Co Cd

Old New

Condition 1

Old New

Condition 2

FIGURE 24.3. Hit rates and false alarm rates from two hypothetical conditions (top panel); hit rates and false alarm rates coplotted across a range of response criteria, as a receiver-operating characteristic (ROC; bottom panel), d' indicates the discriminability of studied and unstudied stimuli.

0 .1 .2 .3 ,4 .5 .6 .7 .8 .9 1 False Alarm Rate (FAR)

FIGURE 24.3. Hit rates and false alarm rates from two hypothetical conditions (top panel); hit rates and false alarm rates coplotted across a range of response criteria, as a receiver-operating characteristic (ROC; bottom panel), d' indicates the discriminability of studied and unstudied stimuli.

distribution of evidence for studied items is approximately 1.25 times larger than for the distribution for unstudied items.

The form of ROC curves has also been brought to bear on the question that we introduced earlier, namely, what processes underlie the mirror effect in recognition? Consider the relationship between word frequency and recognition, as discussed in the previous section. The evidence from speed-accuracy trade-off functions was equivocal as to the question of whether a slow-acting deliberative process combines with general memory familiarity to produce

False Alarm Rate (FAR)

FIGURE 24.4. ROC and normalized ROC (zROC) functions from an experiment on recognition memory. The slope of the line is indicated by m.

Z-Transformed False Alarm Rate (zFAR)

FIGURE 24.4. ROC and normalized ROC (zROC) functions from an experiment on recognition memory. The slope of the line is indicated by m.

the empirical dissociation seen between hit rate and false-alarm rate as a function of word frequency. In the preceding case, the argument concerned whether subjects made a postmnemonic assessment of the normative familiarity of the stimulus, thereby deriving a value against which to compare the actual experienced familiarity of the word.

Another argument is that two different processes can contribute to the endorsement of an item on a recognition test. The first is the same as that por trayed in the earlier argument: Stimuli enjoy some temporary boost in familiarity as a function of exposure, and this familiarity value provides some evidence of the recency or probability of past encounters with this word. Notably, however, the familiarity itself conveys nothing about the specific nature of the previous experience, so it can lead to spurious false alarms to other recently exposed but contraindicated stimuli (Jacoby, 1999) or even to unstudied stimuli that are systematically related to studied materials (Roediger & McDermott, 1995).

Familiarity is hypothesized to be augmented by an additional process, often called recollection, that serves to retrieve specific aspects of the prior encounter with the stimulus. One might recollect that a word was presented in italic typeface, or that a recommendation regarding life insurance came from a particularly disreputable agent, or that an author's name is familiar only because of a well-publicized tawdry scandal. Obviously the details of a recollective experience can alter the way in which we engage a stimulus: We might choose to interact differently with a well-respected member of our field than with a convicted felon. With respect to word frequency, it has been suggested that the advantage that studied low-frequency words enjoy owes to a greater rate of recollection for such words, and that the lower false-alarm rate for unstudied low-frequency items reflects lower baseline familiarity (Reder et al., 2000).

Whereas familiarity is presumed to reflect a continuum of mnemonic evidence, recollection is typically thought to be a finite-state process. That is, recollected evidence directly implicates a specific prior experience as the locus of familiarity for an item, and that evidence specifies conclusively the status of the stimulus in question: It was experienced in the appropriate, sought-after context, or it was not. This process is finite-state in the sense that the evidence either promotes or discourages a response, with no degrees in intervening uncertainty. Finite-state models imply psychological thresholds: There is a point (or multiple points) at which there is an abrupt transition from "no evidence" to "evidence." This stands in contrast to the evidence continuum that familiarity provides, in which no amount of familiarity perfectly implicates prior study; similarly, a complete absence of familiarity does not unequivocally imply the lack of prior exposure.

Unlike the ROC functions described for Gaussian-based evidence distributions, thresholds do not imply ROCs that intersect the origin and the point (1, 1) in probability space, nor are they necessarily linear in binormal space throughout the function. Thus, departures from linearity in the form of the zROC can be taken as evidence for the contribution of threshold-based evidence to the recognition decision.

To use this logic to address the question of how familiarity and recollection contribute to recognition, and how they can be related to the word-frequency mirror effect, Arndt and Reder (2002) estimated ROCs for the recognition of low- and high-frequency words under special conditions designed to promote the use of recollection-based recognition. Under these conditions, subjects were asked to discriminate between studied items and the plurality-reversed complements of previously studied items. Researchers have presumed that a plurality-reversed distractor should elicit approximately equal familiarity to that of the original studied item, thus leaving recollection as the only basis for correct discrimination (Hintzman & Curran, 1994; Hintzman, Curran, & Oppy, 1992). In contrast to the standard ROCs elicited by recognition, as described earlier, ROCs elicited from this task are nonlinear in Gaussian coordinates (Rotello, Macmillan, & Van Tassel, 2000) as are ROCs from other tasks thought to emphasize the contribution of recollection (Yonelinas, 1997, 1999).

In comparing these functions for high- and low-frequency words, Arndt and Reder (2002) reported nonlinear zROCs for plurality-reversed recognition and linear zROCs for standard recognition, thus replicating prior findings. More importantly, the low-frequency zROC was more convex than the high-frequency zROC, a result that suggested that a threshold recollection process played a larger role in low-frequency item recognition then in high-frequency item recognition, consistent with the interpretation of Reder et al. (2000).

More generally, it is important to note that ROC functions can be derived from theories that cannot predict raw hit rates or false-alarm rates. Thus, only by combining the two and generalizing across different levels of decision bias can such functions be derived. I hope to have shown here that the evaluation and comparison of such functions is central to progress in understanding recognition memory.

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