Often researchers are interested in comparing multiple experimental groups (e.g. tumor size) with a reference group (e.g. normal tissue) on the basis of thousands of features (e.g. genes) and determine if a differentially expressed feature is up or down regulated in a pairwise comparison. There are two sources of false discoveries, one due to multiple testing involving several pairwise comparisons and the second due to falsely declaring a feature to be up (or down) regulated when it is not (known as directional error). Together, the total error rate is called the mixed directional false discovery rate (mdFDR).