Casio FX-CG10 - Manual (Page 261)

6-68
9. Statistic Formula
k Test
Test
1-Sample Z Test
z = ( o – μ
0
)/( σ /
' n )
2-Sample Z Test z = (
o
1
–
o
2
)/ ( σ / n
1
) + ( σ / n
2
) 2
1 2
2
1-Prop Z Test
z = ( x / n – p
0
)/ p
0
(1 – p
0
)/ n
2-Prop Z Test
z = ( x
1
/ n
1
– x
2
/ n
2
)/ pˆ (1 – pˆ )(1/ n
1
+ 1/ n
2
)
1-Sample t Test t = ( o – μ
0
)/(s
x
/
' n )
2-Sample t Test (pooled)
t = (
o
1
–
o
2
)/ s
p
2 (1/ n
1
+ 1/ n
2
)
df = n
1
+ n
2
− 2
s
p = (( n
1
– 1)s
x 1
2 + ( n
2
– 1)s
x 2
2 )/( n
1
+ n
2
– 2)
2-Sample t Test (not pooled)
t = (
o
1
–
o
2
)/ s
x 1
2 / n
1
+ s
x 2
2 / n
2
C = (s
x 1
2 / n
1
)/(s
x 1
2 / n
1
+ s
x 2
2 / n
2
)
df = 1/(C 2 /( n
1
– 1) + (1 – C ) 2 /( n
2
– 1))
LinearReg t Test
t = r ( n – 2)/(1 – r 2 )
b =
Σ
( x
i
– o )( y
i
– p )/
Σ
( x
i
– o ) 2 a = p – b o
i=1
n
i=1
n
χ 2 GOF Test
O
i
: The i -th element of the
observed list
E
i
: The i -th element of the
expected list
χ 2 two-way Test
O
ij
: The element at row i , column
j of the observed matrix
E
ij
: The element at row i , column
j of the expected matrix
2-Sample F Test F = s
x 1
2 /s
x 2
2
ANOVA Test
F = MS / MSe
SS =
Σ
n
i
(
o
i
−
o
) 2
MS = SS / Fdf MSe = SSe / Edf
i=1
k
Fdf = k − 1 Edf =
Σ
( n
i
– 1)
SSe =
Σ
( n
i
– 1)s
xi
2
i=1
k
i=1
k
χ
2 =
Σ
( O
i
− E
i
) 2 / E
i
i
k
χ
2 =
Σ
( O
i
− E
i
) 2 / E
i
i
k
χ
2 =
ΣΣ
( O
ij
− E
ij
) 2 / E
ij
i
k
j
R
E
ij
=
Σ
O
ij •
Σ
O
ij
/
Σ Σ
O
ij
i=1
k
i=1
k
j=1
R
j=1
R
χ
2 =
ΣΣ
( O
ij
− E
ij
) 2 / E
ij
i
k
j
R
E
ij
=
Σ
O
ij •
Σ
O
ij
/
Σ Σ
O
ij
i=1
k
i=1
k
j=1
R
j=1
R