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Power laws from individual differences in learning and forgetting: mathematical analyses
It has frequently been claimed that learning performance improves with practice according to the so-called “Power Law of Learning.” Similarly, forgetting may follow a power law. It has been shown on the basis of extensive simulations that such power laws may emerge through averaging functions with o...
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Formato: | Texto |
Lenguaje: | English |
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Springer-Verlag
2011
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3098361/ https://www.ncbi.nlm.nih.gov/pubmed/21468774 http://dx.doi.org/10.3758/s13423-011-0076-y |
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author | Murre, Jaap M. J. Chessa, Antonio G. |
author_facet | Murre, Jaap M. J. Chessa, Antonio G. |
author_sort | Murre, Jaap M. J. |
collection | PubMed |
description | It has frequently been claimed that learning performance improves with practice according to the so-called “Power Law of Learning.” Similarly, forgetting may follow a power law. It has been shown on the basis of extensive simulations that such power laws may emerge through averaging functions with other, nonpower function shapes. In the present article, we supplement these simulations with a mathematical proof that power functions will indeed emerge as a result of averaging over exponential functions, if the distribution of learning rates follows a gamma distribution, a uniform distribution, or a half-normal function. Through a number of simulations, we further investigate to what extent these findings may affect empirical results in practice. |
format | Text |
id | pubmed-3098361 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2011 |
publisher | Springer-Verlag |
record_format | MEDLINE/PubMed |
spelling | pubmed-30983612011-07-07 Power laws from individual differences in learning and forgetting: mathematical analyses Murre, Jaap M. J. Chessa, Antonio G. Psychon Bull Rev Article It has frequently been claimed that learning performance improves with practice according to the so-called “Power Law of Learning.” Similarly, forgetting may follow a power law. It has been shown on the basis of extensive simulations that such power laws may emerge through averaging functions with other, nonpower function shapes. In the present article, we supplement these simulations with a mathematical proof that power functions will indeed emerge as a result of averaging over exponential functions, if the distribution of learning rates follows a gamma distribution, a uniform distribution, or a half-normal function. Through a number of simulations, we further investigate to what extent these findings may affect empirical results in practice. Springer-Verlag 2011-04-06 2011 /pmc/articles/PMC3098361/ /pubmed/21468774 http://dx.doi.org/10.3758/s13423-011-0076-y Text en © The Author(s) 2011 https://creativecommons.org/licenses/by-nc/4.0/This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. |
spellingShingle | Article Murre, Jaap M. J. Chessa, Antonio G. Power laws from individual differences in learning and forgetting: mathematical analyses |
title | Power laws from individual differences in learning and forgetting: mathematical analyses |
title_full | Power laws from individual differences in learning and forgetting: mathematical analyses |
title_fullStr | Power laws from individual differences in learning and forgetting: mathematical analyses |
title_full_unstemmed | Power laws from individual differences in learning and forgetting: mathematical analyses |
title_short | Power laws from individual differences in learning and forgetting: mathematical analyses |
title_sort | power laws from individual differences in learning and forgetting: mathematical analyses |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3098361/ https://www.ncbi.nlm.nih.gov/pubmed/21468774 http://dx.doi.org/10.3758/s13423-011-0076-y |
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