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UJI HUBUNGAN: KORELASIUJI HUBUNGAN: KORELASI
http://alhiko.blogspot.comhttp://pbm-alhiko.blogspot.com
Abdul Hadi Kadarusno, SKM, MPH
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O u t l i n eO u t l i n e• Pengantar: Analisis Data Statistik• Korelasi Pearson • Korelasi Spearman (Kendal Tau) .• Soal Latihan
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KEGIATAN STATISTIKKEGIATAN STATISTIK
PENGOLAHAN DATA
PENYAJIAN DATA
PENGUMPULAN DATA
KESIMPULAN
ANALISIS DATA
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UJI KORELASI dari PEARSONUJI KORELASI dari PEARSON
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UJI KORELASI PRODUCT MOMENTDARI PEARSON
• Mencari hubungan 2 variabel, denganskala interval atau ratio, data normal
• Arah hubungannya positif dan negatif• Nilai hubungan dipresentasikan dalam
bentuk angka dari : (-1) –s/d – (+1), • Bila hasil perhitungan (-) maka
hubungannya negatif dan bila hasilperhitungannya (+) maka hubungan antarvariabelnya positif.
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66
POLA HUBUNGAN PADA POLA HUBUNGAN PADA DIAGRAM SCATTERDIAGRAM SCATTER
xx
yy
xx
yy
xx
yy
xx
yy
xx
yy
xx
yy
Hubungan PositifJika X naik, makaY juga naik dan
jika X turun, makaY juga turun
Hubungan NegatifJika X naik, makaY akan turun danjika X turun, maka
Y akan naik
Tidak ada hubunganantara X dan Y
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• Rumus Perhitungan :
• (Σx)(Σy)• Σ xy -• N
• rxy = • 2 2
• 2 (Σx) 2 (Σy)• ( Σx - ) ( Σy - )• N N
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• Contoh :
1206310125769125828140837135726115665110554125703120672135841
TD (mm Hg) : y
BB (Kg) : x
No
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• Tentukan Ho & Hα :Ho : Tidak ada hubungan antara BB dan Tek.DrhHα : Ada hubungan antara BB dan Tek.Darah
• Tentukan Batas penerimaan / PenolakanHo: n = 10, α = 0,05 Membaca diTabel r Pearson
Penyelesaian Soal:
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Perhitungan:
15705014400156251562519600182251322512100156251440018225
y 2
523683969577667246889518443563025490044897056
x 2
1250120125125140135115110125120135
TD : y
90420718∑75606310950076910250828116208379720726759066560505548750703804067211340841
x.yBB : xNo
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Rangkuman
• ∑ x = 718 (∑ x) 2 = 515.524 • ∑ y = 1.250 (∑ y) 2 = 1.562.500• ∑ x.y = 90.420 (∑ x) . (∑ y) = 897.500• ∑ x2 = 52.368• ∑ y2 = 15.7050
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• Hitung dengan Rumus :
• (Σx)(Σy)• Σ xy -• N
• rxy = • 2 2
• 2 (Σx) 2 (Σy)• ( Σx - ) ( Σy - )• N N
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Hasil Perhitungan :• r hitung = 0,82945 (positif)• r tabel : n = 10, α = 0,05, • didapat r tabel = 0,632 (tabel r Pearson)
r hitung (0,82945) > r tabel (0,632)
Kesimpulan :Ho ditolak dan Hα diterima (Adahubungan antara BB dan Tek.Darah)
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UJI KORELASI TATA JENJANG dari SPEARMAN
UJI KORELASI TATA JENJANG dari SPEARMAN
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UJI KORELASI TATA JENJANGUJI KORELASI TATA JENJANGSPEARMANSPEARMAN
• Mencari hubungan 2 variabel, dengan skalaordinal, interval atau ratio.
• Rumus Perhitungan :
6 Σ di2
rho = 1 –
N3
– N
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Cara Cara PerhitunganPerhitungan ::1. Ho : tidak ada hubungan antara X dan Y
Hα : ada hubungan antara X dan Y
2. Tentukan α = 0,05.3. Lakukan perhitungan:
• Nilai variabel (x) dan (y) dibuat peringkat
• Cari selisih peringkat (x) dan peringkat (y)
• Kuadratkan selisih peringkat (x) dan (y)
• Jumlahkan kuadrat selisih (x) & (y) = (di2)
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716910
706711
90867.
75708.
84809.
88
83
81
69
75
79
Prestasi
856.
825.
794.
753.
772.
781.
MotivasiNo
• Contoh kasus:
(y)(x)
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Langkah2 penyelesaian:1. Tentukan Ho : Tidak ada hubungan
antara Motivasi dengan Prestasi. (Hα= ?)
2. Tentukan batas penerimaan danpenolakan Ho α = 0,05 dan N = 11.
3. Lakukan perhitgn tabel penolong!
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32716910
21706711
111190867.
4374708.
9884809.
88
83
81
69
75
79
Prestasi
10
9
7
4
5
6
Rank Mtvs
10856.
8825.
7794.
1753.
5772.
6781.
Rank PrestsMotivasiNo
Nilai (x) dan (y) dibuat peringkat
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Data tiap variable lebih baik jika diurutkanterlebih dulu (Ascending/Descending):
67
69
70
75
77
78
79
80
82
85
86
Motivasi
270210
169111
575.57.
474.48.
37139.
79
81
83
84
88
90
Prestasi
666.
775.
884.
993.
10102.
11111.
Rank PrestsRank MtvsNo
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1-12111
2
8
3
11
10
9
7
4
5
6
Rank Mtv
3
9
4
11
10
8
7
1
5
6
Rank Prests
1-110
14Total
007.
1-18.
1-19.
0
1
0
9
0
0
d2
06.
15.
04.
33.
02.
01.
dNo
Cari selisih peringkat (x) dan (y) Kuadratkan
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3. Perhitungan dgn rumus:
6 Σ di2 6 . 14
• rhohitung = 1 – = 1 –
N3
– N 113
– 11
• rhohitung = 0,936
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4. Bandingkan Hasil perhitungan dgn Tabel:
rho hitung = 0,936
• rho tabel = n (11), α = 0,05 didapat = 0,619
gunakan Tabel rho Spearman
rho hitung > rho tabel
5. Kesimpulan :
Ho ditolak dan Hα diterima = …
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Perbedaan cara penarikan kesimpulanhitung manual dan komputerize
• r hitung > r tabel Ho ditolak
• asym sig./ sig. < α (alfa) Ho ditolak
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SoalSoal LatihanLatihan1. Suatu penelitian ingin menguji
hubungan antara kadar debu diudara dengan jumlah pesertaISPA di sejumlah daerah. Hasilnya diperoleh data sbb(lihat halaman slanjutnya).
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LanjutanLanjutan……SoalSoal LatihanLatihan
716910
1009711
90867.
75708.
841189.
108
83
88
69
125
179
Jlh Penderita ISPA
856.
925.
794.
1253.
1772.
1081.
Kadar Debu (ppm)Daerah
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DaftarDaftar PustakaPustaka / / ReferensiReferensi• Singgih Santoso, (2000), Buku Latihan SPSS
Statistik Paramametrik, Jakarta: PT. ElexMedia Komputindo. Halm. 220 – 241.
• Singgih Santoso, (2001), Buku Latihan SPSS Statistik Non Paramametrik, Jakarta: PT. ElexMedia Komputindo. Halm. 101 – 113.
• Singgih Santoso, (2005), Bank Soal Statistikdengan SPSS, Jakarta: PT. Elex Media Komputindo. Halm. 69 – 76 dan 219 – 231.
• Sutrisno Hadi, Prof, Drs, MA, (2000), StatistikJilid 2, Yogyakarta: Penerbit Andi. Halm. 257 –285.
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•• SEKIANSEKIAN•• TERIMA TERIMA
KASIHKASIH•• SELAMAT SELAMAT
BELAJARBELAJAR
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