Useful scientific theories are useful: A reply to Rouder, Pratte, and Morey (2010)

In a recognition memory experiment, Mickes, Wixted, and Wais (2007) reported that distributional statistics computed from ratings made using a 20-point confidence scale (which showed that the standard deviation of the ratings made to lures was approximately 0.80 times that of the targets) essentially matched the distributional statistics estimated indirectly by fitting a Gaussian signal-detection model to the receiver-operating characteristic (ROC). We argued that the parallel results serve to increase confidence in the Gaussian unequal-variance model of recognition memory. Rouder, Pratte, and Morey (2010) argue that the results are instead uninformative. In their view, parametric models of latent memory strength are not empirically distinguishable. As such, they argue, our conclusions are arbitrary, and parametric ROC analysis should be abandoned. In an attempt to demonstrate the inherent untestability of parametric models, they describe a non-Gaussian equal-variance model that purportedly accounts for our findings just as well as the Gaussian unequal-variance model does. However, we show that their new model—despite being contrived after the fact and in full view of the to-be-explained data—does not account for the results as well as the unequal-variance Gaussian model does. This outcome manifestly demonstrates that parametric models are, in fact, testable. Moreover, the results differentially favor the Gaussian account over the probit model and over several other reasonable distributional forms (such as the Weibull and the lognormal).