STATYSTIC NON-PARAMETRIC
NAMA
:
NURUL CHAIRUNNISA UTAMI PUTRI
NIM
:
1620070008
FAK / JUR :
SAINS & TEKNOLOGI / MATEMATIKA
http://roelcup.wordpress.com
UNIVERSITAS ISLAM AS-SYAFI’IYAH JAKARTA TIMUR
2010
KORELASI POINT BISERIAL
Rumus : 𝛤𝑝𝑏𝑖 =
𝑥𝑖 − 𝑥𝑡 𝑝 √ 𝑆𝑡 1−𝑝
Keterangan : 𝑥𝑖 = Mean Butir yang Menjawab Benar 𝑥𝑡 = Mean Skor Total 𝑆𝑡 = Simpangan Baku Total 𝑝 = Proposi yang Menjawab Benar
CONTOH SOAL : Multiple Choice (𝐴, 𝐵, 𝐶, 𝐷, 𝐸) o Jika jawab Benar → Skor 1 o Jika jawab Salah → Skor 0 Uji Validitas & Reliabilitas Data Uji Validitas yaitu Mencari Korelasi antara Butir Soal & Totalnya Case : Soal = 7 Buah Peserta =10 B = Benar / Proposi
Datanya Adalah : BUTIR Peserta
Total (X) 1
2
3
4
5
6
7
1
1
1
1
1
0
0
0
4
2
1
1
0
1
1
1
0
5
3
0
1
1
1
0
0
0
3
4
1
1
0
0
0
0
0
2
5
0
1
0
0
0
0
0
1
6
1
1
1
1
1
1
1
7
7
1
1
1
1
1
1
0
6
8
0
0
0
0
0
0
0
0
9
1
1
0
0
1
0
0
3
10
1
1
1
1
1
0
0
5
B
7
9
5
6
5
3
1
36
36 = 3,6 10 2 1 = (𝑛 ∙ ∑ 𝑥 2 − (∑ 𝑥) ) 𝑛 ∙ (𝑛 − 1)
𝑥𝑡 = 𝑆𝑡 2
𝑆𝑡 2 =
1 (10 ∙ 174 − (36)2 ) 10 ∙ (10 − 1)
1 (1740 − 1296) 90 1 (444) = 90
𝑆𝑡 2 = 𝑆𝑡 2
𝑆𝑡 2 = 4,9333 𝑆𝑡 = √4,9333 𝑆𝑡 = 2,2211
1. Antara Butir Ke-1 dengan Total Peserta
Butir ke-1
Total (X)
𝑥2
1 2 3 4 5 6 7 8 9 10
1 1 0 1 0 1 1 0 1 1
4 5 3 2 1 7 6 0 3 5
16 25 9 4 1 49 36 0 9 25
B
7
36
174
7 = 0,7 10 (4 ∙ 1) (5 ∙ 1) (3 ∙ 0) (2 ∙ 1) (1 ∙ 0) (7 ∙ 1) (6 ∙ 1) (0 ∙ 0) (3 ∙ 1) 𝑥𝑖 = + + + + + + + + 7 7 7 7 7 7 7 7 7 (5 ∙ 1) + 7 4 5 0 2 0 7 6 0 3 5 𝑥𝑖 = + + + + + + + + + 7 7 7 7 7 7 7 7 7 7 32 𝑥𝑖 = 7 𝑝=
𝑥𝑖 = 4,5714 𝛤𝑝𝑏𝑖 =
𝑥𝑖 − 𝑥𝑡 𝑝 √ 𝑆𝑡 1−𝑝
𝛤𝑝𝑏𝑖 =
4,5714 − 3,6 0,7 √ 2,2211 1 − 0,7
𝛤𝑝𝑏𝑖 =
0,97 0,7 √ 2,2211 0,3
𝛤𝑝𝑏𝑖 = (0,4374)√2,3333 𝛤𝑝𝑏𝑖 = (0,4374)(1,5275) 𝛤𝑝𝑏𝑖 = 0,6681
2. Antara Butir Ke-2 dengan Total Peserta
Butir ke-2
Total (X)
𝑥2
1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 0 1 1
4 5 3 2 1 7 6 0 3 5
16 25 9 4 1 49 36 0 9 25
B
9
36
174
9 = 0,9 10 (4 ∙ 1) (5 ∙ 1) (3 ∙ 1) (2 ∙ 1) (1 ∙ 1) (7 ∙ 1) (6 ∙ 1) (0 ∙ 0) (3 ∙ 1) 𝑥𝑖 = + + + + + + + + 9 9 9 9 9 9 9 9 9 (5 ∙ 1) + 9 4 5 3 2 1 7 6 0 3 5 𝑥𝑖 = + + + + + + + + + 9 9 9 9 9 9 9 9 9 9 36 𝑥𝑖 = 9 𝑝=
𝑥𝑖 = 4 𝛤𝑝𝑏𝑖 =
𝑥𝑖 − 𝑥𝑡 𝑝 √ 𝑆𝑡 1−𝑝
𝛤𝑝𝑏𝑖 =
4 − 3,6 0,9 √ 2,2211 1 − 0,9
𝛤𝑝𝑏𝑖 =
0,4 0,9 √ 2,2211 0,1
𝛤𝑝𝑏𝑖 = (0,1801)√9,00 𝛤𝑝𝑏𝑖 = (0,1801)(3,00) 𝛤𝑝𝑏𝑖 = 0,5403
3. Antara Butir Ke-3 dengan Total Peserta
Butir ke-3
Total (X)
𝑥2
1 2 3 4 5 6 7 8 9 10
1 0 1 0 0 1 1 0 0 1
4 5 3 2 1 7 6 0 3 5
16 25 9 4 1 49 36 0 9 25
B
5
36
174
5 = 0,5 10 (4 ∙ 1) (5 ∙ 0) (3 ∙ 1) (2 ∙ 0) (1 ∙ 0) (7 ∙ 1) (6 ∙ 1) (0 ∙ 0) (3 ∙ 0) 𝑥𝑖 = + + + + + + + + 5 5 5 5 5 5 5 5 5 (5 ∙ 1) + 5 4 0 3 0 0 7 6 0 0 5 𝑥𝑖 = + + + + + + + + + 5 5 5 5 5 5 5 5 5 5 25 𝑥𝑖 = 5 𝑝=
𝑥𝑖 = 5 𝛤𝑝𝑏𝑖 =
𝑥𝑖 − 𝑥𝑡 𝑝 √ 𝑆𝑡 1−𝑝
𝛤𝑝𝑏𝑖 =
5 − 3,6 0,5 √ 2,2211 1 − 0,5
𝛤𝑝𝑏𝑖 =
1,4 0,5 √ 2,2211 0,5
𝛤𝑝𝑏𝑖 = (0,6303)√1,00 𝛤𝑝𝑏𝑖 = (0,6303)(1,00) 𝛤𝑝𝑏𝑖 = 0,6303
4. Antara Butir Ke-4 dengan Total Peserta
Butir ke-4
Total (X)
𝑥2
1 2 3 4 5 6 7 8 9 10
1 1 1 0 0 1 1 0 0 1
4 5 3 2 1 7 6 0 3 5
16 25 9 4 1 49 36 0 9 25
B
6
36
174
6 = 0,6 10 (4 ∙ 1) (5 ∙ 1) (3 ∙ 1) (2 ∙ 0) (1 ∙ 0) (7 ∙ 1) (6 ∙ 1) (0 ∙ 0) (3 ∙ 0) 𝑥𝑖 = + + + + + + + + 6 6 6 6 6 6 6 6 6 (5 ∙ 1) + 6 4 5 3 0 0 7 6 0 0 5 𝑥𝑖 = + + + + + + + + + 6 6 6 6 6 6 6 6 6 6 30 𝑥𝑖 = 6 𝑝=
𝑥𝑖 = 5 𝛤𝑝𝑏𝑖 =
𝑥𝑖 − 𝑥𝑡 𝑝 √ 𝑆𝑡 1−𝑝
𝛤𝑝𝑏𝑖 =
5 − 3,6 0,6 √ 2,2211 1 − 0,6
𝛤𝑝𝑏𝑖 =
1,40 0,6 √ 2,2211 0,4
𝛤𝑝𝑏𝑖 = (0,6303)√1,5 𝛤𝑝𝑏𝑖 = (0,6303)(1,2247) 𝛤𝑝𝑏𝑖 = 0,7720
5. Antara Butir Ke-5 dengan Total Peserta
Butir ke-5
Total (X)
𝑥2
1 2 3 4 5 6 7 8 9 10
0 1 0 0 0 1 1 0 1 1
4 5 3 2 1 7 6 0 3 5
16 25 9 4 1 49 36 0 9 25
B
5
36
174
5 = 0,5 10 (4 ∙ 0) (5 ∙ 1) (3 ∙ 0) (2 ∙ 0) (1 ∙ 0) (7 ∙ 1) (6 ∙ 1) (0 ∙ 0) (3 ∙ 1) 𝑥𝑖 = + + + + + + + + 5 5 5 5 5 5 5 5 5 (5 ∙ 1) + 5 0 5 0 0 0 7 6 0 3 5 𝑥𝑖 = + + + + + + + + + 5 5 5 5 5 5 5 5 5 5 26 𝑥𝑖 = 5 𝑝=
𝑥𝑖 = 4 𝛤𝑝𝑏𝑖 =
𝑥𝑖 − 𝑥𝑡 𝑝 √ 𝑆𝑡 1−𝑝
𝛤𝑝𝑏𝑖 =
5,20 − 3,6 0,5 √ 2,2211 1 − 0,5
𝛤𝑝𝑏𝑖 =
1,6 0,5 √ 2,2211 0,5
𝛤𝑝𝑏𝑖 = (0,7204)√1,00 𝛤𝑝𝑏𝑖 = (0,7204)(1,00) 𝛤𝑝𝑏𝑖 = 0,7204
6. Antara Butir Ke-6 dengan Total Peserta
Butir ke-6
Total (X)
𝑥2
1 2 3 4 5 6 7 8 9 10
0 1 0 0 0 1 1 0 0 0
4 5 3 2 1 7 6 0 3 5
16 25 9 4 1 49 36 0 9 25
B
3
36
174
3 = 0,3 10 (4 ∙ 0) (5 ∙ 1) (3 ∙ 0) (2 ∙ 0) (1 ∙ 0) (7 ∙ 1) (6 ∙ 1) (0 ∙ 0) (3 ∙ 0) 𝑥𝑖 = + + + + + + + + 3 3 3 3 3 3 3 3 3 (5 ∙ 0) + 3 0 5 0 0 0 7 6 0 0 0 𝑥𝑖 = + + + + + + + + + 3 3 3 3 3 3 3 3 3 3 18 𝑥𝑖 = 3 𝑝=
𝑥𝑖 = 6 𝛤𝑝𝑏𝑖 =
𝑥𝑖 − 𝑥𝑡 𝑝 √ 𝑆𝑡 1−𝑝
𝛤𝑝𝑏𝑖 =
6 − 3,6 0,3 √ 2,2211 1 − 0,3
𝛤𝑝𝑏𝑖 =
2,4 0,3 √ 2,2211 0,7
𝛤𝑝𝑏𝑖 = (1,0805)√0,4286 𝛤𝑝𝑏𝑖 = (0,1801)(0,6547) 𝛤𝑝𝑏𝑖 = 0,7074
7. Antara Butir Ke-7 dengan Total Peserta
Butir ke-7
Total (X)
𝑥2
1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 1 0 0 0 0
4 5 3 2 1 7 6 0 3 5
16 25 9 4 1 49 36 0 9 25
B
1
36
174
1 = 0,1 10 (4 ∙ 0) (5 ∙ 0) (3 ∙ 0) (2 ∙ 0) (1 ∙ 0) (7 ∙ 1) (6 ∙ 0) (0 ∙ 0) (3 ∙ 0) 𝑥𝑖 = + + + + + + + + 1 1 1 1 1 1 1 1 1 (5 ∙ 0) + 1 0 0 0 0 0 7 0 0 0 0 𝑥𝑖 = + + + + + + + + + 1 1 1 1 1 1 1 1 1 1 7 𝑥𝑖 = 1 𝑝=
𝑥𝑖 = 7 𝛤𝑝𝑏𝑖 =
𝑥𝑖 − 𝑥𝑡 𝑝 √ 𝑆𝑡 1−𝑝
𝛤𝑝𝑏𝑖 =
7 − 3,6 0,1 √ 2,2211 1 − 0,1
0,1 𝛤𝑝𝑏𝑖 = 3,4√ 0,9 𝛤𝑝𝑏𝑖 = (0,1801)√0,1111 𝛤𝑝𝑏𝑖 = (1,5308)(0,3333) 𝛤𝑝𝑏𝑖 = 0,5103
Nurul Chairunnisa Utami Putri : http://roelcup.wordpress.com
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