Piv txwv cov lus nug thiab kev sib tham txog kev txheeb xyuas kev sib raug zoo
Kev tshuaj xyuas kev sib raug zoo yog ib txoj kev suav lej siv los txiav txim siab qib kev sib raug zoo ntawm ob qho hloov pauv. Kev tshuaj xyuas no feem ntau siv rau hauv ntau yam kev kawm, suav nrog kev lag luam, kev puas siab puas ntsws, kev kho mob, thiab kev sib raug zoo hauv zej zog, kom nkag siab tias ob qho hloov pauv muaj feem cuam tshuam li cas. Hauv tsab xov xwm no, peb yuav tham txog ntau qhov piv txwv ntawm cov teeb meem thiab kev sib tham los pab nkag siab txog lub tswv yim ntawm kev tshuaj xyuas kev sib raug zoo.
Kev Nkag Siab Txog Kev Tshawb Fawb Txog Kev Sib Raug Zoo
Kev tshuaj xyuas kev sib raug zoo yog siv los ntsuas lub zog thiab kev coj ntawm kev sib raug zoo ntawm ob tus lej hloov pauv. Tus nqi sib raug zoo no feem ntau yog qhia siv tus lej sib raug zoo, uas tuaj yeem sib txawv ntawm -1 txog 1. Cov nqi no tuaj yeem txhais tau raws li hauv qab no:
– +1: Kev sib raug zoo tag nrho. Ob qho tib si txav mus rau tib qho kev taw qhia.
– 0: Tsis muaj kev sib raug zoo. Ob qho kev hloov pauv tsis muaj kev sib raug zoo linear meej.
– -1: Kev sib raug zoo tsis zoo tag nrho. Ob qho tib si txav mus rau hauv kev taw qhia sib txawv.
Tus coefficient correlation uas siv ntau tshaj plaws yog Pearson correlation. Txawm li cas los xij, kuj tseem muaj lwm txoj kev sib raug zoo, xws li Spearman thiab Kendall, uas tsim nyog dua rau cov ntaub ntawv ordinal lossis nonlinear.
Cov Kauj Ruam Tshawb Fawb Txog Kev Sib Raug Zoo
1. Kev Sau Cov Ntaub Ntawv: Sau cov ntaub ntawv rau ob qho kev hloov pauv uas yuav tsum tau soj ntsuam.
2. Kev Pom Cov Ntaub Ntawv: Tsim ib daim duab qhia txog kev sib raug zoo ntawm ob qho hloov pauv.
3. Kev suav ntawm Correlation Coefficient: Xam Pearson, Spearman, lossis Kendall correlation coefficient.
4. Kev Txhais Lus Txog Cov Txiaj Ntsig: Xaus lus txog lub zog thiab kev coj ntawm kev sib raug zoo raws li tus nqi ntawm cov coefficient sib raug zoo.
5. Kev Ntsuas Qhov Tseem Ceeb: Txheeb xyuas seb qhov kev sib raug zoo uas pom tau puas muaj qhov tseem ceeb hauv kev suav lej.
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Lo lus nug 1: Pearson Correlation
Muab cov ntaub ntawv ntawm qhov siab (cm) thiab qhov hnyav (kg) ntawm 5 tus neeg raws li nram no:
| Tus Neeg | Qhov Siab (cm) | Qhov Hnyav (kg) |
|——-|————-|—————|
| Ib | 160 | 55 |
| B | 165 | 60 |
| C | 170 | 65 |
| D | 175 | 70 |
| E | 180 | 75 |
Xam tus coefficient ntawm Pearson correlation rau cov ntaub ntawv.
Kev Sib Tham:
1. Xam Qhov Nruab Nrab:
– Qhov siab nruab nrab (X̄) = (160 + 165 + 170 + 175 + 180) / 5 = 170
– Qhov hnyav nruab nrab (Ȳ) = (55 + 60 + 65 + 70 + 75) / 5 = 65
2. Xam Qhov Sib Txawv ntawm Qhov Nruab Nrab:
– Kev sib txawv siab: (160 – 170), (165 – 170), (170 – 170), (175 – 170), (180 – 170)
– Kev hloov pauv loj heev: (55 – 65), (60 – 65), (65 – 65), (70 – 65), (75 – 65)
3. Xam Qhov Khoom Sib Txawv:
– (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
Tag Nrho = 100 + 25 + 0 + 25 + 100 = 250
4. Xam Qhov Sib Npaug ntawm Qhov Sib Npaug:
– Qhov siab: (160-170)², (165-170)², (170-170)², (175-170)², (180-170)²
– Qhov hnyav: (55-65)², (60-65)², (65-65)², (70-65)², (75-65)²
Rau qhov siab:
– (160-170)² = 100
– (165-170)² = 25
– (170-170)² = 0
– (175-170)² = 25
– (180-170)² = 100
Tag Nrho = 100 + 25 + 0 + 25 + 100 = 250
Rau qhov hnyav:
– (55-65)² = 100
– (60-65)² = 25
– (65-65)² = 0
– (70-65)² = 25
– (75-65)² = 100
Tag Nrho = 100 + 25 + 0 + 25 + 100 = 250
5. Xam tus lej sib raug zoo ntawm Pearson:
\[
r = \frac{\sum ((X – X̄)(Y – Ȳ))}{\sqrt{\sum (X – X̄)² \sum (Y – Ȳ)²}}
\]
\[
r = \frac{250}{\sqrt{250 \times 250}} = \frac{250}{250} = 1
\]
Kev Txhais Lus: Tus nqi Pearson correlation coefficient ntawm 1 qhia txog kev sib raug zoo zoo meej ntawm qhov siab thiab qhov hnyav.
Lo lus nug 2: Kev sib raug zoo ntawm Spearman
Muab cov ntaub ntawv qeb duas ntawm ob qho kev hloov pauv raws li nram no:
| Tus Neeg | Hloov Pauv X | Hloov Pauv Y |
|——-|————|————|
| Ib | 1 | 3 |
| B | 2 | 1 |
| C | 3 | 4 |
| D | 4 | 2 |
| E | 5 | 5 |
Xam tus coefficient ntawm Spearman correlation raws li cov ntaub ntawv.
Kev Sib Tham:
1. Kev suav qhov sib txawv ntawm qib (d):
- Rau Qib X thiab Y:
– A: 1 – 3 = -2
– B: 2 – 1 = 1
– C: 3 – 4 = -1
– D: 4 – 2 = 2
– E: 5 – 5 = 0
2. Kev suav ntawm Square ntawm qhov sib txawv hauv qeb duas (d²):
– (-2)² = 4
– (1)² = 1
– (-1)² = 1
– (2)² = 4
– (0)² = 0
Tag Nrho (Σd²) = 4 + 1 + 1 + 4 + 0 = 10
3. Xam Tus Coefficient ntawm Spearman Correlation:
\[
r_s = 1 – \frac{6 \sum d^2}{n(n^2 – 1)}
\]
\[
r_s = 1 – \frac{6 \times 10}{5(5^2 – 1)} = 1 – \frac{60}{120} = 1 – 0.5 = 0.5
\]
Kev Txhais Lus: Tus nqi ntawm Spearman's correlation coefficient ntawm 0.5 qhia txog kev sib raug zoo nruab nrab ntawm cov hloov pauv X thiab Y.
Xaus
Los ntawm cov piv txwv saum toj no, peb pom tias kev tshuaj xyuas kev sib raug zoo tuaj yeem siv los txiav txim siab lub zog thiab kev coj ntawm kev sib raug zoo ntawm ob qho hloov pauv. Tus lej sib raug zoo Pearson yog siv rau cov ntaub ntawv lej nrog kev sib raug zoo linear, thaum tus lej sib raug zoo Spearman yog siv rau cov ntaub ntawv ordinal lossis nonlinear. Los ntawm kev nkag siab thiab kev paub txog cov txheej txheem no, peb tuaj yeem tshuaj xyuas cov ntaub ntawv zoo dua thiab ua cov lus xaus tseeb dua hauv ntau qhov kev kawm.
