Math 221 – Principles of Statistics

Testing Claims about the Independence of Two Variables

Purpose: To test whether two variables are independent of each other.


Conditions: Set up a two-way table of observed counts. One way will be for the values of one of the random variables you’re using. The other will be for values of the other random variable. Use it to compute the expected counts for each cell in the table, thus:. The conditions for the test are


(1) All the data in the two-way table come from a single (simple) random sample.


(2) All expected counts are higher than 1.


(3) No more than 20% of the expected counts are less than 5.





Neither of the variables depends the other. Many people say it this way: There is no association between the two variables. The alternative hypothesis is  At least one of the variables depends on at least one of the others, or, There is an association between some of the variables.



Test Statistic: We recommend using software such as SPSS to calculate the  test statistic, the degrees of freedom, and the p-value. However, you can use the formula , with  degrees of freedom, and get the p-value from a  table such as



Table F in Moore & McCabe’s The Practice of Business Statistics.



SPSS instructions for testing claims about independence: Click here.



Examples of testing claims about independence: Click here.



Related topics:


Chi-squared tests master reference page


Tests of homogeneity (several proportions)


Comparing unknown populations


Goodness-of-fit (comparing populations when one population is “known”)



Statistics Reference Pages: Click here

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