According to the internal/external frame of reference model, academic achievement has a strong impact on people’s self-concept, both within and between subjects. We conducted a series of meta-analyses of k = 505 data sets containing the six bivariate correlations between achievement and self-concept in two subjects. Negative paths from achievement to noncorresponding self-concept, indicating dimensional comparison effects, were strongest when the subjects were dissimilar with regard to the math-verbal continuum, reduced but still significantly negative when both subjects belonged to the verbal domain, and near-zero when both subjects belonged to the math/science domain. Additionally, we found stronger positive paths from achievements to corresponding self-concepts, indicating social comparison effects, and stronger dimensional comparison effects for grades than for standardized test scores, and for older rather than younger students. We extend dimensional comparison theory by discussing these results with particular regard to the nonexistence of assimilation effects, the effects of subject similarity on dimensional comparison effects, and other moderators of dimensional comparison effects.

The operational momentum (OM) effect describes a systematic bias in estimating the outcomes of simple addition and subtraction problems. Outcomes of addition problems are overestimated while outcomes of subtraction problems are underestimated. The origin of OM remains debated. First, a flawed uncompression of numerical information during the course of mental arithmetic is supposed to cause OM due to linear arithmetic operations on a compressed magnitude code. Second, attentional shifts along the mental number line are thought to cause OM. A third hypothesis explains OM in 9-month olds by a cognitive heuristic of accepting more (less) than the original operand in addition (subtraction) problems. The current study attempts to disentangle these alternatives and systematically examines potential determinants of OM, such as reading fluency which has been found to modulate numerical–spatial associations. A group of 32 6- and 7-year-old children was tested in non-symbolic addition and subtraction problems, in which they had to choose the correct outcome from an array of several possible outcomes. Reading capacity was assessed for half of the children while attentional measures were assessed in the other half. Thirty-two adults were tested with the identical paradigm to validate its potential of revealing OM. Children (and adults) were readily able to solve the problems. We replicated previous findings of OM in the adults group. Using a Bayesian framework we observed an inverse OM effect in children, i.e., larger overestimations for subtraction compared to addition. A significant correlation between children’s level of attentional control and their propensity to exhibit OM was observed. The observed pattern of results, in particular the inverse OM in children is hard to reconcile with the previously proposed theoretical frameworks. The observed link between OM and the attentional system might be interpreted as evidence partially supporting the attentional shift hypothesis.

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We conducted two studies to test the hypothesis that respect for disapproved outgroups increases tolerance toward them. In Study 1, we employed a panel sample of supporters of the Tea Party movement in the United States and found that Tea Party supporters' respect for homosexuals and Muslims as equal fellow citizens positively predicted Tea Party supporters' tolerance toward these groups. There was no indication that alternative recognition processes (i.e., achievement recognition or need recognition) played a similar role in the development of tolerance. Study 2 replicated the respect-tolerance link with the experimental method and a more comprehensive measure of tolerance. In particular, it demonstrated that the link also holds with regard to tolerance in the public or political sphere. The wider implications of our research for societal pluralism are discussed.

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Autoregressive modeling has traditionally been concerned with time-series data from one unit (N = 1). For short time series (T < 50), estimation performance problems are well studied and documented. Fortunately, in psychological and social science research, besides T, another source of information is often available for model estimation, that is, the persons (N > 1). In this work, we illustrate the N/T compensation effect: With an increasing number of persons N at constant T, the model estimation performance increases, and vice versa, with an increasing number of time points T at constant N, the performance increases as well. Based on these observations, we develop sample size recommendations in the form of easily accessible N/T heatmaps for two popular autoregressive continuous-time models.

Bayesian estimation has become very popular. However, run time of Bayesian models is often unsatisfactorily high. In this illustration, we show how to reduce run time by (a) integrating out nuisance model parameters and by (b) reformulating the model based on covariances and means. The core concept is to use the sample scatter matrix which is in our case Wishart distributed with the model-implied covariance matrix as the scale matrix. To illustrate this approach, we choose the popular multi-level null (intercept-only) model, provide a step-by-step instruction on how to implement this model in a multipurpose Bayesian software, and show how structural equation modeling techniques can be employed to bypass mathematically challenging derivations. A simulation study showed that run time is considerably reduced and an empirical example illustrates our approach. Further, we show how the JAGS sampling progress can be monitored and stopped automatically when convergence and precision criteria are reached.