7-9-7 Tests

2-Sample t Test

Command: TwoSampleTTest ￿

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 =

 

o1 – o2

 

 

 

 

 

 

 

x1σn–12

x2σn–12

 

 

 

+

 

 

 

 

n1

n2

o1 : mean of sample 1 data

o2 : mean of sample 2 data

x1σn-1 : standard deviation of sample 1

x2σn-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 xpσn-1differ 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

 

 

 

 

 

xpσn–1

=

(n1–1)x1σn–12

+(n2–1)x2σn–12

n1

+ n2 – 2

 

 

When the two population standard deviations are not equal (not pooled)

df =

1

C2 +(1–C)2 n1–1n2–1

x1σ n–12

C =

 

 

 

n1

 

2

2

 

 

 

x1σn–1

 

+

x2σn–1

 

 

 

n1

 

 

n2

 

Command Syntax

Syntax 1 (list format)

“∝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)

“∝1 condition”, o1 value, x1σn-1value, n1 value, o2 value, x2σn-1value, n2 value, Pooled condition (On or Off)

* “Pooled” can be omitted. Doing so sets “Off” for “Pooled”.

20050501