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20060301
2-Sample
t
Test
Menu: [Test]-[Two-Sample TTest][Test]-[Two-Sample TTest]
Description: This command compares the population means of two populations when
population standard deviation is unknown. A 2-Sample
t
Test is used for
t
distribution.
t =
o
1
—
o
2
x
1
n
2
n
1
+
x
2 n
2
n
2
o
1
: sample mean of sample 1 data
o
2
: sample mean of sample 2 data
x
1
σ
n
−1
: sample standard deviation of sample 1
x
2
σ
n
−1
: sample standard deviation of sample 2
n
1
: size of sample 1
n
2
: size of sample 2
This formula is applicable when the population standard deviations of the two
populations are not equal. The denominator is different when the population
standard deviations are equal.
The
t
distribution degrees of freedom
df
and
x
p
σ
n
−1
differ according to whether
the population standard deviations of the two populations are equal.
When the two population standard deviations are equal (pooled)
df
=
n
1
+
n
2
– 2
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
When the two population standard deviations are not equal (not pooled)
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
Definition of Terms
μ
1
condition : sample mean value test conditions (“
≠
” specifies two-tail test, “<”
specifies one-tail test where sample 1 is smaller than sample 2, “>”
specifies one-tail test where sample 1 is greater than sample 2.)
List(1) : list where sample 1 data is located
List(2) : list where sample 2 data is located
Freq(1) : frequency of sample 1 (1 or list name)
Freq(2) : frequency of sample 2 (1 or list name)
Pooled : On or Off
o
1
: sample mean of sample 1 data
x
1
σ
n
−1
: sample standard deviation of sample 1 (
x
1
σ
n
−1
> 0)
n
1
: size of sample 1 (positive integer)
o
2
: sample mean of sample 2 data
x
2
σ
n
−1
: sample standard deviation of sample 2 (
x
2
σ
n
−1
> 0)
n
2
: size of sample 2 (positive integer)
1
1
—
—
1
1
—
—
7-9-10
Tests
20070301