) = Û
(
n
1 – n
1 –
df
x,
,
1
2
p
Ü
-
for the alternative hypothesis
2
Samp
Test
α
∫
(
p
=
f
x n
,
–
1 n
,
1
F
Ü
-
for the alternative hypothesis
2
Samp
Test
F
∫
(
p
=
f
x n
,
–
1 n
,
1
0
Ü
-
for the alternative hypothesis s
2
Samp
Test
L
bnd
p
∫
(
-- -
=
f x n
,
–
1 n
1
2
0
where:
[
] = lower and upper limits
Lbnd,Ubnd
The Ü-statistic is used as the bound producing the smallest integral. The remaining bound is
selected to achieve the preceding integral's equality relationship.
2-SampTTest
The following is the definition for the
freedom
is:
df
x
–
x
1
2
t
=
--------------- -
S
where the computation of
variances are not pooled:
2
2
Sx
Sx
1
2
S
=
---------- -
+
---------- -
n
n
1
2
⎛
Sx
1
⎜
---------- -
n
⎝
1
df
=
--------------------------------------------------------------------------- -
2
⎛
Sx
⎞
1
1
------------- -
---------- -
⎜
⎟
n
–
1
n
⎝
⎠
1
1
( ) with degrees of freedom
pdf
and
n
1 –
2
= reported
value
p
σ
)dx
–
1
2
σ
)dx
–
1
2
1
∞
∫
) x d
(
,
–
1
=
f x n
,
2
1
U
bnd
2-SampTTest
and
are dependent on whether the variances are pooled. If the
S
df
2
2
2
⎞
Sx
2
⎟
+
---------- -
n
⎠
2
2
2
2
⎛
Sx
⎞
1
2
------------- -
---------- -
+
⎜
⎟
n
–
1
n
⎝
⎠
2
2
,
n
1 –
,
df
1
>
σ
.
1
2
<
σ
.
1
2
. Limits must satisfy the following:
ƒ s
2
) x d
–
1 n
,
–
1
2
. The two-sample
t
Appendix B: Reference Information
statistic with degrees of
386