7-9-10

Tests

2-Sample t Test

Menu: ������������������[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 =

 

o1 — o2

o1

: sample mean of sample 1 data

 

 

 

 

 

o2

: sample mean of sample 2 data

 

x1 n —1

 

x2 n —12

 

 

2

x1σn−1: sample standard deviation of sample 1

 

 

+

 

 

 

 

n1

n2

x2σn−1: sample 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−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

 

 

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

 

 

 

 

 

 

 

 

 

 

 

 

+

n2–1

 

 

 

 

n1–1

 

 

 

 

 

x1σn–12

 

 

C =

 

 

 

 

n1

 

 

 

 

 

σ

2

σ

2

 

 

 

 

 

Definition of Terms

 

x1n1n–1

+ x2n2n–1

 

 

 

 

 

 

 

 

 

μ1 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

 

 

o1 :

 

sample mean of sample 1 data

x1σn−1 :

 

sample standard deviation of sample 1 (x1σn−1 > 0)

n1 :

 

size of sample 1 (positive integer)

o2 :

 

sample mean of sample 2 data

x2σn−1 :

 

sample standard deviation of sample 2 (x2σn−1 > 0)

n2 :

 

size of sample 2 (positive integer)

20070301