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Interference between numerical and physical size in visual search for numbers
    Brittany Simmons     University of Central Arkansas
    Blair Anthony Wilson     University of Central Arkansas
    Nikolas Georg Sieg     University of Central Arkansas


Most people have experienced a time when they intended to do one thing but instead did something else without really knowing why. If they go somewhere on a daily basis, they take a right turn as if trying to get to work when they really needed to make a left turn to pick up their prescription at the pharmacy. This is called automatic processing. According to Cohen, Dunbar, and McClelland (1990), automatic processing takes less effort than controlled processing in which you actively think about a certain task. Some automatic tasks such as driving were initially controlled but become automatic with extended practice. To determine if a process is automatic, it is carried out even when it interferes with one’s intentions, such as turning right when a left turn is needed.

Automaticity was first demonstrated for word reading by Stroop (1935), and replicated by many others (e.g., Sichel & Chandler, 1969). In some experiments participants were presented with a series of color words, each written in colored ink, and told to identify the ink color and to essentially ignore the meaning of the word itself. Some of the color words were written in the same color ink as the word (such as the word “red” written in red ink), while others were written in a completely different color ink than the word denoted (the word “red” written in green). Response times were slower when the ink color and the meaning of the color word were incongruent than when they were congruent.

Recently, Halligan and Sobel (in press) extended the Stroop effect to the meaning of numerical digits in visual search. In this experiment, participants were told to search for a target number among non-target distractor numbers of various physical and numerical sizes. Targets could be numerically larger (8 or 9) than the distractors (2 and 3) or numerically smaller. Also, targets could be physically larger or smaller than the distractors. There were four conditions: numerically and physically large targets (congruent), numerically and physically small targets (congruent), numerically large but physically small targets (incongruent), and numerically small but physically large targets (incongruent). This study found that in visual search, response times were longer when the target’s numerical and physical size were incongruent than when they were congruent.

This is a surprising result, because visual search is typically presumed to be driven by perceptual characteristics such as physical size, color, or shape (Wolfe & Horowitz, 2004), and not by semantic characteristics such as the meaning of a number. For example, when searching for a car among a crowded parking lot, people search for a particular combination of shape and color. Wolfe and Horowitz (2004) doubted that semantic features such as the meaning of a number can guide visual search. For that reason, physical size should be more important in visual search than numerical size. As a result, we hypothesized that when searching for a target by numerical size, physical size will interfere, but when searching for a target by physical size, numerical size will not interfere. In Halligan and Sobel (in press), participants were told to search for the target by numerical size. What would have happened if participants had been told to search for the target by its physical size? To find out, in Experiment 1 we instructed participants to search by numerical size, and in Experiment 2 we instructed participants to search by physical size. Also, in Halligan and Sobel (in press), the target and distractors were single digits. We wondered if the effect of numerical-physical size congruence would extend to numbers larger than nine, so in both experiments the targets and distractors were numbers consisting of three digits.

Experiment 1: Searching for numerical size

Participants. We obtained permission to carry out both experiments from our university’s Institutional Review Board. All participants were treated within the guidelines of the American Psychological Association. There were 15 participants who participated in exchange for credit in their psychology courses.

Materials. A computer presented visual search displays and collected response times. To control the shape of the digits, standardized shapes were used. The digits consisted of line segments as on the faces of digital clocks. In all four conditions, three-digit numbers were used. Half of participants looked for a numerically small number (less than 500) among numerically large distractor numbers (larger than 500) in the first half of the experiment, and looked for a numerically large number (larger than 500) among numerically small (less than 500) distractors in the second half. The order was counterbalanced across participants. There were four conditions of numerical and physical target size: 1) numerically and physically small target (congruent); 2) numerically and physically large target (congruent); 3) numerically small but physically large target (incongruent); 4) numerically large but physically small target (incongruent).

Procedure. Instructions were presented on a series of screens which participants navigated by clicking a “next” button. After reading the instructions, participants searched for a target number, based on its numerical value, among a series of visual displays. Each visual display contained one target number and several (four, six, or eight) distractor numbers, arranged on an imaginary circle centered on a fixation mark. The target number was either on the right side or left side of the display. Participants indicated the target's location by pressing a key on the keyboard; “z” for the left side of the screen and “/” for the right side of the screen. The computer recorded the delay between the visual display appearing on screen and the participants pressing a button. If a participant pressed a wrong button, the word “incorrect” flashed on the screen for a second. Participants were allowed six practice trials at the beginning of the experiment and another set of six practice trials after a break midway through the experiment. There were two levels of target location (left or right), three levels of display size (five, seven, or nine items), two levels of the hundreds digit in the target number (2 or 3 for numerically small, 8 or 9 for numerically large), and the four levels of target size replicated 27 times for a total of 336 experimental trials, which took about 10 minutes to complete.

Mean response times were submitted to a 3x2x2 ANOVA with number of display items (five, seven, or nine), numerical size (large or small), and physical size (large or small) as within-subject variables. The main effect of number of display items was significant F(2,28)=34.6, P < 0.001, indicating that response times increased with the number of search items, as is common in visual search. The main effects of numerical size and physical size were not significant (Ps > 0.1). However, there was a two-way interaction between numerical size and physical size (F(1,14) = 30.5, P < 0.001), indicating that search was fast when numerical and physical size were congruent and slow when they were incongruent.

The faster responses for the congruent conditions than the incongruent conditions replicates Halligan and Sobel (in press), and shows that their result for single digits extends to numbers consisting of more than one digit. As we hypothesized, when participants were instructed to find a target by numerical size, physical size was processed automatically so it interfered with search when numerical and physical size were incongruent. In the displays used for Experiment 1, the target always had a unique numerical size, but it also had a unique physical size. For that reason, using the same stimuli but instructing participants to search for the number with a unique physical size should bring out the exact same behavioral response, but participants will be paying attention to a different target feature (physical size rather than numerical size). Because physical size is more important in visual search than numerical size, we hypothesize that numerical size will not interfere with physical size, so this simple instructional change should eliminate the effect of interference observed in Experiment 1.

Experiment 2: Searching for physical size


Participants. A total of 15 students participated in the second experiment, none of whom participated in the first experiment.

Procedure. The stimuli and procedure were the same in Experiment 2 as in Experiment 1 except the instructions were slightly changed. Participants were told to search for the number with a unique physical size.

Mean response times were submitted to a 3x2x2 ANOVA with number of display items (five, seven, or nine), numerical size (large or small), and physical size (large or small) as within-subject variables. None of the main effects and none of the interactions were significant (all Ps > 0.1). Apparently our manipulation eliminated not just the effects of congruence, but also the commonly observed increase in response time with number of display items (Wolfe, 1998).

Interestingly, according to our findings, changing the instructions of the experiment by having the participant search for the target number based on physical size as opposed to numerical size drastically changed the results. Instead of the incongruent conditions being relatively slow and congruent conditions relatively quick, there was no significant difference between the conditions. This suggests that numerical value does not interfere with the physical size. While we had expected to eliminate the effect of congruence, we were surprised that even the effect of number of items vanished as well.

General Discussion
Previous numerical Stroop visual search experiments (Halligan & Sobel, in press) showed that participants who searched for a target by numerical size experienced interference from physical size: incongruent conditions were slower than congruent conditions. The dominant theory about visual search is that it is guided by visual features such as physical size and that guidance by semantic features such as numerical size is doubtful (Wolfe & Horowitz 2004). Based on that, we hypothesized that physical size should interfere with a search by numerical size, but numerical size should not interfere with a search by physical size. We extended visual search to three-digit items, and in Experiment 1 replicated the congruence effect for participants instructed to search by numerical size. Using the same stimuli but instructing participants to search by physical size in Experiment 2 eliminated the effect of congruence. The combined results from Experiments 1 and 2 supported our hypothesis.

The most surprising result was the lack of an effect of the number of display items in Experiment 2. In visual searches, the slope of response time as a function of the number of display items is typically taken as a marker for the difficulty of the search task (Wolfe, 1998). Easy searches produce flat response time functions and difficult searches produce steep functions. Because the two experiments used the same stimuli and conditions, participants in Experiment 1 could have, but did not realize that simply searching for the item with unique physical size would have made their search task easy. Why didn’t they? We would love to figure out why in further experiments.

Cohen, J. D., Dunbar, K., McClelland, J. L. (1990). On the Control of the Processes: A Parallel Distributed Processing Account of the Stroop Effect. Psychological Review, 97, 332-361. doi:0033-295X/90/
Halligan, J., & Sobel, K. V. (in press). Automaticity of Numerical Processing. Journal of Psychological Inquiry.
Sichel, J., & Chandler, K. A. (1969). The color-word interference test: The effects of varied color-word combinations upon verbal response latency. Journal of Psychology, 72, 219-231. doi: 10.1080/00223980.1969.10543502
Stroop, J. R. (1935). Studies of interference in serial verbal reactions. Journal Of Experimental Psychology: General, 18(6), 643-662. doi: 10.1037/0096-3445.121.1.15
Tzelgov, J., & Ganor-Stern, D. (2005). Automaticity in processing ordinal information. In J.I.D. Campbell (Bd.), Handbook of Mathematical Cognition (pp.55-67). New York: Psychology Press.
Wolfe, J. M., & Horowitz, T. S. (2004). What attributes guide the deployment of visual attention and how do they do it?. Nature Reviews Neuroscience, 5, 495-501. doi:10.1038/nrn1411
Wolfe, J. M. (1998). Visual Search. In H. Pashler (Ed.), Attention. East Sussex, U. K.: Psychology Press Ltd.

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