The robust detection of disease-associated splice events from RNAseq data is challenging due to the potential confounding effect of gene expression levels and the often limited number of patients with relevant RNAseq data. Here we present a novel statistical approach to splicing outlier detection and differential splicing analysis. Our approach tests for differences in the percentages of sequence reads representing local splice events. We describe a software package called Bisbee which can predict the protein-level effect of splice alterations, a key feature lacking in many other splicing analysis resources. We leverage Bisbee's prediction of protein level effects as a benchmark of its capabilities using matched sets of RNAseq and mass spectrometry data from normal tissues. Bisbee exhibits improved sensitivity and specificity over existing approaches and can be used to identify tissue-specific splice variants whose protein-level expression can be confirmed by mass spectrometry. We also applied Bisbee to assess evidence for a pathogenic splicing variant contributing to a rare disease and to identify tumor-specific splice isoforms associated with an oncogenic mutation. Bisbee was able to rediscover previously validated results in both of these cases and also identify common tumor-associated splice isoforms replicated in two independent melanoma datasets.