Correction: Empirical assessment of published effect sizes and power in the recent cognitive neuroscience and psychology literature.

[This corrects the article DOI: 10.1371/journal.pbio.2000797.].

No evidence for a core deficit in developmental dyscalculia or mathematical learning disabilities.

BACKGROUND: Two hypotheses were tested regarding the characteristics of children with mathematical learning disabilities (MLD): (a) that children with MLD would have a 'core deficit' in basic number processing skills; and (b) that children with MLD would be at the end of a developmental continuum and have impairments in many cognitive skills. METHODS: From a large sample (N = 1,303) of typically developing children, we selected a group definable as having MLD. The children were given measures of basic number processing and domain-general constructs. Differences between the observed sample and a simulated population were estimated using Cohen's d and Bayes factors. Receiver operating characteristic curves were plotted, and the area under the curve was computed to ascertain the diagnostic power of measures. RESULTS: Results suggest that the differences between the MLD and control group can be defined along with general characteristics of the population rather than assuming single or multiple 'core deficits'. None of the measures of interest exceeded the diagnostic power that could be derived via simulation from the dimensional characteristics of the general population. CONCLUSIONS: There is no evidence for core deficit(s) in MLD. We suggest that future research should focus on representative samples of typical populations and on carefully tested clinical samples confirming to the criteria of international diagnostic manuals. Clinical diagnoses require that MLD is persistent and resistant to intervention, so studies would deliver results less exposed to measurement fluctuations. Uniform diagnostic criteria would also allow for the easy cross-study comparison of samples overcoming a serious limitation of the current literature.

Dyslexia treatment studies: A systematic review and suggestions on testing treatment efficacy with small effects and small samples.

Poor response to treatment is a defining characteristic of reading disorder. In the present systematic review and meta-analysis, we found that the overall average effect size for treatment efficacy was modest, with a mean standardized difference of 0.38. Small true effects, combined with the difficulty to recruit large samples, seriously challenge researchers planning to test treatment efficacy in dyslexia and potentially in other learning disorders. Nonetheless, most published studies claim effectiveness, generally based on liberal use of multiple testing. This inflates the risk that most statistically significant results are associated with overestimated effect sizes. To enhance power, we propose the strategic use of repeated measurements with mixed-effects modelling. This novel approach would enable us to estimate both individual parameters and population-level effects more reliably. We suggest assessing a reading outcome not once, but three times, at pre-treatment and three times at post-treatment. Such design would require only modest additional efforts compared to current practices. Based on this, we performed ad hoc a priori design analyses via simulation studies. Results showed that using the novel design may allow one to reach adequate power even with low sample sizes of 30-40 participants (i.e., 15-20 participants per group) for a typical effect size of d = 0.38. Nonetheless, more conservative assumptions are warranted for various reasons, including a high risk of publication bias in the extant literature. Our considerations can be extended to intervention studies of other types of neurodevelopmental disorders.

Sample size evolution in neuroimaging research: An evaluation of highly-cited studies (1990-2012) and of latest practices (2017-2018) in high-impact journals.

We evaluated 1038 of the most cited structural and functional (fMRI) magnetic resonance brain imaging papers (1161 studies) published during 1990-2012 and 270 papers (300 studies) published in top neuroimaging journals in 2017 and 2018. 96% of highly cited experimental fMRI studies had a single group of participants and these studies had median sample size of 12, highly cited clinical fMRI studies (with patient participants) had median sample size of 14.5, and clinical structural MRI studies had median sample size of 50. The sample size of highly cited experimental fMRI studies increased at a rate of 0.74 participant/year and this rate of increase was commensurate with the median sample sizes of neuroimaging studies published in top neuroimaging journals in 2017 (23 participants) and 2018 (24 participants). Only 4 of 131 papers in 2017 and 5 of 142 papers in 2018 had pre-study power calculations, most for single t-tests and correlations. Only 14% of highly cited papers reported the number of excluded participants whereas 49% of papers with their own data in 2017 and 2018 reported excluded participants. Publishers and funders should require pre-study power calculations necessitating the specification of effect sizes. The field should agree on universally required reporting standards. Reporting formats should be standardized so that crucial study parameters could be identified unequivocally.

Empirical assessment of published effect sizes and power in the recent cognitive neuroscience and psychology literature.

We have empirically assessed the distribution of published effect sizes and estimated power by analyzing 26,841 statistical records from 3,801 cognitive neuroscience and psychology papers published recently. The reported median effect size was D = 0.93 (interquartile range: 0.64-1.46) for nominally statistically significant results and D = 0.24 (0.11-0.42) for nonsignificant results. Median power to detect small, medium, and large effects was 0.12, 0.44, and 0.73, reflecting no improvement through the past half-century. This is so because sample sizes have remained small. Assuming similar true effect sizes in both disciplines, power was lower in cognitive neuroscience than in psychology. Journal impact factors negatively correlated with power. Assuming a realistic range of prior probabilities for null hypotheses, false report probability is likely to exceed 50% for the whole literature. In light of our findings, the recently reported low replication success in psychology is realistic, and worse performance may be expected for cognitive neuroscience.

Predictors of mathematics in primary school: Magnitude comparison, verbal and spatial working memory measures.

We determined the relative importance of the so-called approximate number system (ANS), symbolic number comparison (SNC) and verbal and spatial short-term and working memory (WM) capacity for mathematics achievement in 1,254 Grade 2, 4 and 6 children. The large sample size assured high power and low false report probability and allowed us to determine effect sizes precisely. We used reading decoding as a control outcome measure to test whether findings were specific to mathematics. Bayesian analysis allowed us to provide support for both null and alternative hypotheses. We found very weak zero-order correlations between ANS measures and math achievement. These correlations were not specific to mathematics, became non-significant once intelligence was considered and ANS measures were not selected as predictors of math by regression models. In contrast, overall SNC accuracy and spatial WM measures were reliable and mostly specific predictors of math achievement. Verbal short-term and WM and SNC reaction time were predictors of both reading and math achievement. We conclude that ANS tasks are not suitable as measures of math development in school-age populations. In contrast, all other cognitive functions we studied are promising markers of mathematics development.

Atypical right hemisphere response to slow temporal modulations in children with developmental dyslexia.

Phase entrainment of neuronal oscillations is thought to play a central role in encoding speech. Children with developmental dyslexia show impaired phonological processing of speech, proposed theoretically to be related to atypical phase entrainment to slower temporal modulations in speech (<10Hz). While studies of children with dyslexia have found atypical phase entrainment in the delta band (~2Hz), some studies of adults with developmental dyslexia have shown impaired entrainment in the low gamma band (~35-50Hz). Meanwhile, studies of neurotypical adults suggest asymmetric temporal sensitivity in auditory cortex, with preferential processing of slower modulations by right auditory cortex, and faster modulations processed bilaterally. Here we compared neural entrainment to slow (2Hz) versus faster (40Hz) amplitude-modulated noise using fNIRS to study possible hemispheric asymmetry effects in children with developmental dyslexia. We predicted atypical right hemisphere responding to 2Hz modulations for the children with dyslexia in comparison to control children, but equivalent responding to 40Hz modulations in both hemispheres. Analyses of HbO concentration revealed a right-lateralised region focused on the supra-marginal gyrus that was more active in children with dyslexia than in control children for 2Hz stimulation. We discuss possible links to linguistic prosodic processing, and interpret the data with respect to a neural 'temporal sampling' framework for conceptualizing the phonological deficits that characterise children with developmental dyslexia across languages.

Inducing attention not to blink: auditory entrainment improves conscious visual processing.

Our ability to allocate attention at different moments in time can sometimes fail to select stimuli occurring in close succession, preventing visual information from reaching awareness. This so-called attentional blink (AB) occurs when the second of two targets (T2) is presented closely after the first (T1) in a rapid serial visual presentation (RSVP). We hypothesized that entrainment to a rhythmic stream of stimuli-before visual targets appear-would reduce the AB. Experiment 1 tested the effect of auditory entrainment by presenting sounds with a regular or irregular interstimulus interval prior to a RSVP where T1 and T2 were separated by three possible lags (1, 3 and 8). Experiment 2 examined visual entrainment by presenting visual stimuli in place of auditory stimuli. Results revealed that irrespective of sensory modality, arrhythmic stimuli preceding the RSVP triggered an alerting effect that improved the T2 identification at lag 1, but impaired the recovery from the AB at lag 8. Importantly, only auditory rhythmic entrainment was effective in reducing the AB at lag 3. Our findings demonstrate that manipulating the pre-stimulus condition can reduce deficits in temporal attention characterizing the human cognitive architecture, suggesting innovative trainings for acquired and neurodevelopmental disorders.

Cognitive components of a mathematical processing network in 9-year-old children.

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular 'number sense'. We suggest an 'executive memory function centric' model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors.

Young-age gender differences in mathematics mediated by independent control or uncontrollability.

We studied whether the origins of math anxiety can be related to a biologically supported framework of stress induction: (un)controllability perception, here indicated by self-reported independent efforts in mathematics. Math anxiety was tested in 182 children (8- to 11-year-olds). Latent factor modeling was used to test hypotheses on plausible causal processes and mediations within competing models in quasi-experimental contrasts. Uncontrollability perception in mathematics, or (in)dependence of efforts, best fit the data as an antecedent of math anxiety. In addition, the relationship of math anxiety with gender was fully mediated by adaptive perception of control (i.e. controllability). That is, young boys differ from girls in terms of their experience of control in mathematics learning. These differences influence math anxiety. Our findings are consistent with recent suggestions in clinical literature according to which uncontrollability makes women more susceptible to fear and anxiety disorders.

Anxiety predicts math achievement in kindergarten children.

Introduction: Math anxiety (MA) is an academic anxiety about learning, doing, and evaluating mathematics, usually studied in school populations and adults. However, MA likely has its origins before children go to school. For example, studies have shown that general anxiety (GA) for everyday events is less separable from MA in primary than in early secondary school. This suggests that GA may be a precursor of MA. For this reason, here, we have examined whether GA is already associated with math achievement at the end of kindergarten. Methods: We tested 488 Hungarian kindergarten children aged 5.7 to 6.9 years (55% girls) and analyzed the effect of GA, sex, and family SES on math achievement in kindergarten children. Results: Strikingly, confirming results from primary school children, we found that GA negatively correlated with math achievement already in this preschool population. Higher GA levels had a stronger negative effect on girls' than boys' math achievement. However, there were no significant sex differences in math achievement in kindergarten. Additionally, family socioeconomic status was the strongest predictor of math achievement. Discussion: We speculate that high GA in preschool is a plausible early precursor of later high MA. Early interventions could aim to control GA levels before children start formal schooling.

A large-scale study on the prevalence of math anxiety in Qatar.

BACKGROUND: Math anxiety (MA) is a worldwide appearing academic anxiety that can affect student mental health and deter students from math and science-related career choices. METHOD: Using the Arabic version of the Modified-Abbreviated Math Anxiety Scale (m-AMAS), the prevalence of MA was investigated in a very large sample of students (N = 10093) from grades 7 to 12 in Qatar. RESULTS: The results showed a better fit to the original two-factor model of the m-AMAS (learning MA and Evaluation MA) than to a single-factor solution. This two-factor model was also confirmed in each grade. Notably, the distribution of MA scores was right-skewed, especially for learning MA. Using the inter-quartiles ranges, norms for MA were provided: A score of ≤16 indicates low MA whereas a score of ≥30 identifies high MA. Previous studies conducted in Western countries defined high math-anxious students as those who score above the 90th percentile corresponding to a score of 30 on the m-AMAS. Using this cut-off criterion, the current study found that one-fifth of students in Qatar were highly math-anxious, with a higher proportion of females than males. We also calculated the percentage of participants selecting each response category for each questionnaire item. Results showed that attending a long math class was the context that elicited the highest levels of learning MA. In contrast, having an unexpected math test was the situation that triggered the highest levels of evaluation MA. CONCLUSION: The prevalence of MA might vary across different cultures.

The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children.

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8.

Conscious access is linked to ongoing brain state: electrophysiological evidence from the attentional blink.

Neuroscience explanations of conscious access focus on neural events elicited by stimuli. In contrast, here, we used the attentional blink paradigm in combination with event-related brain potentials to examine whether the ongoing state of the brain before a stimulus can determine both conscious access and the poststimulus neural events associated with consciousness. Participants were required to detect 2 target letters from digit distractors while their brain activity was being recorded. Trials were classified based on whether the secondcritical target (T2) was detected. We found that T2-detection was predetermined by brain activity prior to the onset of the stimulation stream. Specifically, T2-detected trials were predicated by a frontocentral positive going deflection that started more than 200 ms before the stream began. Accurate T2 detection was also accompanied by enhanced poststimulus neural activity, as reflected by a larger P3b component. Furthermore, prestimulus and poststimulus markers of T2-detection were highly correlated with one another. We therefore argue that conscious experiences are shaped by potentially random fluctuations in neural activity. Overall, the results reveal that conscious access is underpinned by an important relationship involving predictive prestimulus neural activity and responsive poststimulus brain activity.

Gender differences in developmental dyscalculia depend on diagnostic criteria.

Developmental dyscalculia (DD) is a learning difficulty specific to mathematics learning. The prevalence of DD may be equivalent to that of dyslexia, posing an important challenge for effective educational provision. Nevertheless, there is no agreed definition of DD and there are controversies surrounding cutoff decisions, specificity and gender differences. In the current study, 1004 British primary school children completed mathematics and reading assessments. The prevalence of DD and gender ratio were estimated in this sample using different criteria. When using absolute thresholds, the prevalence of DD was the same for both genders regardless of the cutoff criteria applied, however gender differences emerged when using a mathematics-reading discrepancy definition. Correlations between mathematics performance and the control measures selected to identify a specific learning difficulty affect both prevalence estimates and whether a gender difference is in fact identified. Educational implications are discussed.

Maths anxiety and subjective perception of control, value and success expectancy in mathematics.

Mathematics anxiety (MA) is an academic anxiety related to doing, learning and testing mathematics. MA can negatively affect mathematics performance, motivation and maths-heavy science and technology-related career choices. Previous data suggest that subjective perceptions and interpretations of students are key in the genesis of MA. Here, based on expectancy-value and control-value theory, we aimed to identify potential, theoretically based subjective factors probably key to understanding MA. We analysed data from 151 745 fifteen-year-old children from 65 'countries and economies' from the Programme for International Student Assessment (PISA) 2012 dataset. Subjective self-perceptions had a stronger relationship with MA than maths achievement. We found that higher MA was associated with lower perceived control over maths activities and lower subjective expectation of success. Surprisingly, children with higher subjective valuation of maths had higher MA for similar levels of subjective control and success expectancy in maths. Results offer an improved understanding of potential antecedents of MA and suggest that effective interventions could be based on gradual confidence building in maths. These could primarily draw on a deeper understanding of the subject improving subjective success expectancy and feeling of control over maths activities. Cultural variation in findings is discussed.

The time course of symbolic number adaptation: oscillatory EEG activity and event-related potential analysis.

Several functional magnetic resonance imaging (fMRI) studies have used neural adaptation paradigms to detect anatomical locations of brain activity related to number processing. However, currently not much is known about the temporal structure of number adaptation. In the present study, we used electroencephalography (EEG) to elucidate the time course of neural events in symbolic number adaptation. The numerical distance of deviants relative to standards was manipulated. In order to avoid perceptual confounds, all levels of deviants consisted of perceptually identical stimuli. Multiple successive numerical distance effects were detected in event-related potentials (ERPs). Analysis of oscillatory activity further showed at least two distinct stages of neural processes involved in the automatic analysis of numerical magnitude, with the earlier effect emerging at around 200ms and the later effect appearing at around 400ms. The findings support for the hypothesis that numerical magnitude processing involves a succession of cognitive events.

Reduced phase locking to slow amplitude modulation in adults with dyslexia: an MEG study.

Perception of speech at multiple temporal scales is important for the efficient extraction of meaningful phonological elements. Individuals with developmental dyslexia have difficulty in the accurate neural representation of phonological aspects of speech, across languages. Recently, it was proposed that these difficulties might arise in part because of impaired phase locking to the slower modulations in the speech signal (<10 Hz), which would affect syllabic parsing and segmentation of the speech stream (the "temporal sampling" hypothesis, Goswami, 2011). Here we measured MEG responses to different rates of amplitude modulated white noise in adults with and without dyslexia. In line with the temporal sampling hypothesis, different patterns of phase locking to amplitude modulation at the delta rate of 2 Hz were found when comparing participants with dyslexia to typically-reading participants. Typical readers exhibited better phase locking to slow modulations in right auditory cortex, whereas adults with dyslexia showed more bilateral phase locking. The results suggest that oscillatory phase locking mechanisms for slower temporal modulations are atypical in developmental dyslexia.

Functional definition of the N450 event-related brain potential marker of conflict processing: a numerical stroop study.

BACKGROUND: Several conflict processing studies aimed to dissociate neuroimaging phenomena related to stimulus and response conflict processing. However, previous studies typically did not include a paradigm-independent measure of either stimulus or response conflict. Here we have combined electro-myography (EMG) with event-related brain potentials (ERPs) in order to determine whether a particularly robust marker of conflict processing, the N450 ERP effect usually related to the activity of the Anterior Cingulate Cortex (ACC), is related to stimulus- or to response-conflict processing. EMG provided paradigm-independent measure of response conflict. In a numerical Stroop paradigm participants compared pairs of digits and pressed a button on the side where they saw the larger digit. 50% of digit-pairs were preceded by an effective cue which provided accurate information about the required response. 50% of trials were preceded by a neutral cue which did not communicate the side of response. RESULTS: EMG showed that response conflict was significantly larger in neutrally than in effectively cued trials. The N450 was similar when response conflict was high and when it was low. CONCLUSIONS: We conclude that the N450 is related to stimulus or abstract, rather than to response conflict detection/resolution. Findings may enable timing ACC conflict effects.

Representational change and strategy use in children's number line estimation during the first years of primary school.

BACKGROUND: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. METHODS: Typically developing children (n = 67) from Years 1-3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. RESULTS: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. CONCLUSION: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.