Short-term memory for the comparative instructions in symbolic comparison.

In the current study, a novel paradigm was used in which participants (N = 24) first compared the sizes of pairs of animals and then were asked, on half of the trials, to make a follow-up identification judgment regarding either the form of the comparative instruction that had just been used for the preceding comparison (i.e., smaller? or larger?) or the size of the stimuli in the comparison pair. To selectively enhance the difficulty associated with processing each of these aspects, on a large number of comparison trials, either the comparative instruction or the stimulus pair, respectively, was presented only very briefly. Results indicate that memory for the comparative instructions was dependent on the relative size of the stimulus pair such that participants were more likely to correctly identify the smaller form of the comparative instruction after comparing pairs of small stimulus items, as well as more likely to correctly identify the larger form of the comparative instruction after comparing pairs of large stimulus items. Such results are consistent with the view that the size of the stimulus pair contextually activates the representation of the congruent form of the comparative instruction.

Enhancing semantic congruity effects with category-contingent comparative judgments.

In each of two experiments the direction of a binary comparison was contingent on the category of the stimulus pair. In one experiment, participants had to compare the size of animals from memory. On congruent trials, they had to select the smaller animal if both were small and the larger if both were large and on incongruent trials they selected the larger if both were small and the smaller if both were large. In a second experiment, participants had to compare visual extents and the direction of the comparison was contingent on whether the lines were short or long. Response times were increased and semantic congruity effects (SCEs) were greatly amplified with the category-contingent instructions relative to the conventional non-contingent instructions, precisely as predicted by the class of evidence accrual models of decisional processing and contrary to the single-sample stage models of the SCE.

SNARC effects with numerical and non-numerical symbolic comparative judgments: instructional and cultural dependencies.

With English-language readers in an experiment requiring pairwise comparative judgments of the sizes of animals, the nature of the association between the magnitudes of the animal pairs and the left or right sides of response (i.e., the SNARC effect) was reversed depending on whether the participants had to choose either the smaller or the larger member of the pair. In contrast, such a dependence of the direction of the SNARC effect on the form of the comparative instructions was not evident for pairwise comparisons of numerical magnitude made by a similar group of participants. Furthermore, exactly the same configuration of findings was obtained for a single group of Israeli-Palestinian right-to-left reading and writing participants, except that the spatial direction of the SNARC effects for both the animal-size and number comparisons were completely reversed. In a final experiment with English readers, SNARC effects paralleling those for the animal-size comparisons were obtained for pairwise comparative judgments involving the just-learned height relations between 6 imaginary individuals. As will be discussed, such results serve to extend the generality of the SNARC effect far beyond the current modal view that it simply reflects culturally influenced, long-term learned associations between numerical magnitudes and the locations on a fixed mental number line. The implications that these results have for both the Proctor and Cho (2006) polarity correspondence view and the Gevers, Verguts, Reynvoet, Caessens, and Fias (2006) computational model of the SNARC effect will also discussed.

Selective attention and subjective confidence calibration.

In the present experiments, failures of selective visual attention were invoked using the B. A. Eriksen and C. W. Eriksen (1974) flanker task. On each trial, a three-letter stimulus array was flashed briefly, followed by a mask. The identity of the two flanking letters was response congruent, neutral, or incongruent with the identity of the middle target letter. On half of the trials, confidence ratings were obtained after each response. In the first three experiments, participants were highly overconfident in the accuracy of their responding to incongruent flanker stimulus arrays. In a final experiment, presenting a prestimulus target location cue greatly reduced both selective attention failure and overconfidence. The findings demonstrate that participants are often unaware of such selective attention failures and provide support for the notion that, in these cases, decisional processing is driven largely by the identities of the incongruent flankers. In addition, responding was invariably slower and sometimes more accurate when confidence was required than when it was not required, demonstrating that the need to provide posttrial confidence reports can affect decisional processing. Moreover, there was some evidence that the presence of neutral contextual flanking information can slow responding, suggesting that such nondiagnostic information can, indeed, contribute to decisional processing.

Anchoring effects in the judgment of confidence: semantic or numeric priming?

Over the last decade, researchers have debated whether anchoring effects are the result of semantic or numeric priming. The present study tested both hypotheses. In four experiments involving a sensory detection task, participants first made a relative confidence judgment by deciding whether they were more or less confident than an anchor value in the correctness of their decision. Subsequently, they expressed an absolute level of confidence. In two of these experiments, the relative confidence anchor values represented the midpoints between the absolute confidence scale values, which were either explicitly numeric or semantic, nonnumeric representations of magnitude. In two other experiments, the anchor values were drawn from a scale modally different from that used to express the absolute confidence (i.e., nonnumeric and numeric, respectively, or vice versa). Regardless of the nature of the anchors, the mean confidence ratings revealed anchoring effects only when the relative and absolute confidence values were drawn from identical scales. Together, the results of these four experiments limit the conditions under which both numeric and semantic priming would be expected to lead to anchoring effects.

Reading habits for both words and numbers contribute to the SNARC effect.

This study compared the spatial representation of numbers in three groups of adults: Canadians, who read both English words and Arabic numbers from left to right; Palestinians, who read Arabic words and Arabic-Indic numbers from right to left; and Israelis, who read Hebrew words from right to left but Arabic numbers from left to right. Canadians associated small numbers with left and large numbers with right space (the SNARC effect), Palestinians showed the reverse association, and Israelis had no reliable spatial association for numbers. These results suggest that reading habits for both words and numbers contribute to the spatial representation of numbers.

Probability assessment with response times and confidence in perception and knowledge.

In both a perceptual and a general knowledge comparison task, participants categorized the time they took to decide, selecting one of six categories ordered from "Slow" to Fast". Subsequently, they rated confidence on a six-category scale ranging from "50%" to "100%". Participants were able to accurately scale their response times thus enabling the treatment of the response time (RT) categories as potential confidence categories. Probability assessment analyses of RTs revealed indices of over/underconfidence, calibration, and resolution, each subject to the "hard-easy" effect, comparable to those obtained with the actual confidence ratings. However, in both the perceptual and knowledge domains, resolution (i.e., the ability to use the confidence categories to distinguish correct from incorrect decisions) was significantly better with confidence ratings than with RT categorization. Generally, comparable results were obtained with scaling of the objective RTs, although subjective categorization of RTs provided probability assessment indices superior to those obtained from objective RTs. Taken together, the findings do not support the view that confidence arises from a scaling of decision time.

Remembered instructions with symbolic and perceptual comparisons.

Semantic congruity effects (SCEs) were obtained in each of two experiments, one with symbolic comparisons and the other with comparisons of visual extents. SCEs were reliably larger when the instructions indicating the direction of the comparison were represented by consonant-vowel-consonant (CVC) nonsense syllables, which had been associated with the conventional instructions in a preliminary learning phase of the experiment. Enhanced SCEs with the CVC instructions were evident, especially when stimulus pair location and instruction direction did not match. This finding is not readily explained by any non-evidence-accrual theories of the SCE (e.g., expectancy, semantic coding, and reference point) or by their accrual-based extensions. On the other hand, the general class of evidence-accrual views of SCEs, such as those developed in Leth-Steensen and Marley (2000) and in Petrusic (1992), receive considerable empirical support when the locus of the SCE is specified in terms of the congruency of stimulus pair location and the direction of the instruction.

Effects of instruction presentation mode in comparative judgments.

In each of two experiments, the comparative instructions in a symbolic comparison task were either varied randomly from trial to trial (mixed blocks) or left constant (pure blocks) within blocks of trials. In the first experiment, every stimulus was compared with every other stimulus. The symbolic distance effect (DE) was enhanced, and the semantic congruity effect (SCE) was significantly larger, when the instructions were randomized than when they were blocked. In a second experiment, each stimulus was paired with only one other stimulus. The SCE was again larger when instructions were randomized than when they were blocked. The enhanced SCE and DE with randomized instructions follow naturally from evidence accrual views of comparative judgments.

On the mental representation of negative numbers: context-dependent SNARC effects with comparative judgments.

In one condition, positive and negative number pairs were compared in separate blocks of trials. In another condition, the positive and the negative number pairs were intermixed. In the intermixed condition, comparisons involving negative numbers were faster with the left hand than with the right, and comparisons were faster with the right hand than with the left hand with the positive numbers; that is, a spatial numerical association of response codes (SNARC) effect was obtained, in which the mental number line was extended leftward with the negative numbers. On the other hand, in the blocked condition, a reverse SNARC effect was obtained with the negative numbers; that is, negative number pairs have the same underlying spatial representation as the positive numbers in this context. Nongraded semantic congruity effects, obtained in both the blocked and the intermixed conditions, are consistent with the idea that magnitude information is extracted prior to the generation of discrete semantic codes.

Long-term memory for elementary visual percepts: memory psychophysics of context and acquisition effects.

In the first phase of each of two experiments, participants learned to associate a set of labels (i.e., consonant-vowel-consonant [CVC]) with a set of line lengths by using a paired-associate learning procedure. In the second phase of each experiment, these learned labels were used as memorial standards in the method of constant stimuli. Psychometric functions and the associated indices of discriminative performance (i.e., Weber fractions [WFs], just noticeable difference, and point of subjective equality) were then obtained for the remembered standards. In Experiment 1, WFs (i.e., the indices of memory precision) obtained with remembered standards were found to be higher (i.e., had poorer discriminability) than were WFs obtained with perceptual standards. In addition, WFs obtained with the remembered standards exhibited serial position effects (i.e., poorer discriminability for central items in the memory ensemble) and systematically varied with set size (i.e., the number of standards in the memory set), but WFs obtained with perceptual standards did not depend on serial position or set size. In Experiment 2, increasing the number of acquisition trials reduced WFs and diminished serial position effects. In addition, WFs did not vary systematically with the "physical" spacing between the standards in memory, but they did with the ordinal spacing. The results are consistent with a noisy analogue representation of remembered magnitudes, whereby central items in a memory ensemble are subject to lateral inhibition and thus reduced discriminability. Finally, presentation order effects, as defined by the classic time-order error, were observed with purely perceptual comparisons but not with comparisons involving a remembered standard. This latter finding is inconsistent with a strong form of the functional equivalence view of perception and memory.

Adaptive decision processes in perceptual comparisons: effects of changes in the global difficulty context.

Adaptive decision processes were investigated in experiments involving an unexpected change in the global ease or difficulty of the task. Under accuracy stress, a shift from an easy to a difficult context induced a marked increase in decision time, but a shift from a difficult to an easy context did not. Under speed stress, a shift to a more difficult context induced lower accuracy and rated confidence, depending on the difficulty of the decisions. A view of caution developed in D. Vickers's (1979) accumulator theory--whereby one seeks to base decisions on more information--is compared with a view based on slow and fast guessing theory (W. M. Petrusic, 1992; W. M. Petrusic & J. V. Baranski, 1989a)--whereby one seeks to base decisions on more diagnostic information. On balance, the findings support the latter view.

Judging confidence influences decision processing in comparative judgments.

Current theories of confidence in human judgment assume that confidence and the decision it is based on are inextricably tied to the same process (decisional locus theories) or that confidence processing begins only once the primary decision has been completed (postdecisional locus theories). In the absence of auxiliary assumptions, however, neither class of theory permits the judgment of confidence to affect primary decision processing. In the present study, we examined the effect of rendering confidence judgments on the properties of the decision process in a sensory discrimination task. An examination of the properties of the time taken to determine confidence (i.e., the time taken to render the judgment of confidence) revealed clear evidence of postdecisional confidence processing. Concomitantly, the requirement of confidence judgments was found to substantially increase decisional response times, suggesting that some confidence processing occurs during the primary decision process. We discuss the implications of these findings for contemporary models of confidence in human judgment.