TY  - JOUR
A1  - Schwarz, Wolfgang
A1  - Reike, Dennis
T1  - The number-weight illusion
JF  - Psychonomic bulletin & review : a journal of the Psychonomic Society
N2  - When objects are manually lifted to compare their weight, then smaller objects are judged to be heavier than larger objects of the same physical weights: the classical size-weight illusion (Gregory, 2004). It is also well established that increasing numerical magnitude is strongly associated with increasing physical size: the number-size congruency effect e.g., (Besner & Coltheart Neuropsychologia, 17, 467-472 1979); Henik & Tzelgov Memory & Cognition, 10, 389-395 1982). The present study investigates the question suggested by combining these two classical effects: if smaller numbers are associated with smaller size, and objects of smaller size appear heavier, then are numbered objects (balls) of equal weight and size also judged as heavier when they carry smaller numbers? We present two experiments testing this hypothesis for weight comparisons of numbered (1 to 9) balls of equal size and weight, and report results which largely conform to an interpretation in terms of a new number-weight illusion.
KW  - Size-weight illusion
KW  - Number-size congruency effect
KW  - Numerical distance effect
KW  - Paired comparison
KW  - Reafference principle
Y1  - 2018
U6  - https://doi.org/10.3758/s13423-018-1484-z
SN  - 1069-9384
SN  - 1531-5320
VL  - 26
IS  - 1
SP  - 332
EP  - 339
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Schwarz, Wolfgang
A1  - Eiselt, Anne-Kathrin
T1  - Numerical distance effects in visual search
JF  - Attention, perception, & psychophysics : AP&P ; a journal of the Psychonomic Society, Inc.
N2  - We present three experiments in which observers searched for a target digit among distractor digits in displays in which the mean numerical target-distractor distance was varied. Search speed and accuracy increased with numerical distance in both target-present and target-absent trials (Exp. 1A). In Experiment 1B, the target 5 was replaced with the letter S. The results suggest that the findings of Experiment 1A do not simply reflect the fact that digits that were numerically closer to the target coincidentally also shared more physical features with it. In Experiment 2, the numerical distance effect increased with set size in both target-present and target-absent trials. These findings are consistent with the view that increasing numerical target-distractor distance affords faster nontarget rejection and target identification times. Recent neurobiological findings (e.g., Nieder, 2011) on the neuronal coding of numerosity have reported a width of tuning curves of numerosity-selective neurons that suggests graded, distance-dependent coactivation of the representations of adjacent numbers, which in visual search would make it harder to reject numerically closer distractors as nontargets.
KW  - Numerical distance effect
KW  - Visual search
KW  - Category effect
KW  - Mental number line
KW  - Numerical magnitude
Y1  - 2012
U6  - https://doi.org/10.3758/s13414-012-0342-8
SN  - 1943-3921
VL  - 74
IS  - 6
SP  - 1098
EP  - 1103
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Reike, Dennis
A1  - Schwarz, Wolfgang
T1  - Categorizing digits and the mental number line
JF  - Attention, perception, & psychophysics : AP&P ; a journal of the Psychonomic Society, Inc.
N2  - Following the classical work of Moyer and Landauer (1967), experimental studies investigating the way in which humans process and compare symbolic numerical information regularly used one of two experimental designs. In selection tasks, two numbers are presented, and the task of the participant is to select (for example) the larger one. In classification tasks, a single number is presented, and the participant decides if it is smaller or larger than a predefined standard. Many findings obtained with these paradigms fit in well with the notion of a mental analog representation, or an Approximate Number System (ANS; e.g., Piazza 2010). The ANS is often conceptualized metaphorically as a mental number line, and data from both paradigms are well accounted for by diffusion models based on the stochastic accumulation of noisy partial numerical information over time. The present study investigated a categorization paradigm in which participants decided if a number presented falls into a numerically defined central category. We show that number categorization yields a highly regular, yet considerably more complex pattern of decision times and error rates as compared to the simple monotone relations obtained in traditional selection and classification tasks. We also show that (and how) standard diffusion models of number comparison can be adapted so as to account for mean and standard deviations of all RTs and for error rates in considerable quantitative detail. We conclude that just as traditional number comparison, the more complex process of categorizing numbers conforms well with basic notions of the ANS.
KW  - Categorization
KW  - Numerical distance effect
KW  - Mental number line
KW  - Diffusion models
Y1  - 2019
U6  - https://doi.org/10.3758/s13414-019-01676-w
SN  - 1943-3921
SN  - 1943-393X
VL  - 81
IS  - 3
SP  - 614
EP  - 620
PB  - Springer
CY  - New York
ER  -