Numerosities and space; indeed a cognitive illusion! A reply to de Hevia and Spelke (2009)

de Hevia and Spelke (de Hevia and Spelke (2009). Spontaneous mapping of number and space in adults and young children, Cognition, 110, 198–207) investigated the mapping of number onto space. To this end, they introduced a non-symbolic flanker task. Here subjects have to bisect a line that is flanked by a 2-dot and a 9-dot array. Similar to the symbolic line bisection task, a bias towards the larger numerosity was observed. We re-investigated these results both by creating new flanker stimuli that controlled for different (non-numerical) stimulus properties and by developing a new measurement tool. We demonstrate that the bisection bias was caused by the larger area subtended by the 9-dot array compared to the 2-dot array and not numerosity. Our study puts constraints on the results of the study by de Hevia and Spelke. The role of visual cues in numerosity processing in general is discussed.     

Families of Choice? Exploring the Supportive Networks of Lesbians,Gay Men,and Bisexuals1

Despite the judicial and cultural progress that has been made in Flanders (i.e., Dutch‐speaking part of Belgium), lesbians, gay men, and bisexuals (LGBs) are still a stigmatized sexual minority. They are assumed to rely extensively on the support of friends to compensate for lack of familial support (i.e., family‐of‐choice hypothesis). In this article, we compare the support networks of 2,754 Flemish LGBs and 1,199 Flemish citizens and find convincing support for the family‐of‐choice hypothesis. LGBs seem to rely primarily on friends, while the average Fleming primarily relies on family for confidant support. We discuss the supportive potential captured in these friendship networks and raise the question “Are friends all a person needs?”     

The representation of multiplication and division facts in memory

Recently, using a training paradigm, Campbell and Agnew (2009) observed cross-operation response time savings with nonidentical elements (e.g., practice 3 + 2, test 5 - 2) for addition and subtraction, showing that a single memory representation underlies addition and subtraction performance. Evidence for cross-operation savings between multiplication and division have been described frequently (e.g., Campbell, Fuchs-Lacelle, & Phenix, 2006) but they have always been attributed to a mediation strategy (reformulating a division problem as a multiplication problem, e.g., Campbell et al., 2006). Campbell and Agnew (2009) therefore concluded that there exists a fundamental difference between addition and subtraction on the one hand and multiplication and division on the other hand. However, our results suggest that retrieval savings between inverse multiplication and division problems can be observed. Even for small problems (solved by direct retrieval) practicing a division problem facilitated the corresponding multiplication problem and vice versa. These findings indicate that shared memory representations underlie multiplication and division retrieval. Hence, memory and learning processes do not seem to differ fundamentally between addition-subtraction and multiplication-division.     

Conflict adaptation by means of associative learning

Cognitive control is responsible for adapting information processing in order to carry out tasks more efficiently. Contrasting global versus local control accounts, it has recently been proposed that control operates in an associative fashion, that is, by binding stimulus-response associations after detection of conflict (Verguts & Notebaert, 2009). Here, this prediction is explicitly tested for the first time. In a task-switching study where both tasks use the same relevant information, we previously reported conflict adaptation over tasks (Notebaert & Verguts, 2008). In the current experiment, we demonstrate that this is restricted to conditions where both tasks use the same effectors, thereby supporting the associative control account.     

Sequential analysis of the numerical Stroop effect reveals response suppression

Automatic processing of irrelevant stimulus dimensions has been demonstrated in a variety of tasks. Previous studies have shown that conflict between relevant and irrelevant dimensions can be reduced when a feature of the irrelevant dimension is repeated. The specific level at which the automatic process is suppressed (e.g., perceptual repetition, response repetition), however, is less understood. In the current experiment we used the numerical Stroop paradigm, in which the processing of irrelevant numerical values of 2 digits interferes with the processing of their physical size, to pinpoint the precise level of the suppression. Using a sequential analysis, we dissociated perceptual repetition from response repetition of the relevant and irrelevant dimension. Our analyses of reaction times, error rates, and diffusion modeling revealed that the congruity effect is significantly reduced or even absent when the response sequence of the irrelevant dimension, rather than the numerical value or the physical size, is repeated. These results suggest that automatic activation of the irrelevant dimension is suppressed at the response level. The current results shed light on the level of interaction between numerical magnitude and physical size as well as the effect of variability of responses and stimuli on automatic processing.     

Subtyping children and adolescents who are overweight based on eating pathology and psychopathology

Children and adolescents who are overweight can differ on dimensions measuring dietary restraint and psychopathology. Classifying clinical obese children and adolescents based on these psychological characteristics is shown to be useful in making differential prognoses. The present study aimed to research the validity of subtyping children and adolescents with overweight (N?=?138) in a non-clinical sample. Using cluster analysis, results revealed three subtypes: a dietary restraint/internalizing group (DR?+?IN; n?=?41), a pure internalizing group (IN; n?=?20) and a non-symptomatic group (NS; n?=?77). The DR?+?IN group outscored both other groups on measures of eating pathology, whereas the IN group outscored both other groups on measures of negative offect. Interestingly, the three groups did not differ on degree of overweight. The results seem to suggest that different psychological mechanisms can be observed in subgroups of young overweight adolescents. Further research should explore how individual psychological characteristics can be helpful when stipulating weight loss treatment programmes.     

On the Duties of Commission in Commercial Life. A Kantian Criticism of Moral Institutionalism

In latter-day discussions on corporate morality, duties of commission are fiercely debated. Moral institutionalists argue that duties of commission—such as a duty of assistance—overstep the boundaries of moral duty owed by economic agents. “Moral institutionalism” is a newly coined term for a familiar position on market morality. It maintains that market morality ought to be restricted, excluding all duties of commission. Neo-Classical thinkers such as Baumol and Homann defend it most eloquently. They underpin their position with concerns that go to the core of liberalism—the dominant western political theory that sustains the ideals of both the free market and the free, rational person. Those authors claim that liberalism calls for a fully differentiated market because it resents the politicization of the market. Fully differentiated markets exclude duties of commission. They also claim that full differentiation of the market closes the troublesome gap between moral motivation and moral virtue. Full differentiation redeems the promise of “easy virtue”. In this paper moral institutionalism will be rejected from a Kantian point of view, mostly inspired by Herman’s thesis on the invisibility of morality. Liberalism may perhaps ban the politicization of the market; it does not forbid its moralization. The idea of a fully differentiated market must also be rejected because it is either morally over-demanding (to the morally autonomous person) or morally hazardous (to the person with failing moral motivation). Contrary to what the moral institutionalists claim, right action, morally, is actually quite difficult in fully differentiated markets.     

Simple imputation methods versus direct likelihood analysis for missing item scores in multilevel educational data

Missing data, such as item responses in multilevel data, are ubiquitous in educational research settings. Researchers in the item response theory (IRT) context have shown that ignoring such missing data can create problems in the estimation of the IRT model parameters. Consequently, several imputation methods for dealing with missing item data have been proposed and shown to be effective when applied with traditional IRT models. Additionally, a nonimputation direct likelihood analysis has been shown to be an effective tool for handling missing observations in clustered data settings. This study investigates the performance of six simple imputation methods, which have been found to be useful in other IRT contexts, versus a direct likelihood analysis, in multilevel data from educational settings. Multilevel item response data were simulated on the basis of two empirical data sets, and some of the item scores were deleted, such that they were missing either completely at random or simply at random. An explanatory IRT model was used for modeling the complete, incomplete, and imputed data sets. We showed that direct likelihood analysis of the incomplete data sets produced unbiased parameter estimates that were comparable to those from a complete data analysis. Multiple-imputation approaches of the two-way mean and corrected item mean substitution methods displayed varying degrees of effectiveness in imputing data that in turn could produce unbiased parameter estimates. The simple random imputation, adjusted random imputation, item means substitution, and regression imputation methods seemed to be less effective in imputing missing item scores in multilevel data settings.     

Some Results on Mean Square Error for Factor Score Prediction

For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix Γ _p = Φ ^1/2 Λ _p ′Ψ _p ⁻¹ Λ _p Φ ^1/2. This matrix increases with the number of observable variables p. A necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of Γ _p or, equivalently, divergence of signal-to-noise (Schneeweiss & Mathes, 1995). The same condition is necessary and sufficient for convergence to zero of the positive definite MSE differences of factor predictors, convergence to zero of the distance between factor predictors, and convergence to the unit value of the relative efficiencies of predictors. Various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors. The author is obliged to Maarten Speekenbrink and Peter van Rijn for their assistance with plotting the figures. In addition, I am obliged to the referees for their stimulating remarks.     

Implications of Indeterminate Factor-Error Covariances for Factor Construction, Prediction, and Determinacy

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results. Requests for reprints should be sent to Wim P. Krijnen, Lisdodde 1, 9679 MC Scheemda, The Netherlands.