Lapid, Ulrich, and Rammsayer (2008) compared the discrimination performance for two psychophysical methods -that is, the (temporal) two-alternative forced choice (2AFC) task and the reminder task. They reported generally higher difference limens (DLs) for the 2AFC than for the reminder task and attributed this difference to a particular feature of the 2AFC task. García-Pérez and Alcalá-Quintana (2010) performed a reanalysis of Lapid et al.'s data, using a different psychometric function than Lapid et al. In contrast to Lapid et al., these authors reach the opposite conclusion that the two tasks produce similar DL estimates. In this response to their article, it will be shown that DLs are indeed larger in 2AFC tasks than in reminder tasks, contrary to García-Pérez and Alcalá-Quintana's reanalysis. In particular, (1) the conclusions of Lapid et al. are confirmed by further reanalyses that rely on fewer assumptions than do either the original analyses of Lapid et al. or the reanalyses of García-Pérez and Alcalá-Quintana, and (2) the reanalyses of García-Pérez and Alcalá-Quintana are based on demonstrably false assumptions that lead to inappropriate estimates of DL.This article consists of three parts. In the first part, I outline the assumptions of the psychometric functions employed in Lapid et al. (2008). This part also introduces the mathematical/technical background of 2AFC psychometric functions and the customary approaches for estimating the DL in 2AFC tasks. Readers who are interested mainly in the data reanalysis should skip this part. In the second part, I rechecked the data in Lapid et al. to settle the empirical question. I performed analyses that did not require specific assumptions about the proper psychometric function or about lapses. In addition, I also performed analyses with an improved version of García-Pérez and Alcalá-Quintana's (2010) logistic psychometric function. The results of these were clear-cut. DLs are meaningfully larger (by about 50% or slightly more) for the 2AFC than for the reminder task. At the end of this second part, I review the work of Ulrich and Vorberg (2009) and explain why this effect occurs. In the third part, I critically evaluate the assumptions underlying García-Pérez and Alcalá-Quintana's 2AFC analysis. I highlight the problems associated with these assumptions and show how these problems cause them to misinterpret Lapid et al.'s results. This part also critically assesses the psychophysical reality of the difference model with guessing that they propose as an explanation of Lapid et al.'s results. The third part concludes with some additional remarks about García-Pérez and Alcalá-Quintana.
BACKGROUND ON PSYCHOPHYSICAL TASKS AND PSYCHOMETRIC FUNCTIONS