Goodness-of-fit test

Determine whether a statistical model fits your data by analyzing the difference between your observed values and their expected values in the model. For continuous data, you can assess goodness-of-fit visually with a probability plot, or quantitatively with a hypothesis test such as the Anderson-Darling test. For categorical data, you can use a chi-square test or Minitab's goodness-of-fit test for Poisson data. Minitab also performs goodness-of-fit tests for logistic regression models.

Goodness-of-fit tests use the following hypotheses:

·    H0 : The model adequately describes your data

·    H1 : The model does not adequately describe your data

For example, you want to find the distribution that best models the failure times of light bulbs. You run life testing on a sample of light bulbs to observe their failure times. You compare three distributions for the goodness-of-fit they offer your data with Minitab's probability plot.

The p-value for the exponential distribution is low enough to reject the null hypothesis of a good fit. At an alpha-level of 0.05, both the normal distribution and the 3-parameter Weibull distribution provide a good fit for your data. Some analysts choose the distribution with the highest p-value, but any distribution with a nonsignificant p-value is acceptable.