Ajụjụ Ihe Nlereanya na Mkparịta ụka nke Nyocha Mmekọrịta
Nnyocha njikọ bụ usoro ọnụọgụgụ eji achọpụta oke mmekọrịta dị n'etiti mgbanwe abụọ. A na-ejikarị nyocha a eme ihe n'ọtụtụ ngalaba dị iche iche, gụnyere akụnụba, akparamàgwà mmadụ, ọgwụ, na mmekọrịta mmadụ na ibe ya, iji ghọta etu mgbanwe abụọ si ejikọta nke ọma. N'isiokwu a, anyị ga-atụle ọtụtụ nsogbu na mkparịta ụka iji nyere aka ịghọta echiche nke nyocha njikọ.
Ịghọta Nyocha Mmekọrịta
A na-eji nyocha njikọta tụọ ike na ntụziaka nke mmekọrịta dị n'etiti mgbanwe ọnụọgụ abụọ. A na-egosipụtakarị uru njikọ a site na iji ihe njikọ, nke nwere ike ịdị site na -1 ruo 1. Enwere ike ịkọwa ụkpụrụ ndị a dị ka ndị a:
– +1: Mmekọrịta dị mma zuru oke. Ihe abụọ a na-agbanwe agbanwe na-aga n'otu ụzọ.
– 0: Enweghị njikọ. Ihe abụọ a enweghị mmekọrịta kwụ ọtọ doro anya.
– -1: Mmekọrịta na-adịghị mma zuru oke. Mgbanwe abụọ a na-agagharị n'akụkụ dị iche iche.
Ihe a na-ejikarị eme ihe bụ njikọ Pearson. Agbanyeghị, e nwekwara ụzọ njikọ ndị ọzọ, dịka Spearman na Kendall, nke dabara adaba maka data ordinal ma ọ bụ nonlinear.
Nzọụkwụ Nyocha Mmekọrịta
1. Nchịkọta Data: Nakọta data maka ihe abụọ a ga-enyocha.
2. Nlereanya Data: Mepụta atụmatụ gbasaa iji hụ ụkpụrụ mmekọrịta dị n'etiti mgbanwe abụọ ahụ.
3. Ngụkọta nke Njikọta: Gbakọọ ọnụọgụ njikọ Pearson, Spearman, ma ọ bụ Kendall.
4. Nkọwa nke Nsonaazụ: Mechie ike na ntụziaka nke mmekọrịta ahụ dabere na uru njikọ.
5. Ule Mkpa: Chọpụta ma njikọ ahụ a hụrụ ọ dị mkpa n'ọnụọgụgụ.
Ajụjụ na Mkparịta ụka Ihe Nlereanya
Ajụjụ nke 1: Mmekọrịta Pearson
E nyere data gbasara ịdị elu (cm) na ibu (kg) nke mmadụ ise dịka ndị a:
| Onye | Ogologo (cm) | Ibu (kg) |
|——-|————-|————|
| A | 160 | 55 |
| B | 165 | 60 |
| C | 170 | 65 |
| D | 175 | 70 |
| E | 180 | 75 |
Gbakọọ ọnụọgụgụ mmekọrịta Pearson maka data ahụ.
Azịza:
1. Ịgbakọ nkezi:
– Ogologo nkezi (X̄) = (160 + 165 + 170 + 175 + 180) / 5 = 170
– Oke ibu (Ȳ) = (55 + 60 + 65 + 70 + 75) / 5 = 65
2. Ịgbakọ Mgbanwe site na Nkezi:
– Ngbanwe dị elu: (160 – 170), (165 – 170), (170 – 170), (175 – 170), (180 – 170)
– Ngbanwe dị oke njọ: (55 – 65), (60 – 65), (65 – 65), (70 – 65), (75 – 65)
3. Ịgbakọ Ngwaahịa Ngbanwe:
– (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
Ngụkọta = 100 + 25 + 0 + 25 + 100 = 250
4. Ịgbakọ Oke nke Ngbanwe:
– Ogologo: (160-170)², (165-170)², (170-170)², (175-170)², (180-170)²
– Ibu: (55-65)², (60-65)², (65-65)², (70-65)², (75-65)²
Maka ịdị elu:
– (160-170)² = 100
– (165-170)² = 25
– (170-170)² = 0
– (175-170)² = 25
– (180-170)² = 100
Ngụkọta = 100 + 25 + 0 + 25 + 100 = 250
Maka ibu:
– (55-65)² = 100
– (60-65)² = 25
– (65-65)² = 0
– (70-65)² = 25
– (75-65)² = 100
Ngụkọta = 100 + 25 + 0 + 25 + 100 = 250
5. Ịgbakọ Pearson Correlation Coefficient:
\[
r = \frac{\sum ((X – X̄)(Y – Ȳ))}{\sqrt{\sum (X – X̄)² \sum (Y – Ȳ)²}}
\]
\[
r = \frac{250}{\sqrt{250\ugboro 250}} = \frac{250}{250} = 1
\]
Nkọwa: Uru njikọ Pearson nke 1 na-egosi mmekọrịta dị mma zuru oke n'etiti ịdị elu na ibu.
Ajụjụ nke 2: Mmekọrịta Spearman
Dabere na data nhazi nke mgbanwe abụọ dị ka ndị a:
| Onye | Mgbanwe X | Mgbanwe Y |
|——-|—————|————|
| A | 1 | 3 |
| B | 2 | 1 |
| C | 3 | 4 |
| D | 4 | 2 |
| E | 5 | 5 |
Gbakọọ ọnụọgụgụ mmekọrịta Spearman dabere na data ahụ.
Azịza:
1. Ngụkọta nke Ọdịiche Ọkwa (d):
- Maka ọkwa X na Y:
– A: 1 – 3 = -2
– B: 2 – 1 = 1
– C: 3 – 4 = -1
– D: 4 – 2 = 2
– E: 5 – 5 = 0
2. Ngụkọta nke Square nke Ọdịiche na Ọkwa (d²):
– (-2)² = 4
– (1)² = 1
– (-1)² = 1
– (2)² = 4
– (0)² = 0
Ngụkọta (Σd²) = 4 + 1 + 1 + 4 + 0 = 10
3. Ịgbakọ ọnụọgụgụ njikọta Spearman:
\[
r_s = 1 – \frac{6 \sum d^2}{n(n^2 – 1)}
\]
\[
r_s = 1 – \frac{6 \ugboro 10}{5(5^2 – 1)} = 1 – \frac{60}{120} = 1 – 0.5 = 0.5
\]
Nkọwa: Uru njikọ Spearman nke 0.5 na-egosi mmekọrịta dị mma n'etiti mgbanwe X na Y.
Mmechi
Site na ihe atụ ndị dị n'elu, anyị na-ahụ otu esi eji nyocha njikọ chọpụta ike na ntụziaka nke mmekọrịta dị n'etiti mgbanwe abụọ. A na-eji ọnụọgụgụ njikọ Pearson eme ihe maka data ọnụọgụgụ nwere mmekọrịta kwụ ọtọ, ebe a na-eji ọnụọgụgụ njikọ Spearman eme ihe maka data ordinal ma ọ bụ nonlinear. Site n'ịghọta na ịmụta usoro ndị a, anyị nwere ike inyocha data nke ọma ma mee nkwubi okwu ziri ezi n'ọtụtụ ngalaba ọmụmụ.
