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20070201
u 2-Sample t Test
2-Sample t Test compares the population means when the population standard deviations
are unknown. The 2-Sample
t Test is applied to t-distribution.
The following applies when pooling is in effect.
d
f
= n
1
+ n
2
– 2
t
=
o
1
– o
2
n
1
1
+
n
2
1
x
p
n–1
2
σ
t
=
o
1
– o
2
n
1
1
+
n
2
1
x
p
n–1
2
σ
x
p n–1
=
σ
n
1
+ n
2
– 2
(n
1
–1)x
1
n–1
2
+(n
2
–1)x
2
n–1
2
σ
σ
x
p n–1
=
σ
n
1
+ n
2
– 2
(n
1
–1)x
1
n–1
2
+(n
2
–1)x
2
n–1
2
σ
σ
¯x1 : mean of sample 1
¯x2 : mean of sample 2
x1
σ
n-1 : standard deviation of
sample 1
x2
σ
n-1 : standard deviation of
sample 2
n1 : size of sample 1
n2 : size of sample 2
xp
σ
n-1 : pooled sample standard
deviation
df : degrees of freedom
The following applies when pooling is not in effect.
t =
o
1
– o
2
x
1 n–1
2
σ
n
1
+
x
2 n–1
2
σ
n
2
t =
o
1
– o
2
x
1 n–1
2
σ
n
1
+
x
2 n–1
2
σ
n
2
df =
1
C
2
n
1
–1
+
(1–C )
2
n
2
–1
df =
1
C
2
n
1
–1
+
(1–C )
2
n
2
–1
C =
x
1 n–1
2
σ
n
1
+
x
2 n–1
2
σ
n
2
x
1 n–1
2
σ
n
1
C =
x
1 n–1
2
σ
n
1
+
x
2 n–1
2
σ
n
2
x
1 n–1
2
σ
n
1
6-5-13
Tests
¯x1 : mean of sample 1
¯x2 : mean of sample 2
x1
σ
n-1 : standard deviation of
sample 1
x2
σ
n-1 : standard deviation of
sample 2
n1 : size of sample 1
n2 : size of sample 2
df : degrees of freedom
Perform the following key operations from the statistical data list.
3(TEST)
2(t)
2(2-S)