9.9: Test of Independence
 Page ID
 5791
ChiSquared II – Testing for Independence
It is a common belief that age influences food preference. Suppose you wanted to test that hypothesis. How could you test observed data to see if the two variables (age and food preference) influence each other?
Look to the end of the lesson to see the answer.
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ChiSquared Test of Independence
A chisquare (χ2) test can be used to determine if observed data indicates that two variables are dependent in much the same way that the test can be used to determine goodness of fit.
Just as with a goodness of fit test, we will calculate expected values, calculate a chisquare statistic, and compare it to the appropriate chisquare value from a reference to see if we should reject H0, which is that the variables are not related.
In fact, the only major difference in process between a goodness of fit test and a test of independence is how we calculate the expected values, as you will see in the first example.
Just for reference:
 The formula to calculate chisquare is:
 Some good resources for a chisquare critical value calculator's are Daniel Soper's website and Easy Calculation's website. You can also search "free critical chisquare value calculator".
 The formula for calculating expected values in a test of independence is:
Where C is the observed column total for the cell, R is the observed row total for the cell, and n is the total number of samples. (see Example A for clarification of the use of the formula)
 The degrees of freedom in a test of independence are calculated as:
df=(rows−1)(columns−1)
Finding Expected Values
Given the following contingency table, what is the expected value for each of the four cells in the body of the table?
A 
B 
TOTAL 

X 
23 
37 
60 
Y 
19 
41 
60 
TOTAL 
42 
78 
120 
To calculate the expected values, use the formula expected cell value=C×Rn for each cell:
Additional Resources
Video: Test Requiring the ChiSquare Distribution
Practice: Test of Independence