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. For example, logistic regression calculates chi-square statistics to assess the fit of the model. 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. A different example is the goodness-of-fit test for Poisson data in the Basic Statistics menu, which uses chi-square statistics to determine whether your data follow a Poisson distribution.

If your data are discrete, 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? Suppose you expect a crayon box to contain one blue, one red, and one green crayon, but instead it contains one blue, zero red, and two green crayons. The "green" and "red" categories did not meet their expectation, but "blue" did. Therefore, "blue" contributes nothing to the resulting chi-square value; all the divergence in the data comes from the "green" and "red" categories.

Note

Minitab does not use Yate's Correction factor when it calculates the chi-square statistic.

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