Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking

While reaction time data have shown that decomposed processing of two-digit numbers occurs, there is little evidence about how decomposed processing functions. Poltrock and Schwartz (1984) argued that multi-digit numbers are compared in a sequential digit-by-digit fashion starting at the leftmost digit pair. In contrast, Nuerk and Willmes (2005) favoured parallel processing of the digits constituting a number. These models (i.e., sequential decomposition, parallel decomposition) make different predictions regarding the fixation pattern in a two-digit number magnitude comparison task and can therefore be differentiated by eye fixation data. We tested these models by evaluating participants' eye fixation behaviour while selecting the larger of two numbers. The stimulus set consisted of within-decade comparisons (e.g., 53_57) and between-decade comparisons (e.g., 42_57). The between-decade comparisons were further divided into compatible and incompatible trials (cf. Nuerk, Weger, & Willmes, 2001) and trials with different decade and unit distances. The observed fixation pattern implies that the comparison of two-digit numbers is not executed by sequentially comparing decade and unit digits as proposed by Poltrock and Schwartz (1984) but rather in a decomposed but parallel fashion. Moreover, the present fixation data provide first evidence that digit processing in multi-digit numbers is not a pure bottom-up effect, but is also influenced by top-down factors. Finally, implications for multi-digit number processing beyond the range of two-digit numbers are discussed.     

A Structural Equation Analysis of the Wide Range Assessment of Memory and Learning in a Clinical Sample

A maximum likelihood confirmatory factor analysis was performed by applying LISREL VII to the Wide Range Assessment of Memory and Learning (WRAML) in a clinical sample (N = 271). Analyses were designed to determine which of 10 hypothesized oblique factor solutions could best explain memory as measured by the WRAML. Competing latent variable models were identified in previous studies and monographs on memory. Findings supported a three-factor model including Verbal Memory, Visual Memory, and Attention/Concentration factors. Our results are consistent with previous studies suggesting that attention is an important component of memory as measured by the WRAML. This study replicates previous research in which the Learning Index was not empirically supported.     

The Numerical Stroop Effect in Primary School Children: A Comparison of Low,Normal, and High Achievers

Sixty-six primary school children were selected, of which 21 scored low on a standardized math achievement test, 23 were normal, and 22 high achievers. In a numerical Stroop experiment, children were asked to make numerical and physical size comparisons on digit pairs. The effects of congruity and numerical distance were determined. All children exhibited congruity and distance effects in the numerical comparison. In the physical comparison, children of all performance groups showed Stroop effects when the numerical distance between the digits was large but failed to show them when the distance was small. Numerical distance effects depended on the congruity condition, with a typical effect of distance in the congruent, and a reversed distance effect in the incongruent condition. Our results are hard to reconcile with theories that suggest that deficits in the automaticity of numerical processing can be related to differential math achievement levels. Immaturity in the precision of mappings between numbers and their numerical magnitudes might be better suited to explain the Stroop effects in children. However, as the results for the high achievers demonstrate, in addition to numerical processing capacity per se, domain-general functions might play a crucial role in Stroop performance, too.     

Ipsilateral Loudness Adaptation Over Multiple Intensity Levels

Three mirror tracing experiments were conducted to investigate the connection between perception and motor behavior. In the first experiment, some subjects traced a hex-maze, other subjects traced a hex-maze after observing a model trace, others traced a hex-maze after reading instructions on mirror images, and others traced a hex-maze after having observed a model and heard the instructions. There were no significant differences between the groups' error scores, but their time scores differed significantly, although not always in the predicted direction. In Experiment 2, the subjects were to trace selected letters of the alphabet. Error scores for the second experiment did not differ much from those for the first experiment. In Experiment 3, the experimenter gave each subject commands for the correct directions of movement, using the subject's body as a frame of reference. There was little improvement in motor performance. These results suggest that the visual information presented in the mirror captured the subjects' attention and blocked their motor tracing program.     

Multiple timescales of body schema reorganization due to plastic surgery

Plastic surgery modifies the distribution of mass centers of a person’s body segments, changing his or her posture. The functional reorganization processes that lead subjects to re-integrate these body changes into a new stable body (posture) schema is poorly understood but current theories suggest the possible contribution of two components: a feedback mechanism that strongly depends on sensory input and an internal model that is relatively less dependent on sensory input and improves posture control, for example by compensating for delayed feedback. To assess the relative contributions of these two mechanisms during the functional reorganization of a posture scheme, we have conducted a longitudinal postural study in a population of healthy adults who were subject to breast plastic surgery to reduce or augment body weight. We measured participants’ orthostatic posture and ground reaction force immediately after, after 4 months, and 1 year after the surgery. To investigate the role of visual sensory information in the reorganization process we tested the participants with eyes open and closed. Our results indicate that participants find a new dynamical equilibrium within a few days. However, posture maintenance remains sub-optimal long after the center of masses and the resultant of ground reaction force stop changing; in some cases, for more than 4 months. Furthermore, the re-adaptation process is faster and more efficient in the eyes-open than in the eyes-closed condition. These results suggest that the reorganization involves different subsystems (responsible for the biomechanical changes, the re-calibration of feedback mechanisms, and the re-adaptation of internal models), which act at different timescales.     

A model of saccadic landing positions in reading under the influence of sensory noise

During reading, saccadic eye movements are produced to move the high acuity foveal region of the eye to words of interest for efficient word processing. Distributions of saccadic landing positions peak close to a word's centre but are relatively broad compared to simple oculomotor tasks. Moreover, landing-position distributions are modulated both by distance of the launch site and by saccade type (e.g., one-step saccade, word skipping, refixation). Here we present a mathematical model for the computation of a saccade intended for a given target word. Two fundamental assumptions are related to (1) the sensory computation of the word centre from inter-word spaces and (2) the integration of sensory information and a priori knowledge using Bayesian estimation. Our model was developed for data from a large corpus of eye movements from normal reading. We demonstrate that the model is able simultaneously to account for a systematic shift of saccadic mean landing position with increasing launch-site distance and for qualitative differences between one-step saccades (i.e., from a given word to the next word) and word-skipping saccades.     

On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models

In item response theory, the classical estimators of ability are highly sensitive to response disturbances and can return strongly biased estimates of the true underlying ability level. Robust methods were introduced to lessen the impact of such aberrant responses on the estimation process. The computation of asymptotic (i.e., large‐sample) standard errors (ASE) for these robust estimators, however, has not yet been fully considered. This paper focuses on a broad class of robust ability estimators, defined by an appropriate selection of the weight function and the residual measure, for which the ASE is derived from the theory of estimating equations. The maximum likelihood (ML) and the robust estimators, together with their estimated ASEs, are then compared in a simulation study by generating random guessing disturbances. It is concluded that both the estimators and their ASE perform similarly in the absence of random guessing, while the robust estimator and its estimated ASE are less biased and outperform their ML counterparts in the presence of random guessing with large impact on the item response process.