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 =

 

 

M1 — M2

 

 

M1

: sample mean of sample 1 data

 

 

 

 

 

 

 

 

 

M2

: sample mean of sample 2 data

 

 

 

s

2

 

s

 

2

 

 

 

 

x1

+

x2

 

 

sx1

: sample standard deviation of sample 1

 

 

 

 

 

 

 

 

 

 

n1

n2

 

 

 

 

sx2

: 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 sp 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

 

 

 

 

 

 

sp =

 

(n1–1)sx12

+(n2–1)sx22

 

n1

+ n2 – 2

 

 

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

df =

 

 

1

 

 

 

 

 

C2

 

+

(1–C)2

 

 

 

 

 

 

n1–1

 

n2–1

 

 

 

 

 

sx12

C =

 

 

 

 

 

n1

 

 

 

 

sx12

 

sx22

 

 

 

 

 

 

 

 

 

+

 

 

 

 

 

 

 

n1

 

 

 

n2

 

 

 

Definition of Terms

μ1 condition : sample mean value test conditions (“ξ” 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

M1 :

sample mean of sample 1 data

sx1 :

sample standard deviation of sample 1 (sx1 > 0)

n1 :

size of sample 1 (positive integer)

M2 :

sample mean of sample 2 data

sx2 :

sample standard deviation of sample 2 (sx2 > 0)

n2 :

size of sample 2 (positive integer)

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