This paper presents an index of goodness-of-fit for comparing m models over n trials. The index allows for differentiated weighting of the trials as to their importance in the comparison of the models. Several possible weighting schemes are suggested and the conditions on the weights which assure asymptotic normality of the index distribution are presented. A relative goodness-of-fit test using the index is proposed which is distribution-free under the null hypothesis. Both single model and simultaneous inferential tests are presented for large values of n. An application of the index and subsequent inferences are provided using three probability learning models and human subject data. (Author)