What does the goodness of fit hypothesis test examine?

The goodness of fit hypothesis test is designed to assess how well a statistical model, particularly in the context of categorical data, matches the observed frequencies with the expected frequencies under a specific theoretical distribution. This test determines whether the observed data fits a particular distribution (such as uniform distribution, normal distribution, etc.) or whether there are significant deviations between what was expected and what was actually observed.

In practice, this means that the test quantitatively measures discrepancies between the expected counts of data in different categories and the actual counts observed in those categories. A common application of this test is in the chi-square goodness of fit, which helps researchers ascertain whether their sample data can be considered as drawn from a particular population distribution.

This focus on the relationship between observed and expected frequencies is distinct from other types of statistical analyses. For example, assessing the relationship between two variables typically involves correlation or regression analyses. The overall fit of a regression model evaluates how well a model explains the variability of the outcome variable based on predictor variables. Meanwhile, comparing means between groups is associated with tests like t-tests or ANOVA. Thus, the goodness of fit hypothesis test specifically centers on the alignment of observed data to the anticipated outcomes, making it vital for such categorical data analyses.