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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 [email protected] [email protected]

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