Evidence for distinct magnitude systems for symbolic and non-symbolic number

Psychological Research - Cognitive models of magnitude representation are mostly based on the results of studies that use a magnitude comparison task. These studies show similar distance or ratio...     

A unidimensional measure of Hong's psychological reactance scale

Research using Hong's Psychological Reactance Scale has been fraught with methodological concerns. Researchers have been unable to find a stable, a nd replicable factor structure. Here, results suggested t hat Hong's Psychological Reactance Scale is a unidimensional one with an average alpha of .74 (SD=.46). This value was attained by first analyzing correlation matrices reproduced from three reports on Hong's Psychological Reactance Scale and then verifying this new factor structure with original data. Tests for internal consistency supported a 1-factor solution. Tests for external consistency supported prior findings in relation to Psychological Reactance and offer evidence that the 1-factor solution is externally valid. While the authors contend that a 1-factor solution is appropriate, further testing is needed for external consistency and refinement of the measure.     

Effect of reference number on magnitude estimation

The psychophysical function obtained by the method of magnitude estimation was influenced by the reference number (modulus) assigned to a “standard” line and the position of this standard in the range of comparison stimuli. Data from two experiments with judgments of apparent length of lines show how both variables systematically affect the slope of the power function. AllowingO to choose his own reference numbers, even though these numbers varied among as, tended to produce less variability in slope than ifE imposed fixed reference numbers forO to use.     

Sensori-motor spatial training of number magnitude representation

An adequately developed spatial representation of number magnitude is associated with children's general arithmetic achievement. Therefore, a new spatial-numerical training program for kindergarten children was developed in which presentation and response were associated with a congruent spatial numerical representation. In particular, children responded by a full-body spatial movement on a digital dance mat in a magnitude comparison task. This spatial-numerical training was more effective than a non-spatial control training in enhancing children's performance on a number line estimation task and a subtest of a standardized mathematical achievement battery (TEDI-MATH). A mediation analysis suggested that these improvements were driven by an improvement of children's mental number line representation and not only by unspecific factors such as attention or motivation. These results suggest a benefit of spatial numerical associations. Rather than being a merely associated covariate, they work as an independently manipulated variable which is functional for numerical development.     

Polarity correspondence in comparative number magnitude judgments

When asked which of two digits is greater, participants respond more quickly if physical size corresponds to number magnitude, such as in 3 7, than when the two attributes contradict each other, such as in 3 7. This size congruence effect in comparative number judgments is a well-documented phenomenon. We extended existing findings by showing that this effect does not depend on physical size of the number alone but can be observed with number symmetry. In addition, we observed that symmetric numbers are judged as being smaller than asymmetric numbers, which renders an interpretation of the number symmetry congruence effect in terms of physical size implausible. We refer to the polarity correspondence principle (Proctor & Cho, 2006) to explain the present findings.     

The development of automaticity in accessing number magnitude

This study traces developmental changes in automatic and intentional processing of Arabic numerals using a numerical-Stroop paradigm. In Study 1, university students compared the numerical or physical size of Arabic numerals varying along both dimensions. In Study 2, first graders (mean age = 6 years 6 months), third graders (mean age = 8 years 4 months), and fifth graders (mean age = 10 years 3 months) were tested to examine developmental changes in numerical and physical comparisons. In the numerical comparison task, a size congruity effect was found at all ages (i.e., relative to a neutral control, congruent physical sizes facilitated, and incongruent sizes interfered with, the numerical comparison). The pattern of facilitation and interference, however, was modulated by age. In the physical comparison task, the incongruity between physical and numerical size affected only older children and adults. These findings strongly suggest that the automatization in number processing is achieved gradually as numerical skills progress.     

Psychometric properties of the Hong psychological reactance scale

The Hong Psychological Reactance Scale (HPRS; Hong & Felda, 1996) was developed to measure the individual difference in reactance proneness, that is, a person's trait propensity to experience psychological reactance. We performed confirmatory factor analyses to test the dimensionality of the 11-item version of the HPRS. Three message outcome variables (i.e., perceived threat to freedom, attitude, and intention) served as reference variables to test the construct validity of the HPRS. Data from 3 studies (Ns = 188, 200, and 233) of reactions to persuasive health messages confirmed the existence of 4 first-order factors but also provided evidence that the HPRS can be treated as unidimensional at the second order. The relationships between the second-order factor and the message outcome variables provided evidence of the validity of the scale.     

Rapid communication The mental number line dominates alternative,explicit coding of number magnitude

Numerical judgments are facilitated for left-space responses to a smaller number and right-space responses to a larger number (the spatial–numerical association of response codes, SNARC, effect). Despite support for a mental number line (i.e., spatial) explanation of the SNARC effect, this account has been challenged by an intermediate-coding theory that makes use of a polarity-correspondence principle. The latter is a general explanatory framework whereby stimulus and response dimensions are represented in a categorical, binary manner, with complementary categories coded as having either positive or negative polarity. When stimulus and response polarity match, responding is facilitated. In the present experiment we pitted explicitly presented close–far coding against an implicit mental number line (i.e., left–right coding). Subjects categorized numbers (1, 4, 6, and 9) as greater or less than a standard (5) using keys defined only as close to and far from a starting key. We found that, despite instructing subjects to use a close–far coding scheme, they exhibited a typical SNARC effect, with small-number responses facilitated on the left and large-number responses on the right. These results are discussed in the context of results supporting the polarity explanation and with respect to representational pluralism.     

Temporal order judgment reveals how number magnitude affects visuospatial attention

The existence of spatial components in the mental representation of number magnitude has raised the question regarding the relation between numbers and spatial attention. We present six experiments in which this relation was examined using a temporal order judgment task to index attentional allocation. Results demonstrate that one important consequence of numerical processing is the automatic allocation of spatial attention, which in turn affects the perception of the temporal order of visual events. Given equal onset time, left-side stimuli are perceived to occur before right-side stimuli when a small number (1, 2) is processed, whereas right-side stimuli are perceived to occur before left-side stimuli when a larger number (8, 9) is processed. In addition, we show that this attentional effect is specific to quantity processing and does not generalize to non-numerical ordinal sequences.     

Cognitive control in number magnitude processing: evidence from eye-tracking

The unit-decade compatibility effect describes longer response times and higher error rates for incompatible (e.g., 37_52) than compatible (e.g., 42_57) number comparisons. Recent research indicated that the effect depends on the percentage of same-decade filler items. In the present study, we further examined this relationship by recording participants’ eye-fixation behaviour. In four conditions, participants had to compare item sets with different filler item types (i.e., same-decade and same-unit filler items) and different numbers of same-decade filler items (i.e., 25, 50, and 75 %). We found a weaker unit-decade compatibility effect with most fixations on tens in the condition with same-unit filler items. Moreover, the compatibility effect increased with the percentage of same-decade filler items which was accompanied by less fixations on tens and more fixations on units. Thus, our study provides first eye-tracking evidence for the influence of cognitive control in number processing.     

Effects of number of alternatives on the psychological refractory period

The effects of changing the number of choices in the first response on “psychological refractoriness” were found to be partially consistent with intermittency theory but modifications may be needed to explain the results when the number of choices in the second response is increased.     

The role of working memory in the association between number magnitude and space

In two experiments, participants performed a magnitude comparison task in single and dual-task conditions. In the dual conditions, the comparison task was accomplished while phonological or visuospatial information had to be maintained for a later recall test. The results showed that the requirement of maintaining visuospatial information produced the lack of spatial-numerical association of response codes (SNARC) effect. The SNARC effect was not found even when the performance in the comparison task did not decline, as indicated by a similar distance effect in all conditions. These results show a special role for the visuospatial component of working memory in the processing of spatial representation of numbers and an interesting dissociation between SNARC and distance effects.     

Spanish adaptation of the scale of psychological empowerment in the workplace

The objective of this study is to adapt and translate into Spanish Spreitzer's Psychological Empowerment Scale (1995a). A process of translation and reverse-translation was applied to the scale's items, whose psychometric properties were then examined using a sample of 272 professional nurses at public hospitals in the province of Seville. The data were subjected to confirmatory factor analysis. The significance of the factor loadings demonstrated the need to create a new model eliminating one item. The 11-item model was shown to possess adequate construct validity and internal consistency. The results confirm the original, four-factor structure obtained by Spreitzer, with the exception of item 10, and support the utilization of the Spanish version of this scale in the workplace. Future research should more extensively investigate its construct validity, and test the nomological network of the operationalized construct within the field of psychological well-being and in the context of the workplace.     

A method for increasing the reinforcement magnitude of intracranial stimulation

Schedules of intermittent brain-stimulation reinforcement have been shown to maintain performances when a reinforcement is defined as several response-produced, brief trains of stimulation. The present experiments show that the number of response-produced trains permitted per reinforcement is a variable analogous to amount or magnitude of reinforcement in the conventional food-reinforcement experiment. Systematic effects were obtained when that variable was manipulated within a multiple schedule and also on variable-interval schedules programmed concurrently.     

A revision of the response ratio hypothesis for magnitude estimation

The response ratio hypothesis for magnitude estimation proposes that the relevant variables involved in the subject's behavior are ratios of stimulus random variables, and ratios of response random variables. We add to these “errors of calculation.” Such error random variables add flexibility to the hypothesis, but do not enable it to explain effects of stimulus range.