Goodness-of-fit tests are used to validate the use of a particular distribution to describe data arising from sampling or experimentation. Numerous goodness-of-fit tests have been developed. The power divergence family of test statistics includes Pearson’s chi-squared test, the likelihood ratio test, and the Freeman-Tukey chi-squared test. We consider these special cases as well as the family of test statistics and the Nass test. These may also be applied to test the fit of continuous distributions by forming discrete intervals on the continuous scale of measurement. However, the Kolmogorov-Smirnov test is generally preferred when the distribution is continuous and is described in this chapter. Like all data handling systems, they are applied best when the problems and limitations of their use are understood. We begin by focusing on the application of goodness-of-fit tests to discrete distributions.