Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.

The test statistic for a test of independence is similar to that of a goodness-of-fit test:

where:

• O = observed values
• E = expected values (which should be at least 5)

A test of independence determines whether two factors are independent or not. The test of independence is always right-tailed because of the calculation of the test statistic. If the expected and observed values are not close together, then the test statistic is very large and way out in the right tail of the chi-square curve, as it is in a goodness-of-fit.

The number of degrees of freedom for the test of independence is:

The following formula calculates the expected number (E):

This text is adapted from Openstax, Introductory Statistics, Section 11.3 Test of Independence