Mixing strong and weak targets provides no evidence against the unequal-variance explanation of ʐROC slope: a comment on Koen and Yonelinas (2010)

Koen and Yonelinas (2010; K&Y) reported that mixing classes of targets that had short (weak) or long (strong) study times had no impact on ʐROC slope, contradicting the predictions of the encoding variability hypothesis. We show that they actually derived their predictions from a mixture unequal-variance signal detection (UVSD) model, which assumes 2 discrete levels of strength instead of the continuous variation in learning effectiveness proposed by the encoding variability hypothesis. We demonstrated that the mixture UVSD model predicts an effect of strength mixing only when there is a large performance difference between strong and weak targets, and the strength effect observed by K&Y was too small to produce a mixing effect. Moreover, we re-analyzed their experiment along with another experiment that manipulated the strength of target items. The mixture UVSD model closely predicted the empirical mixed slopes from both experiments. The apparent misfits reported by K&Y arose because they calculated the observed slopes using the actual range of ʐ-transformed false-alarm rates in the data, but they computed the predicted slopes using an extended range from - 5 to 5. Because the mixed predictions follow a slightly curved ʐROC function, different ranges of scores have different linear slopes. We used the actual range in the data to compute both the observed and predicted slopes, and this eliminated the apparent deviation between them.