Tau (τ) compares an observed enrichment score to all others in a reference database. In principle, τ can be computed by comparison to scores from any database of reference signatures, and the most common approach is to generate a null distribution by random permutation. However, a more stringent test that avoids having to make assumptions regarding the complex correlation structure of gene expression data is to use a compendium of diverse, biologically relevant perturbational signatures, such as those in CMap-LlOOOvl, as it is these reference signatures against which any novel connection must compete. Thus, query results are scored with τ as a standardized measure ranging from -100 to 100; a τ of 90 indicates that only 10% of reference perturbations showed stronger connectivity to the query. Because the reference is fixed, τ can be used to compare results across queries - a connection with a significant p-value and FDR but low τ would suggest a highly promiscuous relationship whose connections are not unique.
