reliabilitas formula konsistensi internal

Beberapa Formula Reliabilitas
Wahyu Widhiarso

FORMULA RELIABILITAS

Wahyu Widhiarso

ASUMSI DLM TEORI KLASIK
ASUMSI #1
ASUMSI #2
ASUMSI #3
ASUMSI #4
ASUMSI #5
FORMULA RELIABILITAS

XTE
( X )  T

et  0
e1e 2  0
e1t 2  0

Wahyu Widhiarso

1

TES PARALEL

X  Y1  Y2

Asumsi 1

x1  x 2

Asumsi 2

s 2y  s 2y

Asumsi 3

s e1e 2  0

1

Asumsi 4

2

rt1t 2  ry1y 2

Asumsi 5

Wahyu Widhiarso

FORMULA RELIABILITAS

Unsur Reliabilitas

rxx '

S


S

2
t
2
x

rxx '

Se2
 1 2
Sx

S2t  diketahui secara langsung

S2t  tidak diketahui secara langsung

Se2  tidak diketahui secara langsung

FORMULA RELIABILITAS

Wahyu Widhiarso

2

KONSISTENSI INTERNAL
PEMBELAHAN DUA BAGIAN
•
•
•
•
•

Spearman-Brown
Flanagan
Rulon
Guttman
Feldt

Wahyu Widhiarso

FORMULA RELIABILITAS

FORMULA SPEARMAN BROWN

rt1t 2  ry1y 2

Varian Skor Tampak (Sx2)

s y1  s y 2

s 2x  s 2y1  s 2y 2  2(s y1 s y 2 )(ry1y 2 )
 2s 2y1  2s y1 (ry1y 2 )
 2s 2y1 (1  ry1y 2 )

 2s 2y1 (1  ry1y 2 )

FORMULA RELIABILITAS

Wahyu Widhiarso

3

FORMULA SPEARMAN BROWN
T  T1  T2

s T2 1  s T2 2
Varian Skor Murni (St2)

s 2t  s (2t1  t 2 )

 s 2t1  s 2t2  2s t1 s t 2
 2s 2t1  2s 2t1
 4s 2t1

Wahyu Widhiarso

FORMULA RELIABILITAS

FORMULA SPEARMAN BROWN

rxx' 

rxx '

s

s

2
t
2
x

FORMULA RELIABILITAS

2s 2y1 (1  ry1y 2 )

 s 2t
 2 21
 sy

 1

 2ry1y 2


ry1y 2  korelasi antar belahan

4s 2y1


1

 (1  ry y )
1 2

1
(1  ry1y 2 )

ry1y2 

s2t1
s2y1

2ry1y 2

(1  ry1y 2 )

rxx' 

2ry1y 2

(1  ry1y 2 )
Wahyu Widhiarso

4

FORMULA SPEARMAN BROWN
Skor Belah

Subjek

X

1

9

5

4

2

5

3

2

3

5

2

3

4

5

3

2

5

4

2

2

Sy12=1.22

Sy22=0.89

Varian

Y2

Y1

Kovarian

Sxy=0.75

Wahyu Widhiarso

FORMULA RELIABILITAS

FORMULA FLANAGAN
Varian Skor
Tampak (St2)

s 2x

s2
rxx'  2t
sx

rxx ' 

4s y1y 2
s 2x

FORMULA RELIABILITAS

S TE  0

S E1E2  0

X TE

T  T1  T2

s y1y 2  s ( t1  e1 )( t 2  e 2 )

 s t 1t 2  s t1e 2  s t 2e 2  s e 2e 2
 s t 1t 2
s

s 2T1  s T22

s 2tx  s (2t1  t 2 )

 s 2t1  s 2t2  2s t1 s t 2

 2s 2t1  2s 2t1
 4s 2t1

 4s y1y 2

2
t1

S

2
tx

 4s y1y 2

Varian Skor
Murni (St2)

Wahyu Widhiarso

5

FORMULA FLANAGAN
Skor Belah

Subjek

X

1

9

5

4

2

5

3

2

3

5

2

3

4

5

3

2

5

4

2

2

Varian

Y1

Y2

Sx2=3.80

Kovarian

Sxy=0.75

Wahyu Widhiarso

FORMULA RELIABILITAS

FORMULA RULON

rxx'  1

FORMULA RELIABILITAS

s( y1y2 )
s2x

Wahyu Widhiarso

6

FORMULA RULON
Skor Belah

Subjek

X

Y1

Y2

d (Y1-Y2)

1

9

5

4

1

2

5

3

2

1

3

5

2

3

-1

4

5

3

2

1

5

4

2

2

Sx2=3.80

Varian

0
Sd

2=0.75

Kovarian

Wahyu Widhiarso

FORMULA RELIABILITAS

FORMULA GUTTMAN




s 2y1  s 2y 2
rxx'  2 1 
s 2x


FORMULA RELIABILITAS





Wahyu Widhiarso

7

FORMULA GUTTMAN
Skor Belah

Subjek

X

1

9

5

4

2

5

3

2

3

5

2

3

4

5

3

2

5

4

2

2

Sx2=3.80

Sy12=1.22

Sy22=0.89

Varian

Y1

Y2

Kovarian

Wahyu Widhiarso

FORMULA RELIABILITAS

FORMULA ALPHA CRONBACH
s 2x  s 2t  (s e21  s e22  ...s 2ei )
 s 2t   s e2i
s  k s
2
t

 st 
  x   se21
k
1 2 2
  2  s t x  sei
k 
2

2
t

s2yi
s2yi

 1  2
2
2
 s yi   2   s t   s ei
k 
 k 
  2  s 2t   s 2ei
k 
 1 
   s 2t   s e2i
 k 
FORMULA RELIABILITAS

Varian Skor
Tampak (St2)

Sei2 : habis

1
s 2x   s 2yi  s 2t -   s 2t
k
1
2 
 s t 1  
 k
2  k -1 
 st 

 k 

s 2x

Varian Skor
Murni (St2)

 k  2
2
s 2t  
 s x   s yi
 k -1 
2
 k    s yi
rxx'  
 1 s 2x
 k -1  





Wahyu Widhiarso

8

FORMULA ALPHA CRONBACH
Skor Belah

X
X

Y1
T

T1

8

8

7
6

Y2
E1

Y3

T2

E2

T3

8

8

7

7

7

6

6

6

3

5

5

5

3

4

4

4

2

3

3

3

1

2

S x2

ST2

2

E3

2

SE12

SE22

SE32

Sx2 = ST2+SE12+SE22+SE32=ST2+SEi2

Wahyu Widhiarso

FORMULA RELIABILITAS

y1  t1  e1
s t1e1  0
s e1e 2  0

FORMULA FLANAGAN
rxx ' 

sy1y2  s( t1 e1 )(t 2 e2 )
 s( t1 e1 )(t 2 e2 )
 st1t 2  st1e2  st 2e2  se2e2
 st1e 2
 s2t1
s y1y2  s

2
t1

FORMULA RELIABILITAS

s 2tx
s 2x

t x  t1  t 2
s 2t1  s 2t2

s 2tx  s (2t1  t 2 )
 s 2t1  s 2t2  2s t1 s t 2
 s 2t1  s 2t2  2s 2t1
 2s 2t1  2s 2t1
 4s 2t1

rxx ' 

4s 2y1y 2
s

2
x

s 2t  4s 2t1
Wahyu Widhiarso

9

Cronbach

2
 k    s y i
rxx'  
 1s 2x
 k - 1  






 k    p(1 - p)
rxx'  
 1 k
1
s 2x


KR-20

FORMULA RELIABILITAS






s 2y  p(1  p)

Wahyu Widhiarso

10