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9. Statistic Formula
I Test
Test
1-Sample
Z Test
= (o –
0
)/(/' )
2-Sample Z Test
= (o
1
– o
2
)/ (/
1
) + (/
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
= (o –
0
)/(s
/' )
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 =
(x
i
– o)(y
i
– p)/
(x
i
– o)
2
a = p – bo
i=1
n
i=1
n
C
2
GOF Test
O
i
: The i-th element of the observed
list
E
i
: The i-th element of the expected
list
C
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
=
n
i
(o
i
− o)
2
MS = SS/Fdf MSe = SSe/Ed
f
i=1
k
Fdf = k −1 Edf =
(n
i
– 1)
SSe =
(n
i
– 1)s
xi
2
i=1
k
i=1
k
2
=
(O
i
− E
i
)
2
/E
i
i
k
2
=
(O
i
− E
i
)
2
/E
i
i
k
2
=
(O
ij
− E
ij
)
2
/E
i
j
i
k
j
R
E
ij
=
x
ij •
x
ij
/
n
i=1
k
j=1
R
2
=
(O
ij
− E
ij
)
2
/E
i
j
i
k
j
R
E
ij
=
x
ij •
x
ij
/
n
i=1
k
j=1
R