This thesis considers Nonparametric Predictive Inference (NPI) for ordinal data and accuracy of diagnostic tests. We introduce NPI for ordinal data, which are categor- ical data with an ordering of the categories. Such data occur in many application areas, for example medical and social studies. The method uses a latent variable representation of the observations and categories on the real line. Lower and upper probabilities for events involving the next observation are presented, with specic attention to comparison of multiple groups of ordinal data. We introduce NPI for accuracy of diagnostic tests with ordinal outcomes, with the inferences based on data for a disease group and a non-disease group. We intro- duce empirical and NPI lower and upper Receiver Operating Characteristic (ROC) curves and the corresponding areas under the curves. We discuss the use of the Youden index related to the NPI lower and upper ROC curves in order to deter- mine the optimal cut-o point for the test. Finally, we present NPI for assessment of accuracy of diagnostic tests involving three groups of real-valued data. This is achieved by developing NPI lower and upper ROC surfaces and the corresponding volumes under these surfaces, and we also consider the choice of cut-o points for classications based on such diagnostic tests.