Su'aalo Tusaale ah iyo Doodo ku saabsan Falanqaynta Xiriirka
Falanqaynta isku xidhka waa hab tirakoob oo loo isticmaalo in lagu go'aamiyo heerka xiriirka ka dhexeeya laba doorsoome. Falanqayntan waxaa si joogto ah loogu isticmaalaa qaybo kala duwan, oo ay ku jiraan dhaqaalaha, cilmi-nafsiga, daawada, iyo cilmiga bulshada, si loo fahmo sida ay isugu dhow yihiin laba doorsoome. Maqaalkan, waxaan kaga hadli doonnaa dhowr tusaale oo dhibaatooyin iyo doodo ah si aan u fahanno fikradda falanqaynta isku xidhka.
Fahmidda Falanqaynta Xidhiidhka
Falanqaynta isku xidhka waxaa loo isticmaalaa in lagu cabbiro xoogga iyo jihada xiriirka ka dhexeeya laba doorsoome oo tirooyin ah. Qiimahan isku xidhka waxaa badanaa lagu muujiyaa iyadoo la adeegsanayo isku xidhka isku xidhka, kaas oo u dhexeeya -1 ilaa 1. Qiimayaashan waxaa loo fasiri karaa sidan soo socota:
– +1: Isku xidhnaan togan oo dhammaystiran. Labada doorsoomeba waxay u socdaan jiho isku mid ah.
– 0: Xiriir la'aan ma jirto. Labada doorsoome ma laha xiriir toosan oo cad.
– -1: Isku xidhnaan taban oo qumman. Labada doorsoomeba waxay u socdaan jihooyin iska soo horjeeda.
Isku-xidhka isku-xidhka ee ugu badan ee la isticmaalo waa isku-xidhka Pearson. Si kastaba ha ahaatee, waxaa sidoo kale jira habab kale oo isku-xidhka ah, sida Spearman iyo Kendall, kuwaas oo ku habboon xogta caadiga ah ama kuwa aan tooska ahayn.
Tallaabooyinka Falanqaynta Isku-xidhka
1. Ururinta Xogta: Ururinta xogta labada doorsoome ee la falanqeynayo.
2. Muuqaalka Xogta: Samee sawir kala firdhisan si aad u aragto qaabka xiriirka ka dhexeeya labada doorsoome.
3. Xisaabinta Isku-xidhka Isku-xidhka: Xisaabi isku-xidhka Pearson, Spearman, ama Kendall.
4. Fasiraadda Natiijooyinka: Ku soo gabagabayso xoogga iyo jihada xiriirka iyadoo lagu salaynayo qiimaha isku-xidhka.
5. Tijaabada Muhiimadda: Go'aami in isku xirnaanta la helay ay tahay mid tirakoob ahaan muhiim ah.
Su'aalo iyo Doodo Tusaale ah
Su'aal 1aad: Xiriirka Pearson
Xogta dhererka (cm) iyo miisaanka (kg) ee 5 qof ayaa la bixiyay sida soo socota:
| Qof | Dherer (cm) | Miisaanka (kg) |
|——-|—————-|————|
| A | 160 | 55 |
| B | 165 | 60 |
| C | 170 | 65 |
| D | 175 | 70 |
| E | 180 | 75 |
Xisaabi isku-xidhka Pearson ee xogta.
Dood:
1. Xisaabinta Celceliska:
– Celceliska dhererka (X̄) = (160 + 165 + 170 + 175 + 180) / 5 = 170
– Miisaanka celceliska (Ȳ) = (55 + 60 + 65 + 70 + 75) / 5 = 65
2. Xisaabinta Kala Duwanaanta Celceliska:
– Kala leexasho sare: (160 – 170), (165 – 170), (170 – 170), (175 – 170), (180 – 170)
– Kala leexasho daran: (55 – 65), (60 – 65), (65 – 65), (70 – 65), (75 – 65)
3. Xisaabinta Badeecada Kala Duwanaanshaha:
– (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
Wadarta = 100 + 25 + 0 + 25 + 100 = 250
4. Xisaabinta Labajibbaaranaha Kala Duwanaanshaha:
– Dhererka: (160-170)², (165-170)², (170-170)², (175-170)², (180-170)²
– Miisaanka: (55-65)², (60-65)², (65-65)², (70-65)², (75-65)²
Dhererka:
– (160-170)² = 100
– (165-170)² = 25
– (170-170)² = 0
– (175-170)² = 25
– (180-170)² = 100
Wadarta = 100 + 25 + 0 + 25 + 100 = 250
Miisaanka:
– (55-65)² = 100
– (60-65)² = 25
– (65-65)² = 0
– (70-65)² = 25
– (75-65)² = 100
Wadarta = 100 + 25 + 0 + 25 + 100 = 250
5. Xisaabinta Isku-xidhka Pearson:
\[
r = \frac{\sum ((X – X̄)(Y – Ȳ))}{\sqrt{\sum (X – X̄)² \sum (Y – Ȳ)²}}
\]
\[
r = \frac{250}{\sqrt{250 \times 250}} = \frac{250}{250} = 1
\]
Fasiraadda: Qiimaha isku-xidhka Pearson ee 1 wuxuu muujinayaa xiriir togan oo qumman oo u dhexeeya dhererka iyo miisaanka.
Su'aal 2: Xiriirka Spearman
Marka la eego xogta kala sarreynta laba doorsoome sida soo socota:
| Qof | Doorsoome X | Doorsoome Y |
|——-|————|————|
| A | 1 | 3 |
| B | 2 | 1 |
| C | 3 | 4 |
| D | 4 | 2 |
| E | 5 | 5 |
Xisaabi isku-xidhka Spearman iyadoo lagu salaynayo xogta.
Dood:
1. Xisaabinta Farqiga Darajooyinka (d):
– Darajada X iyo Y:
– A: 1 – 3 = -2
– B: 2 – 1 = 1
– C: 3 – 4 = -1
– D: 4 – 2 = 2
– E: 5 – 5 = 0
2. Xisaabinta Labajibbaaranaha Farqiga u dhexeeya Darajada (d²):
– (-2)² = 4
– (1)² = 1
– (-1)² = 1
– (2)² = 4
– (0)² = 0
Wadarta (Σd²) = 4 + 1 + 1 + 4 + 0 = 10
3. Xisaabinta Isku-xidhka Spearman:
\[
r_s = 1 – \frac{6 \sum d^2}{n(n^2 – 1)}
\]
\[
r_s = 1 – \frac{6 \times 10}{5(5^2 – 1)} = 1 – \frac{60}{120} = 1 – 0.5 = 0.5
\]
Fasiraadda: Qiimaha isku-xidhka Spearman ee 0.5 wuxuu muujinayaa xiriir dhexdhexaad ah oo togan oo u dhexeeya doorsoomayaasha X iyo Y.
Gabagabo
Tusaalooyinka kor ku xusan, waxaan ku aragnaa sida falanqaynta isku xidhka loo isticmaali karo si loo go'aamiyo xoogga iyo jihada xiriirka ka dhexeeya laba doorsoome. Isku xidhka Pearson waxaa loo isticmaalaa xogta tirooyinka leh xiriirka toosan, halka isku xidhka Spearman loo isticmaalo xogta toosan ama kuwa aan tooska ahayn. Marka la fahmo oo la barto farsamooyinkan, waxaan si fiican u falanqeyn karnaa xogta oo aan ka samayn karnaa go'aanno sax ah oo ku saabsan qaybaha kala duwan ee daraasadda.
