Decision strategies determined from the shape of the same-different roc curve: What are the effects of incorrect assumptions?

The literature includes many studies that use the shape of the receiver operating characteristic (ROC) curve derived from the same-different test to ascertain the decision strategy used by the judge: a symmetrical ROC curve indicates a β-decision strategy, and an asymmetrical ROC curve indicates a τt-decision strategy. These studies have not considered the effect that breaches of the assumptions that underlie the standard same - different model would have on inferences drawn from the shape of the ROC curve. Three such assumptions are investigated: the equal-variance assumption; the assumption of no stimulus order effects; and the assumption that the discriminability of the two stimuli is the same when presented first or second in the test sequence. Simulations indicate that the shape of the ROC curve is very tolerant of the breach of these assumptions. Consequently, inferences about the decision strategy used by a judge are fairly robust, and confidence in published results is upheld.