Thomas J. Faulkenberry

Response trajectories capture the continuous dynamics of the size congruity effect.

In a comparison task involving numbers, the size congruity effect refers to the general finding that responses are usually faster when there is a match between numerical size and physical size (e.g., 2-8) than when there is a mismatch (e.g., 2-8). In the present study, we used computer mouse tracking to test two competing models of the size congruity effect: an early interaction model, where interference occurs at an early representational stage, and a late interaction model, where interference occurs as dynamic competition between response options. In three experiments, we found that the curvature of responses for incongruent trials was greater than for congruent trials. In Experiment 2 we showed that this curvature effect was reliably modulated by the numerical distance between the two stimulus numbers, with large distance pairs exhibiting a larger curvature effect than small distance pairs. In Experiment 3 we demonstrated that the congruity effects persist into response execution. These findings indicate that incongruities between numerical and physical sizes are carried throughout the response process and result from competition between parallel and partially active response options, lending further support to a late interaction model of the size congruity effect.

Visual search for conjunctions of physical and numerical size shows that they are processed independently.

The size congruity effect refers to the interaction between numerical magnitude and physical digit size in a symbolic comparison task. Though this effect is well established in the typical 2-item scenario, the mechanisms at the root of the interference remain unclear. Two competing explanations have emerged in the literature: an early interaction model and a late interaction model. In the present study, we used visual conjunction search to test competing predictions from these 2 models. Participants searched for targets that were defined by a conjunction of physical and numerical size. Some distractors shared the target’s physical size, and the remaining distractors shared the target’s numerical size. We held the total number of search items fixed and manipulated the ratio of the 2 distractor set sizes. The results from 3 experiments converge on the conclusion that numerical magnitude is not a guiding feature for visual search, and that physical and numerical magnitude are processed independently, which supports a late interaction model of the size congruity effect.

Testing a direct mapping versus competition account of response dynamics in number comparison

ABSTRACT Tracking hand movements during number tasks has become a powerful method for disentangling competing models of numerical representation. In two experiments, participants used a computer mouse to choose whether presented numbers were greater than or less than 5. In Experiment 1, trajectories became more curved towards the incorrect response as targets approached the standard 5, indicating increasing response competition. However, trajectories showed a rightward bias modulated by numerical distance and target size, indicating a direct mapping between hand movement and an ordered, spatial number representation. In Experiment 2, I changed the direction of mouse movements bottom-to-top orientation to left-to-right. Trajectories again became more curved towards the incorrect response as targets approached 5, but this time, there was no modulation of trajectory bias by target size or distance. The results call into question a direct mapping account and instead lend support to a competition model of response dynamics in number comparison.

Bottom-up and top-down attentional contributions to the size congruity effect

The size congruity effect refers to the interaction between the numerical and physical (i.e., font) sizes of digits in a numerical (or physical) magnitude selection task. Although various accounts of the size congruity effect have attributed this interaction to either an early representational stage or a late decision stage, only Risko, Maloney, and Fugelsang (Attention, Perception, & Psychophysics, 75, 1137–1147, 2013) have asserted a central role for attention. In the present study, we used a visual search paradigm to further study the role of attention in the size congruity effect. In Experiments 1 and 2, we showed that manipulating top-down attention (via the task instructions) had a significant impact on the size congruity effect. The interaction between numerical and physical size was larger for numerical size comparison (Exp. 1) than for physical size comparison (Exp. 2). In the remaining experiments, we boosted the feature salience by using a unique target color (Exp. 3) or by increasing the display density by using three-digit numerals (Exps. 4 and 5). As expected, a color singleton target abolished the size congruity effect. Searching for three-digit targets based on numerical size (Exp. 4) resulted in a large size congruity effect, but search based on physical size (Exp. 5) abolished the effect. Our results reveal a substantial role for top-down attention in the size congruity effect, which we interpreted as support for a shared-decision account.

Reversing the Manual Digit Bias in Two-Digit Number Comparison

Though recent work in numerical cognition has supported a strong tie between numerical and spatial representations (e.g., a mental number line), less is known about such ties in multi-digit number representations. Along this line, Bloechle, Huber, and Moeller (2015) found that pointing positions in two-digit number comparison were biased leftward toward the decade digit. Moreover, this bias was reduced in unit-decade incompatible pairs. In the present study, we tracked computer mouse movements as participants compared two-digit numbers to a fixed standard (55). Similar to Bloechle et al. (2015), we found that trajectories exhibited a leftward bias that was reduced for unit-decade incompatible comparisons. However, when positions of response labels were reversed, the biases reversed. That is, we found a rightward bias for compatible pairs that was reduced for incompatible pairs. This result calls into question a purely embodied representation of place value structure and instead supports a competition model of two-digit number representation.

Task instructions modulate unit–decade binding in two-digit number representation

Previous studies have found decomposed processes, as well as holistic processes, in the representation of two-digit numbers. The present study investigated the influence of task instruction on such processes. Participants completed both magnitude and parity tasks in one of three instructional conditions, where they were asked to either consider two-digit numbers as a whole or to focus on one specific digit. In two experiments, we found that when participants were asked to consider the two digits as an integrated number, they always exhibited a unit–decade compatibility effect, indicating a failure of selective attention on the digit relevant to the given task. However, the mere presence of the neighboring digit is not a sufficient condition for the compatibility effect: when participants were explicitly asked to process a specific digit, their success/failure to selectively ignore the irrelevant digit depended on task requirements. Further, computer mouse tracking indicated that the locus of the compatibility effect was related to late response-related processing. The results signify the deep involvement of top-down processes in unit–decade binding for two-digit number representation.