User Guide

pf
F
α
∫
xn
1
1 n
2
1–,–,()dx=
pf
0
F
∫
xn
1
1 n
2
1–,–,()dx=
p
2
--- fxn
1
1 n
2
1–,–,()xd
0
L
bnd
∫
fxn
1
1 n
2
1–,–,()xd
U
bnd
∞
∫
==
t
x
1
x
2
–
S
----------------=
S
Sx
1
2
n
1
-----------
Sx
2
2
n
2
-----------+=
df
Sx
1
2
n
1
-----------
Sx
2
2
n
2
-----------+
⎝⎠
⎜⎟
⎛⎞
2
1
n
1
1–
--------------
Sx
1
2
n
1
-----------
⎝⎠
⎜⎟
⎛⎞
2
1
n
2
1–
--------------
Sx
2
2
n
2
-----------
⎝⎠
⎜⎟
⎛⎞
2
+
----------------------------------------------------------------------------=
Appendix B: Reference Information 386
2-SampÜTest for the alternative hypothesis .
2-SampÜTest for the alternative hypothesis .
2-SampÜTest for the alternative hypothesis s
1
ƒ s
2
. Limits must satisfy the following:
where: [Lbnd,Ubnd] = lower and upper limits
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
2-SampTTest. The two-sample t statistic with degrees of
freedom
df is:
where the computation of S and df are dependent on whether the variances are pooled. If the
variances are not pooled:
df(x, , )
=
Ûpdf( ) with degrees of freedom df, ,
and
p
= reported p value
n
1
1– n
2
1– n
1
1–
n
2
1–
σ
1
σ
2
>
σ
1
σ
2
<