What is the chi-square statistic?

The chi-square statistic is a measure of divergence between your data's distribution and an expected or hypothesized distribution of your choice. For example, it is used to:
  • Test the independence or determine association between categorical variables. For example, if you have a two-way table of election results by voters' genders, chi-square statistics can help determine whether a vote is independent of the voter's gender, or if there is some association between vote and gender. If the p-value associated with your chi-square statistic is less than your selected α, the test rejects the null hypothesis that the two variables are independent.
  • Determine whether a statistical model fits the data adequately. If the p-value associated with your chi-square statistic is less than your selected α, the test rejects the null hypothesis that the model fits the data.

For categorical data, Minitab can report each category's contribution to the chi-square value, which quantifies how much of the total chi-square value is attributable to each category's divergence. For example, if a goodness-of-fit test rejects the null hypothesis, is this outcome caused by all categories differing moderately from their expectations, or to a single category differing strongly from its expectation? For example, suppose you expect a sample of 100 cars in a very large parking lot to contain 50 sedans, 27 trucks, and 23 vans, but instead it contains 61 sedans, 16 trucks, and 23 vans. The "sedan" and "truck" categories did not meet their expectation, but "van" did. Therefore, "van" contributes nothing to the resulting chi-square value; all the divergence in the data comes from the "sedan" and "truck" categories.

Note

Minitab does not use Yates' correction factor when it calculates the chi-square statistic.

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