χ² goodness-of-fit test

The goodness-of-fit test checks whether the frequencies of the categories fit expected proportions, for example a uniform distribution or 9 : 3 : 3 : 1. p below .05 means: the frequencies depart from the expectation.

Example: χ²(3, N = 556) = 0.47, p = .925: the frequencies do not speak against the expected proportions 9 : 3 : 3 : 1.

Caution: If fewer than 1 is expected in a category, or fewer than 5 in more than a fifth of the categories, the p is uncertain (Cochran 1954). A non-significant result does not show the expectation.