How do we convert a number into a finger trajectory?

How do we understand two-digit numbers such as 42? Models of multi-digit number comprehension differ widely. Some postulate that the decades and units digits are processed separately and possibly serially. Others hypothesize a holistic process which maps the entire 2-digit string onto a magnitude, represented as a position on a number line. In educated adults, the number line is thought to be linear, but the “number sense” hypothesis proposes that a logarithmic scale underlies our intuitions of number size, and that this compressive representation may still be dormant in the adult brain. We investigated these issues by asking adults to point to the location of two-digit numbers on a number line while their finger location was continuously monitored. Finger trajectories revealed a linear scale, yet with a transient logarithmic effect suggesting the activation of a compressive and holistic quantity representation. Units and decades digits were processed in parallel, without any difference in left-to-right vs. right-to-left readers. The late part of the trajectory was influenced by spatial reference points placed at the left end, middle, and right end of the line. Altogether, finger trajectory analysis provides a precise cognitive decomposition of the sequence of stages used in converting a number to a quantity and then a position.     

Monaural Loudness Adaptation for Middle-Intensity Middle-Frequency Signals: The Importance of Measurement Technique

Using the Simple Adaptation technique (SA) and the Ipsilateral Comparison Paradigm (ICP), the authors studied monaural loudness adaptation to a middle-intensity [60 dB(A)] tone at signal frequencies of 250, 1000, and 4000 Hz in the left and right ears. Adaptation effects were absent when the SA procedure was used. However, they were observed uniformly across all frequency values with the ICP, a result that challenges the assertion in the literature, on the basis of SA measures, that loudness adaptation for middle-intensity signals occurs only at frequencies above 4000 Hz. The ICP features periodic intensity modulations (±10 dB relative to the base signal) to accommodate listeners' needs for referents by which they can gauge subtle changes in the loudness of the adapting tone, a key component that is missing in the SA method. Adaptation effects in this investigation were similar in both ears, supporting the equal susceptibility assumption common in loudness adaptation studies.     

Do Children Perceive Postural Constraints When Estimating Reach or Action Planning?

Estimation of whether an object is reachable from a specific body position constitutes an important aspect in effective motor planning. Researchers who estimate reachability by way of motor imagery with adults consistently report the tendency to overestimate, with some evidence of a postural effect (postural stability hypothesis). This idea suggests that perceived reaching limits depend on an individual's perceived postural constraints. Based on previous work with adults, the authors expected a significant postural effect with the Reach 2 condition, as evidenced by reduced overestimation. Furthermore, the authors hypothesized that the postural effect would be greater in younger children. They then tested these propositions among children aged 7, 9, and 11 years by asking them to estimate reach while seated (Reach 1) and in the more demanding posture of standing on 1 foot and leaning forward (Reach 2). Results indicated no age or condition difference, therefore providing no support for a postural effect. When the authors compared these data to a published report of adults, a developmental difference emerged. That is, adults recognize the perceived postural constraint of the standing position resulting in under- rather than overestimation, as displayed in the seated condition. Although preliminary, these observations suggest that estimates of reach (action planning) continue to be refined between late childhood and young adulthood.     

Communal Versus Individual Learning of a Math-Estimation Task: African American Children and the Culture of Learning Contexts

The authors compared the performance of 78 African American 5th-grade students who studied a math-estimation task in one of two learning contexts. Learning contexts differed in the degree to which they afforded the expression of communalism. ANCOVA confirmed that posttest performance was best for students who studied in the high communal-learning context. The findings support A. W. Boykin's (1994) contention that the cultural context of learning can be a critical mediator of children's performance.     

The effect of facial attractiveness on temporal perception

Previous research suggests that feelings of fear, dislike, shame and sadness affect our perception of duration (Droit-Volet et al., 2004; Gil et al., 2009). The current study sought to expand our understanding of the variables which moderate temporal perception by examining whether the attractiveness of a face influenced its perceived duration. Participants completed a verbal estimation task in which they judged the duration of attractive, unattractive and neutral faces. The results showed that participants underestimated the duration of unattractive faces relative to attractive and neutral faces. Estimates of unattractive faces were also less accurate than those of the attractive and neutral faces. The results are consistent with Gil et al.'s (2009) suggestion that the duration of disliked stimuli are underestimated relative to liked and neutral stimuli because they detract attention from temporal perception. Analysis of the slope and intercept of the estimation gradients supports Zakay and Block's (1997) suggestion that reduced attention to time results in a multiplicative underestimation of duration.     

Limiting attentional resources influences performance and output monitoring of an event-based prospective memory task

One of the most frequently used markers in research on numerical cognition is the distance effect. Recently, we have suggested that a distance effect can have different origins depending on the experimental task. By dissociating the comparison distance effect from the priming distance effect we revealed the need to study the origin of this effect before drawing any conclusions from it (van Opstal, Gevers, de Moor, &; Verguts, 2008). Because a distance effect in a same–different task is also commonly used to study number representations (e.g., Dehaene &; Akhavein, 1995), the present study aimed at uncovering the origin of the effect in this task. Computational and empirical results indicate clearly that the distance effect in the same–different task originates from number representations rather than a decision process.     

A Thurstonian Analysis of Preference Change

This paper presents a Thurstonian model for the analysis of preference change. Preferences are expressed in the form of rankings, possibly with ties. A vector-autoregression framework is used to investigate relationships between past and current rankings. It is shown that this approach yields a parsimonious and easily interpretable representation of individual preference differences in time-dependent ranking data. A detailed analysis of the 1992 National Election Study illustrates the proposed approach.     

Identification and Testing of Modes in Beliefs

Characterizing diversity in beliefs is of paramount importance in empirical research on human behavior. In game theory, the focus is on the hypothesis formation. We present a data set with ideal properties for characterizing such diversity. The data consist of hypotheses on the empirical distribution of opponent choices. Using nonparametric techniques, we identify modes in the data corresponding to subpopulations of behavioral types and find the statistical significance of these modes in the underlying population distribution.     

Efficient nonparametric approaches for estimating the operating characteristics of discrete item responses

Rationale and the actual procedures of two nonparametric approaches, called Bivariate P.D.F. Approach and Conditional P.D.F. Approach, for estimating the operating characteristic of a discrete item response, or the conditional probability, given latent trait, that the examinee's response be that specific response, are introduced and discussed. These methods are featured by the facts that: (a) estimation is made without assuming any mathematical forms, and (b) it is based upon a relatively small sample of several hundred to a few thousand examinees.Some examples of the results obtained by the Simple Sum Procedure and the Differential Weight Procedure of the Conditional P.D.F. Approach are given, using simulated data. The usefulness of these nonparametric methods is also discussed.This research was mostly supported by the Office of Naval Research (N00014-77-C-0360, N00014-81-C-0569, N00014-87-K-0320, N00014-90-J-1456).     

Dealing with Multiple Solutions in Structural Vector Autoregressive Models

Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.