Techniques for in vitro genomic and proteomic analysis are generating large amounts of quantitative biological data, with high-density DNA microarrays capable of producing 30,000 measurements from a single sample of RNA. Such data offer fertile ground for systematic computational analyses to identify new cancer targets or potential therapeutic agents. For such techniques to be most useful, computational methods must generate conclusions that are quantitatively supportable in a rigorous statistical sense, not just provide a means of visualization. False patterns may arise when the ratio between the number of measurements and the number of experimental samples is very high. We present a general method for rigorously identifying correlations between variation in high-bandwidth biological measurements and outcomes or phenotypes. We apply the technique to DNA copy number data and expression data from multiple malignancy types. We demonstrate identification of specific abnormalities linked with poor outcomes, as well as automatic classification of tumor samples by phenotype using an augmentation of the method. The techniques have been implemented in the context of an integrated Web-based data system designed to facilitate interaction between biologists and computational researchers.