Testing a model of componential processing of multi-symbol numbers—evidence from measurement units

Abstract

Research on numerical cognition has addressed the processing of nonsymbolic quantities and symbolic digits extensively. However, magnitude processing of measurement units is still a neglected topic in numerical cognition research. Hence, we investigated the processing of measurement units to evaluate whether typical effects of multi-digit number processing such as the compatibility effect, the string length congruity effect, and the distance effect are also present for measurement units. In three experiments, participants had to single out the larger one of two physical quantities (e.g., lengths). In Experiment 1, the compatibility of number and measurement unit (compatible: 3 mm_6 cm with 3 < 6 and mm < cm; incompatible: 3 cm_6 mm with 3 < 6 but cm > mm) as well as string length congruity (congruent: 1 m_2 km with m < km and 2 < 3 characters; incongruent: 2 mm_1 m with mm < m, but 3 > 2 characters) were manipulated. We observed reliable compatibility effects with prolonged reaction times (RT) for incompatible trials. Moreover, a string length congruity effect was present in RT with longer RT for incongruent trials. Experiments 2 and 3 served as control experiments showing that compatibility effects persist when controlling for holistic distance and that a distance effect for measurement units exists. Our findings indicate that numbers and measurement units are processed in a componential manner and thus highlight that processing characteristics of multi-digit numbers generalize to measurement units. Thereby, our data lend further support to the recently proposed generalized model of componential multi-symbol number processing.

A general model framework for multisymbol number comparison.

“…Close distance trials (1 yuan vs. 5 jiao and 4 yuan vs. 5 jiao) were incompatible trials (yuan > jiao, but 1 < 5 and 4 < 5) and far distance trials (6 yuan vs. 5 jiao and 9 yuan vs. 5 jiao) were compatible trials (yuan > jiao, but 6 > 5 and 9 > 5). In a recent study, Huber et al (2015a) showed that such a compatibility effect can also be shown when comparing physical quantities comprised of a single digit and a unit of measurement suggesting componential processing. Thus, the holistic distance effect found for Chinese prices might be accounted by such a regular compatibility effect instead of indicating that prices might be processed holistically.…”

“…This is useful in case of natural numbers as it assists comparing natural numbers (i.e., a single-digit number, e.g., 3, is always smaller than a two- or three-digit number, e.g., 726). However, considering the number of characters may result in systematic errors in case of decimal numbers (i.e., longer digit strings not necessarily imply larger numbers, e.g., 0.2843 < 0.7; Kallai & Tzelgov, 2014) and units of measurements (e.g., 5 mm <1m; Huber et al, 2015a).…”

“…The sign-decade compatibility effect reflects faster responses for sign-decade compatible number pairs (e.g., −16 < +68; − < + and 1 < 6) than sign-decade incompatible number pairs (e.g., −38 < +12; − < +, but 3 > 1). Following this rationale, not only the comparison of digits may lead to interference, but also the comparison of symbols in general may introduce interference (see also Huber, Bahnmueller, Klein, & Moeller, 2015a). Supporting the parallel componential model, the effect was not only present in RT but also in participants’ eye-fixation behavior, where sign-decade compatibility modulated the number of fixations on polarity signs similar to two-digit numbers, with more fixations on polarity signs for incompatible number pairs (see also Moeller, Fischer, Nuerk, & Willmes, 2009a for a similar finding in two-digit number comparison).…”

Avoidance of Novelty Contributes to the Uncanny Valley

“…We analyzed the reaction time (RT) for categorization and proportion of “photograph” responses on each photograph proportion. After we excluded the outlier data from the trials in which the RT was outside the mean ± 3 SD ( Ziegler et al, 2001 ; Cohen and German, 2010 ; Constable et al, 2011 ; Chuang et al, 2015 ; Huber et al, 2015 ; Takahashi et al, 2015 ), we calculated the average RT of the categorization of each image. We performed a one-way ANOVA on the RT and defined the images whose RT was significantly longer than those of 0 and 100% as the hard-to-categorize images.…”

A Taxonomy Proposal for Types of Interactions of Language and Place-Value Processing in Multi-Digit Numbers

“…Referring to the former, for text problems it was observed that words associated with an addition procedure (e.g., “more,” “buy”) facilitated processing of text problems requiring additions whereas words associated with subtraction (e.g., “less,” “sell”) interfered with addition problem solving (e.g., Verschaffel et al, 1992 ; see also Daroczy et al, 2015 for a review on linguistic and numerical factors in text problems; Figure 1 , D3). Referring to the latter, place-value processing also seems to be recycled for the processing of measurement units as typical effects observed for two-digit numbers (e.g., unit-decade compatibility effect) were also demonstrated for measurement units ( Huber et al, 2015a ; Figure 1 , D2). Thus, these studies show that magnitude information is not only expressed and processed via Arabic digits and number words but also via other words and symbols which in some cases share processing specificities observed for place-value processing in multi-digit numbers.…”