a. English fluency
Length of Residence  
English Fluency  Less than Five Years (Low)  More than five Years (High)  Totals 
Low  20  10  30 
High 



Totals  25  20  50 
b. Total family income
Length of Residence  
Income  Less than Five Years (Low)  More than five Years (High)  Totals 
Low  18  8  26 
High 



Totals  25  25  50 
c. Extent of contact with country of origin
Length of Residence  
Contact  Less than Five Years (Low)  More than five Years (High)  Totals 
Rare  5  20  25 
Frequent 



Totals  25  25  50 
(a)
To find:
The gamma and the relationship in terms of strength and direction.
Given:
A small sample of nonEnglishspeaking immigrants to the United States has been interviewed about their level of assimilation.
The given table of information is,
Length of Residence  
English Fluency  Less than Five Years (Low)  More than five Years (High)  Totals 
Low  20  10  30 
High  5  15  20 
Totals  25  20  50 
Approach:
If the gamma value is less than 0.30, it is said that there is a weak association between the categories.
If the gamma value is greater than 0.60, it is said that there is a strong association between the categories.
The gamma compares the number of pairs of cases ranked in the same order on both variables (
Formula used:
To compare the number of pairs of cases ranked in the same order on both variables (
Calculation:
From the given table of information,
The value of
And the value of
(b)
To find:
The gamma and the relationship in terms of strength and direction.
(c)
To find:
The gamma and the relationship in terms of strength and direction.
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