What is a chi-square test?

A chi-square test is a hypothesis test that compares the observed distribution of your data to an expected distribution of data.

There are several types of chi-square tests:
Chi-square goodness-of-fit test
Use this analysis to test how well a sample of categorical data fits a theoretical distribution.
For example, you can test whether a die is fair by rolling the die many times and using a chi-square goodness-of-fit test to determine whether the results follow a uniform distribution. In this case, the chi-square statistic quantifies how much the observed distribution of counts varies from the hypothesized distribution.
Chi-square tests of association and independence
The calculations for these tests are the same, but the question you're trying to answer may be different.
  • Test of association: Use a test of association to determine whether one variable is associated with a different variable. For example, determine whether the sales for different colors of cars depends on the city where they are sold.
  • Test of independence: Use a test of independence to determine whether the observed value of one variable depends on the observed value of a different variable. For example, determine whether the candidate that a person votes for is independent of the voter's gender.

Minitab does not use Yates' correction factor when it performs a chi-square test.

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