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Uji Korelasi

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Uji Korelasi

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About this activity

Statistik

Created by

Natasya Cahya
Natasya Cahya
Indonesia

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Uji Korelasi
 

Uji KorelasiOnline version

Statistik

by Natasya Cahya
1

A.Korelasi Product Moment

Korelasi Product Moment atau Pearson digunakan untuk mengetahui hubungan antara     dua variabel yang berupa angka (interval atau rasio).

           Contohnya: apakah motivasi belajar berhubungan dengan prestasi akademik?

2

Syarat Penggunaan

a.      Kedua data berupa angka (skor, nilai, waktu).

b.     Hubungan linier (tidak melengkung).

c.      Data berdistribusi normal.

d.     Tiap pasangan data (X, Y) bebas.

           Jika syarat tidak terpenuhi → gunakan Spearman Rho.

3

Rumus Singkat

4

Langkah-langkah

a.      Siapkan data X dan Y.

b.     Hitung ∑X, ∑Y, ∑X², ∑Y², dan ∑XY.

c.      Masukkan ke rumus → dapatkan nilai r.

d.     Bandingkan dengan r tabel.

|r hitung| > r tabel → ada hubungan signifikan.

|r hitung| ≤ r tabel → tidak signifikan

5

Interpretasi Nilai r

  • r = +1 → hubungan positif sempurna
  • r = –1 → hubungan negatif sempurna
  • r = 0 → tidak ada hubungan
6

B.KORELASI TATA JENJANG ATAU SPEARMAN RHO

Spearman Rho digunakan untuk data ordinal (data peringkat/ranking). Cocok bila:

a.      Data tidak normal

b.     Data berbentuk urutan (peringkat siswa, posisi, dll)

c.      Hubungan tidak harus linier

7

Rumus

8

Langkah-langkah

a.      Ubah data menjadi peringkat.

b.     Hitung selisih peringkat (D).

c.      Kuadratkan (D²) dan jumlahkan.

d.     Masukkan ke rumus → dapatkan nilai ρ.

9

Interpretasi nilai p

10

C.Korelasi Phi

Korelasi Phi (Φ) digunakan untuk dua variabel nominal (dua kategori, misalnya “ya/tidak”, “lulus/tidak lulus”).

           Contoh: Apakah ikut bimbel berhubungan dengan kelulusan?

11

Rumus

12

Langkah-langkah

a.      Buat tabel 2×2 berdasarkan data.

b.     Masukkan ke rumus Phi.

c.      Interpretasi hasil:

  •  Φ positif → hubungan searah.
  • Φ negatif → berlawanan arah.

           Contoh: Φ = 0.41 → hubungan positif sedang.

13

Uji Signifikansi

14

D.Korelasi poin serial

15

Rumus

16

Keterangan

  • M₁ = rata-rata kelompok 1
  • M₀ = rata-rata kelompok 0
  • Sₜ = standar deviasi total
  • p = proporsi kelompok 1
  • q = proporsi kelompok 0
17

Langkah-Langkah

a. Beri kode (misal: laki-laki = 1, perempuan = 0).

b. Hitung rata-rata tiap kelompok (M₁ dan M₀).

c. Hitung simpangan baku total (Sₜ).

d. Hitung p dan q.

e. Masukkan ke rumus.

18

Interprestasi

a. Nilai rₚb mendekati +1 → hubungan positif kuat

b. Nilai rₚb mendekati −1 → hubungan negatif kuat

c. Nilai rₚb ≈ 0 → tidak ada hubungan

Contoh: rₚb = 0.812 → hubungan sangat kuat antara jenis kelamin dan nilai ujian.
 
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