Univariate inductive statistics - nominal variable

Chi-Square Goodness of Fit Test

This test enables you to compare the distribution of classes of observations with an expected distribution. The handling of small expected frequencies is controversial. Koehler and Larnz (1980) assert that the chi-square approximation is adequate provided all of the following are true:

• total of observed counts (N) ≥ 10
• number of classes (c) ≥ 3
• all expected values ≥ 0.25

Some statistical software offers exact methods for dealing with small frequencies but these methods are not appropriate for all expected distributions, hence they can be specious.

Example:
Suppose we suspected an unusual distribution of blood groups in patients undergoing one type of surgical procedure. We know that the expected distribution for the population served by the hospital which performs this surgery is 44% group O, 45% group A, 8% group B and 3% group AB. We can take a random sample of routine pre-operative blood grouping results and compare these with the expected distribution.