Goodness of fit measures for discrete categorical data

A goodness of fit χ 2 test evaluates the degree to which an observed discrete distribution over one dimension differs from another. A typical application of this test is to consider whether a specialisation of a set, i.e. a subset, differs in its distribution from a starting point (Wallis forthcoming). Like the chi-square test for homogeneity (2 × 2 or generalised row r × column c test), the null hypothesis is that the observed distribution matches the expected distribution. The expected distribution is proportional to a given prior distribution we will term D, and the observed O distribution is typically a subset of D.