Reexamining the goodness-of-fit problem for interval-scale scores

A classic data-analytic problem is the statistical evaluation of the distributional form of interval-scale scores. The investigator may need to know whether the scores originate from a single Gaussian distribution or from a mixture of Gaussian distributions or from a different probability distribution. The relative merits of extant goodness-of-fit metrics are discussed. Monte Carlo power analyses are provided for several of the more powerful goodness-of-fit metrics.