Goodness-of-Fit Tests

Goodness-of-fit tests include various tests that measure how well a statistical model (which is built from theory) fits the observed data. Depending on the types of distributions and the nature of the variables being examined, different goodness-of-fit tests are used. Commonly used tests include Pearson’s chi-square (χ2) test and R2 measure of goodness of fit. This entry describes the rationale of each test and the steps taken to conduct each test.

Pearson’s χ2 Test

Pearson’s χ2 test is a goodness-of-fit test used in the context of discrete distributions (i.e., the data are categorical in nature). Introduced by Karl Pearson in 1900, Pearson’s χ2 test evaluates whether the frequency of observations in each category statistically differs from the theoretical prediction. A “good fit” model indicates we can reasonably ...

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