Oleh: M.A.Yulianto.*)
Koefisien korelasi Pearson dapat digunakan untuk menyatakan besar hubungan linier antara dua variabel ketika data adalah data kuantitatif (data berskala interval atau rasio) dan kedua variabel adalah bivariat yang berdistribusi normal. Ketika datanya adalah data kualitatif (data berskala ordinal) maka besar hubungan dua variabel dapat dicari dengan korelasi Spearman atau korelasi Kendall Tau, dan ketika datanya kualitatif berskala nominal dalam bentuk tabel kontingensi maka besar hubungan dua variabel dapat dicari dengan korelasi Cramer. Korelasi-korelasi dengan data kualitatif ini akan dibahas pada sesi tulisan yang lain. Simbol korelasi pada ukuran populasi adalah ρ (dibaca: rho) dan pada ukuran sampel adalah r.
Formula untuk korelasi Pearson adalah sebagai berikut:
koefisien korelasi mempunyai range nilai berkisar antara -1 sampai 1
contoh:
Sebuah perusahaan industri mempunyai data produksi bulanan selama sepuluh bulan dan jumlah jam kerja seperti Tabel 1 dibawah ini.
Tabel 1 Produksi bulanan dan jam kerja.
Bulan |
Produksi (Xi) |
Jam kerja (Yi) |
1 2 3 4 5 6 7 8 9 10 |
30 20 60 80 40 50 60 30 70 60 |
73 50 128 170 87 108 135 69 148 132 |
Menggunakan data dari Tabel 1, nilai koefisien korelasinya adalah:
Besar hubungan linier antara produksi dan jam kerja karyawan pada perusahaan industri tersebut adalah sebesar 0,9978 atau sebesar 99,78 persen. Jika nilai korelasi dikuadratkan akan didapat suatu nilai yang menyatakan besarnya pengaruh variasi suatu variabel terhadap variabel lainnya. Nilai tersebut biasa disebut dengan koefisien determinasi (r2) (coefficient of determination). Koefisien determinasi mempunyai range nilai berkisar antara 0 sampai 1. Dalam hal contoh diatas, variasi produksi mempunyai pengaruh sebesar 99,56 persen terhadap variasi jam kerja karyawan pada perusahaan tersebut.
Uji untuk korelasi Pearson.
Uji ini digunakan untuk menentukan apakah ada hubungan linier yang signifikan antara dua variabel. Uji ini termasuk klasifikasi uji statistik parametrik.
Hipotesanya adalah:
Ho : ρ = 0 VS H1 : ρ ≠ 0
Statistik uji yang digunakan adalah statistik uji t. Formulanya adalah sebagai berikut:
daerah tolak H0:
t <- t(a/2 , n-2) dan t > t(a/2 , n-2)
Menggunakan data dari Tabel 1, uji untuk menentukan apakah ada hubungan linier antar variabel produksi dengan jam kerja dengan menguji koefisien korelasi populasi dengan tingkat signifikansi sebesar 5%.
t(0,025 ;8) = 2,31
Keputusan: H0 ditolak karena t > t(0,025 ;8)
Kesimpulan: ada hubungan linier antara produksi dengan jam kerja dengan tingkat
keyakinan sebesar 95%.
Sampai bertemu pada sesi tulisan yang lain, selamat menikmati statistik.
Jika ada pertanyaan dapat di kirim ke alamat e-mail: yuliantoyorki@yahoo.com
*) Penulis adalah dosen di Sekolah Tinggi Ilmu Statistik, Jakarta.
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