Running Head: SIGNAL-DETECTION, DUAL-PROCESS THEORY A Continuous Dual-Process Model of Remember/Know Judgments John T. Wixted & Mickes University of California, San Diego Corresponding author: John T. Wixted Department of Psychology, 0109 University of California, San Diego La Jolla, CA 92093-0109 e-mail: 858-534-3956 fax: 858-534-7190 Abstract
conditions, tests of source memory show that Know judgments are generally associated with lesser degrees of recollection than Remember judgments, not with the absence of recollection (Johnson et al., 2009; Wais et al., 2008). Moreover, if recollection and familiarity are correlated processes, as seems likely, then Know judgments might be associated with lesser degrees of familiarity as well compared to Remember judgments. To address these issues, Old/New memory strength associated with Remember and Know judgments should at least be equated for confidence, a point made by Rotello and Zeng (2008) in their investigation in reaction times associated with Remember and Know judgments. As the large majority of Remember judgments are associated with high confidence, this may often entail using only high-confidence Old/New decisions, as we did in Experiments 1 and 2. Although the recommendation to equate confidence derives from the CDP model proposed in Figure 4, the selective use of high-confidence Know judgments (vs. high-confidence Remember judgments) should not be viewed as problematic from any dual-process perspective. In fact, standard Remember/Know instructions clearly stipulate that Know judgments should be given only when the participant has high-confidence that the item appeared on the list. Consider, for example, the instructions for Know judgments from Rajaram (1993), which are widely used: “Know” responses should be made when...you are certain of recognizing the words but these words fail to evoke any specific conscious recollection from the study list. [emphasis added] In practice, participants generally do not heed this instruction and instead tend to supply Know judgments when they are not certain of their decision. Thus, it makes sense to take
Table 3. Best-fitting parameter values and chi-square goodness-of-fit statistics for 3 models fit to the group ROC data reported by Rotello et al. (2005). STREAK Criterion Variability Model CDP Model Param Condition Param Condition Param Condition Neutral Conservative Neutral Conservative Neutral Conservative c6 1.28 1.19 c6 1.68 1.77 c6 2.32 2.56 c5 0.92 0.94 c5 1.20 1.39 c5 1.67 2.00 c4 0.63 0.74 c4 0.82 1.08 c4 1.15 1.54 c3 0.37 0.48 c3 0.48 0.70 c3 0.69 0.99 c2 0.04 0.18 c2 0.05 0.27 c2 0.08 0.36 r 0.21 -0.12 µr 1.28 1.92 r 0.92 1.58 dx 0.50 0.43 r 0.96 0.74 μR1 0.81 0.70 dy 0.90 0.89 d 1.15 1.16 μF1 0.78 0.96 s 0.76 0.68 Target 1.33 1.51 R1 1.48 1.98 χ2 493.67 595.64 χ2 10.98 24.39 χ2 12.15 21.80 Figure Captions Figure 1. An illustration of the unequal-variance model of recognition memory. The distribution of memory strengths for targets has a higher mean and a higher variance that
(because σF0 and σF1 both equal 1). The value of ci is a particular confidence criterion on the memory strength (R + F) axis, and the value of r is the decision criterion for Remember judgments on the recollection (R) axis. The proportion of Remember judgments for a confidence rating of i or greater, P(F + R > ci and R > r), corresponds to the mass in the top right quadrant, and the proportion of Know judgments for a confidence rating of i or greater corresponds to the mass in the top left quadrant. For a target item, the probability that aggregate memory strength (F + R) exceeds the decision criterion (ci) is: P(F + R > ci) = . To find the proportion of items for which F + R > ci and R > r (and so receive Remember judgments), the above quantity is multiplied by the relative likelihood of observing a particular value of R, and the entire expression is integrated with respect to R over the range of r to infinity. For Remember judgments to targets, the expression would be: P (F + R > ci and R > r |Target) = , where ϕ is normal probability density function. For Remember judgments to lures, the corresponding expression would be: P (F + R > ci and R > r |Lure) = . Note that r, c2, c3, c4, c5, and c6 represent decision criteria, and all are free parameters. In addition, µF1, µR1, and σR1, are free parameters, whereas µF0 and µR0 are both set to 0, and σR0 , σF0 and σF1 are all set to 1 the subscripts 0 and 1 refer to lures and targets, respectively). Thus, these equations simplify to: P (F + R > ci and R > r |Target) = , P (F + R > ci and R > r |Lure) = .
mass in the lower right quadrant, i.e. S > c and r – S < 0. Thus, the relevant equations for Remember judgments to targets and lures are: P (S > ci and r – S < 0 | Target) = , d r – S < 0 | Lure) = . As in the CDP model, µr (now the mean location of the Remember criterion), c2, c3, c4, c5, and c6 represent decision criteria, and they are all free parameters. In addition, µT (the mean of the target distribution), σT (the standard deviation of the target distribution), and σr (the standard deviation of r), are free parameters, whereas µL and σL (the mean and standard deviation of the lure distribution) are set to 0 and 1, respectively. Thus, the equation for lures simplifies to: P (S > ci and r – S < 0 | Lure) = . Finally, the relevant equations for Know judgments to targets and lures are: P (S > ci and r – S > 0 | Target) = , P (S > ci and r – S > 0 | Lure) = .