scholarly journals Comparative Statistical Analysis of Pre-Existing Non-Symbolic Cognitive Math Models as a Predictor of Math Acuity in Children

2019 ◽  
Author(s):  
Rohan Hundia
Keyword(s):  
Statistical Analysis ◽  
Reaction Time ◽  
Weber Fraction ◽  
Distance Effect ◽  
Number System ◽  
Numerical Distance ◽  
Comparison Task ◽  
Math Task ◽  
Underlying Basis ◽  
Using Data

Approximate Number System (ANS) acuity has been the underlying basis of mathematical magnitude measure in developing children. The early number learning in a child by means of numerosity representation is said to be best estimated by an ANS based model. ANS models are majorly specific to cases where numbers are represented by non-digits and are therefore non-symbolic (dot representations). Prior research also suggests that ANS acuity models could be used to give an estimate of an accuracy of a child in a non-symbolic math task. Common measures of ANS acuity are based on weber fraction based accuracy performance and some others are based on numerical distance effect and reaction time. However though, very few studies have amalgamated reaction time and weber fraction models and compared them at an individualistic level using actual data collected over participants. In this research study, we effectively try to understand how factors like weber fraction, ratio, magnitude of numbers might affect the performance of a participant in a non-symbolic number comparison task. We also seek for any sort established relationship between numerical distance and reaction time and how that might be a predictor of good/bad performance. We carry out statistical analysis on both of these models (individually and combined) using data obtained from an online math task and thereby deduce which model could be a better predictor of a child’s math acuity.

scholarly journals Symbolic numerical distance effect does not follow the values of the numbers

2017 ◽  
Author(s):  
Attila Krajcsi ◽  
Petia Kojouharova
Keyword(s):  
Distance Effect ◽  
Numerical Distance ◽  
Comparison Task ◽  
Number Range ◽  
Numerical Distance Effect ◽  
Potential Sources ◽  
And Performance ◽  
Study Participants ◽  
Strength Of Association

In a comparison task, the larger the distance between the two numbers to be compared, the better the performance, a phenomenon termed the numerical distance effect. According to the dominant explanation, the distance effect is rooted in a noisy representation, and performance is proportional to the size of the overlap between the noisy representations of the two values. According to alternative explanations, the distance effect may be rooted in the association between the numbers and the small-large categories, and performance is better when the numbers show relatively high differences in their strength of association with the small-large properties. In everyday number use the value of the numbers and the association between the numbers and the small-large categories strongly correlate, thus, the two explanations have the same predictions for the distance effect. To dissociate the two potential sources of the distance effect, in the present study participants learned new artificial number digits between 1 and 3, and between 7 and 9, thus, leaving out the numbers between 4 and 6. It was found that the omitted number range (the distance between 3 and 7) was considered in the distance effect as 1, and not as 4, suggesting that the distance effect does not follow the values of the numbers predicted by the dominant explanation, but it follows the small-large property association predicted by the alternative explanations.

scholarly journals Symbolic number comparison is not processed by the analogue number system: different symbolic and nonsymbolic numerical distance and size effects

2017 ◽  
Author(s):  
Attila Krajcsi ◽  
Gabor Lengyel ◽  
Petia Kojouharova
Keyword(s):  
Size Effects ◽  
Goodness Of Fit ◽  
Numerical Cognition ◽  
Reaction Times ◽  
Number System ◽  
Error Rates ◽  
Numerical Distance ◽  
Comparison Task ◽  
Number Comparison ◽  
Symbolic Number

Dominant numerical cognition models suppose that both symbolic and nonsymbolic numbers are processed by the Analogue Number System (ANS) working according to Weber’s law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and nonsymbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times and diffusion model drift rates were systematically analyzed in both nonsymbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model’s prediction is relatively good for the nonsymbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only nonsymbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation.

Neuroticism and Speed-Accuracy Tradeoff in Self-Paced Speeded Mental Addition and Comparison

2010 ◽  
Vol 31 (3) ◽  
pp. 130-137 ◽  
Author(s):  
Hagen C. Flehmig ◽  
Michael B. Steinborn ◽  
Karl Westhoff ◽  
Robert Langner
Keyword(s):  
Reaction Time ◽  
Response Speed ◽  
Time Variability ◽  
Reaction Time Variability ◽  
Comparison Task ◽  
Processing Efficiency ◽  
Mental Addition ◽  
Speed Accuracy ◽  
The Relationship ◽  
Accuracy Tradeoff

Previous research suggests a relationship between neuroticism (N) and the speed-accuracy tradeoff in speeded performance: High-N individuals were observed performing less efficiently than low-N individuals and compensatorily overemphasizing response speed at the expense of accuracy. This study examined N-related performance differences in the serial mental addition and comparison task (SMACT) in 99 individuals, comparing several performance measures (i.e., response speed, accuracy, and variability), retest reliability, and practice effects. N was negatively correlated with mean reaction time but positively correlated with error percentage, indicating that high-N individuals tended to be faster but less accurate in their performance than low-N individuals. The strengthening of the relationship after practice demonstrated the reliability of the findings. There was, however, no relationship between N and distractibility (assessed via measures of reaction time variability). Our main findings are in line with the processing efficiency theory, extending the relationship between N and working style to sustained self-paced speeded mental addition.

A high working memory load eliminates the numerical distance effect

2010 ◽  
Author(s):  
Erin A. Maloney ◽  
Evan F. Risko ◽  
Derek Besner ◽  
Jonathan A. Fugelsang
Keyword(s):  
Working Memory ◽  
Memory Load ◽  
Distance Effect ◽  
Numerical Distance ◽  
Working Memory Load ◽  
Numerical Distance Effect

scholarly journals Numerosity representations in crows obey the Weber–Fechner law

2016 ◽  
Vol 283 (1827) ◽  
pp. 20160083 ◽  
Author(s):  
Helen M. Ditz ◽  
Andreas Nieder
Keyword(s):  
Weber Fraction ◽  
Discrimination Performance ◽  
Brain Structures ◽  
Number System ◽  
Number Line ◽  
Just Noticeable Difference ◽  
Match To Sample ◽  
Close Phylogenetic Relationship ◽  
The One ◽  
Numerical Representations

The ability to estimate number is widespread throughout the animal kingdom. Based on the relative close phylogenetic relationship (and thus equivalent brain structures), non-verbal numerical representations in human and non-human primates show almost identical behavioural signatures that obey the Weber–Fechner law. However, whether numerosity discriminations of vertebrates with a very different endbrain organization show the same behavioural signatures remains unknown. Therefore, we tested the numerical discrimination performance of two carrion crows ( Corvus corone ) to a broad range of numerosities from 1 to 30 in a delayed match-to-sample task similar to the one used previously with primates. The crows' discrimination was based on an analogue number system and showed the Weber-fraction signature (i.e. the ‘just noticeable difference’ between numerosity pairs increased in proportion to the numerical magnitudes). The detailed analysis of the performance indicates that numerosity representations in crows are scaled on a logarithmically compressed ‘number line’. Because the same psychophysical characteristics are found in primates, these findings suggest fundamentally similar number representations between primates and birds. This study helps to resolve a classical debate in psychophysics: the mental number line seems to be logarithmic rather than linear, and not just in primates, but across vertebrates.

scholarly journals Volatility of Jakarta Islamic Index

2014 ◽  
Vol 6 (2) ◽  
pp. 207-222
Author(s):  
Hendri Tanjung
Keyword(s):  
Statistical Analysis ◽  
Normal Distribution ◽  
Stock Exchange ◽  
Daily Data ◽  
Using Data ◽  
Simple Statistical Analysis

Volatility of Jakarta Islamic Index. This study investigates the volatility of Jakarta Islamic Index (JII) in Jakarta Stock Exchange. The method that used in this research is used a simple statistical analysis. The normality of JII return is analyzed to answer whether the return of JII follows normal distribution. By using data of Jakarta Islamic Index from 2nd March 2009 to 30th October 2013 (1122 daily data), it is found that the distribution of return of JII is not normal, even the 5 sigma occurred. This means the return of Jakarta Islamic Index is much volatile than the theory predicted. This will make too much gain or loss in one day in the economy  DOI:10.15408/aiq.v6i2.1231

A STATISTICAL MODEL OF WINTER/SPRING POLAR OZONE

2021 ◽  
pp. 16-24
Author(s):  
N. S. Ivanova ◽  
Keyword(s):  
Statistical Analysis ◽  
Statistical Model ◽  
Zonal Wind ◽  
The Arctic ◽  
Satellite Measurements ◽  
Latitude Zone ◽  
Using Data ◽  
Polar Ozone

Satellite measurements provided by NASA (USA) at http://ozonewatch.gsfc.nasa.gov are used to study the variability and interdependence of polar ozone, polar temperature, and mean zonal wind. A model of winter/spring polar ozone in the Arctic and Antarctic is constructed using data on polar temperatures at 30, 70, and 100 hPa levels and mean zonal wind at 10 and 70 hPa levels in the latitude zone of 45°-75°. The results of the statistical analysis of the 1979-2020 polar ozone calculation errors are presented.

Numerical Values Leave a Semantic Imprint on Associated Signs in Monkeys

2010 ◽  
Vol 22 (1) ◽  
pp. 174-183 ◽  
Author(s):  
Ilka Diester ◽  
Andreas Nieder
Keyword(s):  
Size Effect ◽  
Distance Effect ◽  
Numerical Distance ◽  
Quantity Representation ◽  
Analog Magnitude ◽  
Visual Sign

Animals and humans share an evolutionary ancient quantity representation which is characterized by analog magnitude features: Discriminating magnitudes becomes more difficult with increasing set sizes (size effect) and with decreasing distance between two numerosities (distance effect). Humans show these effects even with number symbols. We wondered whether monkeys would show the same psychophysical effects with numerical signs and addressed this issue by training three monkeys to associate visual shapes with numerosities. We then confronted the monkeys with trials in which they had to match these visual signs with each other. The monkeys' performance in this shape versus shape protocol was positively correlated with the numerical distance and the magnitudes associated with the signs. Additionally, the monkeys responded significantly slower for signs with higher assigned numerical values. These findings suggest that the numerical values imprint their analog magnitudes characteristics onto the associated visual sign in monkeys, an effect that we also found reflected in the discharges of prefrontal neurons. This provides evidence for a precursor of the human number symbol knowledge.

scholarly journals Numerical distance effect in the N240 component in a number-matching task

Neuroreport ◽  
2006 ◽  
Vol 17 (10) ◽  
pp. 991-994 ◽  
Author(s):  
Xinlin Zhou ◽  
Chuansheng Chen ◽  
Qi Dong ◽  
Hongchuan Zhang ◽  
Chunhui Chen ◽  
...  
Keyword(s):  
Distance Effect ◽  
Matching Task ◽  
Numerical Distance ◽  
Numerical Distance Effect
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