ho tloha ho Meeli:
– Ho kheloha ho hoholo: (160 – 170), (165 – 170), (170 – 170), (175 – 170), (180 – 170)
– Ho kheloha ho tebileng: (55 – 65), (60 – 65), (65 – 65), (70 – 65), (75 – 65)
3. Ho Bala Sehlahisoa sa ho Kgeloha:
– (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
Kakaretso = 100 + 25 + 0 + 25 + 100 = 250
4. Ho Bala Sekwere sa ho Kgeloha:
– Bophahamo: (160-170)², (165-170)², (170-170)², (175-170)², (180-170)²
– Boima: (55-65)², (60-65)², (65-65)², (70-65)², (75-65)²
Bakeng sa bophahamo:
– (160-170)² = 100
– (165-170)² = 25
– (170-170)² = 0
– (175-170)² = 25
– (180-170)² = 100
Kakaretso = 100 + 25 + 0 + 25 + 100 = 250
Bakeng sa boima ba 'mele:
– (55-65)² = 100
– (60-65)² = 25
– (65-65)² = 0
– (70-65)² = 25
– (75-65)² = 100
Kakaretso = 100 + 25 + 0 + 25 + 100 = 250
5. Ho Bala Sekhahla sa Kamano ea Pearson:
\[
r = \frac{\sum ((X – X̄)(Y – Ȳ))}{\sqrt{\sum (X – X̄)² \sum (Y – Ȳ)²}}
\]
\[
r = \frac{250}{\sqrt{250 \times 250}} = \frac{250}{250} = 1
\]
Tlhaloso: Boleng ba coefficient ea kamano ea Pearson ea 1 bo bontša kamano e phethahetseng e ntle pakeng tsa bolelele le boima.
Potso ea 2: Kamano ea Spearman
Ha ho fanoe ka lintlha tsa maemo a li-variable tse peli ka tsela e latelang:
| Motho | Phetoho X | Phetoho Y |
|——-|————|———|
| A | 1 | 3 |
| B | 2 | 1 |
| C | 3 | 4 |
| D | 4 | 2 |
| E | 5 | 5 |
Bala coefficient ea kamano ea Spearman ho latela lintlha.
Puisano:
1. Palo ea Phapang ea Maemo (d):
– Bakeng sa maemo a X le Y:
– A: 1 – 3 = -2
– B: 2 – 1 = 1
– C: 3 – 4 = -1
– D: 4 – 2 = 2
– E: 5 – 5 = 0
2. Palo ea Sekwere sa Phapang ho Maemo (d²):
– (-2)² = 4
– (1)² = 1
– (-1)² = 1
– (2)² = 4
– (0)² = 0
Kakaretso (Σd²) = 4 + 1 + 1 + 4 + 0 = 10
3. Ho Bala Sekhahla sa Kamano ea Spearman:
\[
r_s = 1 – \frac{6 \sum d^2}{n(n^2 – 1)}
\]
\[
r_s = 1 – \frac{6 \makgetlo a 10}{5(5^2 – 1)} = 1 – \frac{60}{120} = 1 – 0.5 = 0.5
\]
Tlhaloso: Boleng ba coefficient ea kamano ea Spearman ba 0.5 bo bontša kamano e mahareng e ntle pakeng tsa mefuta-futa X le Y.
Qetello
Ho tsoa mehlaleng e kaholimo, re bona kamoo tlhahlobo ea kamano e ka sebelisoang ho fumana matla le tataiso ea kamano pakeng tsa mefuta e 'meli. Palo ea kamano ea Pearson e sebelisoa bakeng sa data ea lipalo e nang le kamano e otlolohileng, ha palo ea kamano ea Spearman e sebelisoa bakeng sa data ea ordinal kapa e seng ea mola. Ka ho utloisisa le ho tseba mekhoa ena, re ka sekaseka data hamolemo le ho etsa liqeto tse nepahetseng haholoanyane masimong a fapaneng a thuto.
