Operation Manual

Appendix B: Reference Information 380
The degrees of freedom df that make up the mean squares are:
Ü
Ü
2-SampFTest
Below is the definition for the 2-SampÜTe st .
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.
where:
I
Sxi
ni
=
=
=
=
=
number of populations
the mean of each list
the standard deviation of each list
the length of each list
the mean of all lists
Sx1, Sx2 =
Sample standard deviations having
and degrees of freedom df,
respectively.
Ü =
Û-statistic =
df(x, , )
=
Ûpdf( ) with degrees of freedom df, ,
and
p =reported p value
Factordf I 1–numeratordf for==
Errordf n
i
1–
i 1=
I

denominatordf for ==
x
i
x
n
1
1–
n
2
1–
Sx1
Sx2
---------


2
n
1
1–
n
2
1–
n
1
1–
n
2
1–

1

2

pf
F


xn
1
1 n
2
1–,–,dx=

1

2

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


==