User Manual

20050501
2-Sample t Test
Command: TwoSampleTTest䡺
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–1
2
σ
n
1
+
x
2 n–1
2
σ
n
2
o1 : mean of sample 1 data
o2 : mean of sample 2 data
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
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 xp 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 = n1 + n2 – 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
Command Syntax
Syntax 1 (list format)
“ µ 1 condition”, List(1), List(2), Freq(1) (or 1), Freq(2) (or 1), Pooled condition (On
or Off)
* “Freq” can be omitted. Doing so sets “1” for “Freq”.
* “Pooled” can be omitted. Doing so sets “Off” for “Pooled”.
Syntax 2 (parameter format)
“ µ 1 condition”, o1 value, x1 σ n-1 value, n1 value, o2 value, x2 σ n-1 value, n2 value,
Pooled condition (On or Off)
* “Pooled” can be omitted. Doing so sets “Off” for “Pooled”.
7-9-7
Tests