The evaluation of medical imaging devices often involves studies that measure the ability of observers to perform a signal detection task on images obtained from those devices. Data from such studies are frequently regressed ordinally using two-sample receiver operating characteristic (ROC) models. We applied some of these models to a number of randomly chosen data sets from medical imaging and evaluated how well they fit using the Akaike and Bayesian information criteria and cross-validation. We find that for many observer data sets, a single-parameter model is sufficient and that only some studies exhibit evidence for the use of models with more than a single parameter. In particular, the single-parameter power-law model frequently well describes observer data. The power-law model has an asymmetric ROC curve and a constant mean-to-sigma ratio seen in studies analyzed with the bi-normal model. It is identical or very similar to special cases of other two-parameter models.