New and old methods of analyzing two-choice experiments with confidence ratings are evaluated. These include the theory of signal detectability (TSD), Luce's choice theory,nonparametric techniques based on areas under receiver-operating characteristic (ROC) functions, andmethods based on S' and omega, proposed by Balakrishnan and his colleagues. New methods for assessing the bias of a complete ROC function are proposed, together with an additional area-based measure of response bias. Area measures of both sensitivity and bias proved the most consistent. Response bias for a full ROC function was larger than bias at the cut point and also provided additional information. Participants showed voluntary control of bias for all measures except omega. Unequal variance versions of TSD and choice models gave similar fits to data, with the choice model closer to an equal variance version. Discrimination data from Balakrishnan (1999) formed the empirical test bed.