Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas

Este estudio metodológico de simulación presenta de forma ejemplificada dos medidas de asimetría. Aunque pueden ser útiles cuando la distribución es unimodal, no se reportan en la investigación psicológica. Una es la distancia estandarizada de la media a la moda de Pearson. La otra es la medida robu...

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Autores:
Moral de la Rubia, José
Tipo de recurso:
Article of journal
Fecha de publicación:
2023
Institución:
Universidad de San Buenaventura
Repositorio:
Repositorio USB
Idioma:
spa
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oai:bibliotecadigital.usb.edu.co:10819/29335
Acceso en línea:
https://hdl.handle.net/10819/29335
https://doi.org/10.21500/19002386.6542
Palabra clave:
Simetría
estimación de la moda
bootstrap
inferencia estadística
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dc.title.spa.fl_str_mv Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas
dc.title.translated.eng.fl_str_mv Two measures of skewness based on mode: calculation and interpretative rules
title Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas
spellingShingle Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas
Simetría
estimación de la moda
bootstrap
inferencia estadística
title_short Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas
title_full Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas
title_fullStr Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas
title_full_unstemmed Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas
title_sort Dos medidas de asimetría basadas en la moda: cálculo y normas interpretativas
dc.creator.fl_str_mv Moral de la Rubia, José
dc.contributor.author.spa.fl_str_mv Moral de la Rubia, José
dc.subject.spa.fl_str_mv Simetría
estimación de la moda
bootstrap
inferencia estadística
topic Simetría
estimación de la moda
bootstrap
inferencia estadística
description Este estudio metodológico de simulación presenta de forma ejemplificada dos medidas de asimetría. Aunque pueden ser útiles cuando la distribución es unimodal, no se reportan en la investigación psicológica. Una es la distancia estandarizada de la media a la moda de Pearson. La otra es la medida robusta de asimetría de Bickel. Se muestra cómo calcular la estimación puntual y de intervalo con el programa R. Además, se calculan intervalos de confianza al 90 %, 95 % y 99 % con 10 000 extracciones con reemplazamiento de muestras-población con distribución normal y diferentes tamaños para disponer de directrices interpretativas de simetría. Se concluye que la regla ∓0.1 no aplica, la moda de Grenander proporciona los intervalos de confianza más eficientes, pero la asimetría de Bickel es la opción con variables ordinales.
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-07-15T00:00:00Z
2025-08-25T21:59:48Z
dc.date.available.none.fl_str_mv 2023-07-15T00:00:00Z
2025-08-25T21:59:48Z
dc.date.issued.none.fl_str_mv 2023-07-15
dc.type.spa.fl_str_mv Artículo de revista
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dc.relation.references.spa.fl_str_mv Bickel, D. R. (2002). Robust estimators of the mode and skewness of continuous data. Computational Statistics & Data Analysis, 39(2), 153-163. https://doi.org/10.1016/S0167-9473(01)00057-3.
Bono, R., Arnau, J., Alarcón, R. & Blanca, M. J. (2020). Bias, precision, and accuracy of skewness and kurtosis estimators for frequently used continuous distributions. Symmetry, 12(1), article 19, 1-17. https://doi.org/10.3390/sym12010019.
Canty, A. & Ripley, B. (2022). Boot: bootstrap R (S-Plus) functions. R package version 1.3-28. https://cran.r-project.org/web/packages/boot/boot.pdf.
Eberl, A. & Klar, B. (2020). Asymptotic distributions and performance of empirical skewness measures. Computational Statistics & Data Analysis, 146, article 106939. https://doi.org/10.1016/j.csda.2020.106939.
Epanechnikov, V. A. (1969). Non-parametric estimation of a multivariate probability density. Theory of Probability and Its Applications, 14(1), 153-158. https://doi.org/10.1137/1114019.
Freedman, D. & Diaconis, P. (1981). On the histogram as a density estimator: L2 theory. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 57(4), 453-476. https://doi.org/10.1007/BF01025868.
Giorgi, F. M., Ceraolo, C. & Mercatelli, D. (2022). The R language: an engine for bio-informatics and data science. Life, 12(5), article 648. https://doi.org/10.3390/life12050648.
Grenander, U. (1965). Some direct estimates of the mode. Annals of Mathematical Statistics, 36(1), 131-138. https://doi.org/10.1214/aoms/1177700277.
Guidoum, A. C. (2020). Kernel estimator and bandwidth selection for density and its derivatives: the kedd package. arxiv, article 2012.06102v1. https://doi.org/10.48550/arXiv.2012.06102.
Gupta, S. C. & Kapoor, V. K. (2020). Descriptive measures. In Fundamentals of mathematical statistics, twelfth edition (section 2, pp. 1-78). New Delhi: Sultan Chand & Sons.
Henderson, D. J., Papadopoulos, A. & Parmeter, C. F. (2023). Bandwidth selection for kernel density estimation of fat-tailed and skewed distributions. Journal of Statistical Computation and Simulation, article 2173194, 1-26. https://doi.org/10.1080/00949655.2023.2173194 Khan, A. A., Cheema, S. A., Hussain, Z. & Abdel-Salam, G. A. (2021). Measuring skewness: We do not assume much. Scientia Iranica, 28(6), 3525-3537. https://doi.org/10.24200/SCI.2020.52306.2649.
Lane, D. M. (2015). Histograms. En Online statistics education: a multimedia course of study. https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Lane)/02%3A_Graphing_Distributions/2.04%3A_Histograms.
Mokhtar, S. F., Yusof, Z. M. & Sapiri, H. (2023). Confidence intervals by bootstrapping approach: a significance review. Malaysian Journal of Fundamental and Applied Sciences, 19(1), 30-42. https://doi.org/10.11113/mjfas.v19n1.2660.
Moral, J. (2022). Una medida de asimetría unidimensional para variables cualitativas. Revista de Psicología (PUCP), 40(1), 519-551. https://dx.doi.org/10.18800/psico.202201.017.
Moral, J. (2023). Standardized distance from the mean to the median as a measure of skewness. Open Journal of Statistics, 13, 359-378. https://dx.doi.org/10.4236/ojs.2023.133018.
Pakgohar, A. & Mehrannia, H. (2023). Statistical rules in scientific reports (the basics). Iranian Journal of Diabetes and Obesity, 15, article 12205. https://doi.org/10.18502/ijdo.v15i1.12205.
Parzen, E. (1962). On estimation of a probability density function and mode. Annals of Mathematical Statistics, 33(3), 1065-1076. https://doi.org/10.1214/aoms/1177704472.
Pearson, K. (1894). Contributions to the mathematical theory of evolution. I. On the dissection of asymmetrical frequency curves. Philosophical Transactions of the Royal Society of London A, 185, 71-110. https://doi.org/10.1098/rsta.1894.0003.
Poncet, P. (2022). Package ‘modeest’. Mode estimation. https://cran.r-project.org/web/packages/modeest/modeest.pdf.
Ruzankin, P. S. (2022). A class of nonparametric mode estimators. Communications in Statistics - Simulation and Computation, 51(6), 3291-3304. https://doi.org/10.1080/03610918.2019.1711410.
Sarka, D. (2021). Descriptive statistics. In: Advanced Analytics with Transact-SQL (pp. 3-29). Berkeley, CA: Apress. https://doi.org/10.1007/978-1-4842-7173-5_1.
Scott, D. W. (1979). On optimal and data-based histograms. Biometrika, 66(3), 605-610. https://doi.org/10.1093/biomet/66.3.605.
Sheather, S. J. & Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological), 53(3), 683-690. https://doi.org/10.1111/j.2517-6161.1991.tb01857.x.
Shi, J., Luo, D., Wan, X., Liu, Y., Liu, J., Bian, Z. & Tong, T. (2020). Detecting the skewness of data from the sample size and the five-number summary. arXiv, article 2010.05749. https://doi.org/10.48550/arXiv.2010.05749.
Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall.
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spelling Moral de la Rubia, José2023-07-15T00:00:00Z2025-08-25T21:59:48Z2023-07-15T00:00:00Z2025-08-25T21:59:48Z2023-07-15Este estudio metodológico de simulación presenta de forma ejemplificada dos medidas de asimetría. Aunque pueden ser útiles cuando la distribución es unimodal, no se reportan en la investigación psicológica. Una es la distancia estandarizada de la media a la moda de Pearson. La otra es la medida robusta de asimetría de Bickel. Se muestra cómo calcular la estimación puntual y de intervalo con el programa R. Además, se calculan intervalos de confianza al 90 %, 95 % y 99 % con 10 000 extracciones con reemplazamiento de muestras-población con distribución normal y diferentes tamaños para disponer de directrices interpretativas de simetría. Se concluye que la regla ∓0.1 no aplica, la moda de Grenander proporciona los intervalos de confianza más eficientes, pero la asimetría de Bickel es la opción con variables ordinales.This article presents in exemplified form two measures of skewness. Although they may be useful when the distribution is unimodal, they are not reported in psychological research. One is Pearson’s standardized distance from the mean to the mode. The other is the Bickel’s robust measure of skewness. It is shown how to compute the point and interval estimate with the R program. Moreover, interval confidences at 90%, 95% and 99% are calculated with 10 000 draws with replacement from normally distributed samples-population with different sizes to have interpretative guidelines for symmetry. It is concluded that the ∓0.1 rule does not apply with these measures, Grenander’s mode provides the most efficient confidence intervals, but Bickel’s skewness is the option with ordinal variables.application/pdf10.21500/19002386.65422665-42021900-2386https://hdl.handle.net/10819/29335https://doi.org/10.21500/19002386.6542spaUniversidad San Buenaventura - USB (Colombia)https://revistas.usb.edu.co/index.php/Psychologia/article/download/6542/53045423917PsychologiaBickel, D. R. (2002). Robust estimators of the mode and skewness of continuous data. Computational Statistics & Data Analysis, 39(2), 153-163. https://doi.org/10.1016/S0167-9473(01)00057-3.Bono, R., Arnau, J., Alarcón, R. & Blanca, M. J. (2020). Bias, precision, and accuracy of skewness and kurtosis estimators for frequently used continuous distributions. Symmetry, 12(1), article 19, 1-17. https://doi.org/10.3390/sym12010019.Canty, A. & Ripley, B. (2022). Boot: bootstrap R (S-Plus) functions. R package version 1.3-28. https://cran.r-project.org/web/packages/boot/boot.pdf.Eberl, A. & Klar, B. (2020). Asymptotic distributions and performance of empirical skewness measures. Computational Statistics & Data Analysis, 146, article 106939. https://doi.org/10.1016/j.csda.2020.106939.Epanechnikov, V. A. (1969). Non-parametric estimation of a multivariate probability density. Theory of Probability and Its Applications, 14(1), 153-158. https://doi.org/10.1137/1114019.Freedman, D. & Diaconis, P. (1981). On the histogram as a density estimator: L2 theory. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 57(4), 453-476. https://doi.org/10.1007/BF01025868.Giorgi, F. M., Ceraolo, C. & Mercatelli, D. (2022). The R language: an engine for bio-informatics and data science. Life, 12(5), article 648. https://doi.org/10.3390/life12050648.Grenander, U. (1965). Some direct estimates of the mode. Annals of Mathematical Statistics, 36(1), 131-138. https://doi.org/10.1214/aoms/1177700277.Guidoum, A. C. (2020). Kernel estimator and bandwidth selection for density and its derivatives: the kedd package. arxiv, article 2012.06102v1. https://doi.org/10.48550/arXiv.2012.06102.Gupta, S. C. & Kapoor, V. K. (2020). Descriptive measures. In Fundamentals of mathematical statistics, twelfth edition (section 2, pp. 1-78). New Delhi: Sultan Chand & Sons.Henderson, D. J., Papadopoulos, A. & Parmeter, C. F. (2023). Bandwidth selection for kernel density estimation of fat-tailed and skewed distributions. Journal of Statistical Computation and Simulation, article 2173194, 1-26. https://doi.org/10.1080/00949655.2023.2173194 Khan, A. A., Cheema, S. A., Hussain, Z. & Abdel-Salam, G. A. (2021). Measuring skewness: We do not assume much. Scientia Iranica, 28(6), 3525-3537. https://doi.org/10.24200/SCI.2020.52306.2649.Lane, D. M. (2015). Histograms. En Online statistics education: a multimedia course of study. https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Lane)/02%3A_Graphing_Distributions/2.04%3A_Histograms.Mokhtar, S. F., Yusof, Z. M. & Sapiri, H. (2023). Confidence intervals by bootstrapping approach: a significance review. Malaysian Journal of Fundamental and Applied Sciences, 19(1), 30-42. https://doi.org/10.11113/mjfas.v19n1.2660.Moral, J. (2022). Una medida de asimetría unidimensional para variables cualitativas. Revista de Psicología (PUCP), 40(1), 519-551. https://dx.doi.org/10.18800/psico.202201.017.Moral, J. (2023). Standardized distance from the mean to the median as a measure of skewness. Open Journal of Statistics, 13, 359-378. https://dx.doi.org/10.4236/ojs.2023.133018.Pakgohar, A. & Mehrannia, H. (2023). Statistical rules in scientific reports (the basics). Iranian Journal of Diabetes and Obesity, 15, article 12205. https://doi.org/10.18502/ijdo.v15i1.12205.Parzen, E. (1962). On estimation of a probability density function and mode. Annals of Mathematical Statistics, 33(3), 1065-1076. https://doi.org/10.1214/aoms/1177704472.Pearson, K. (1894). Contributions to the mathematical theory of evolution. I. On the dissection of asymmetrical frequency curves. Philosophical Transactions of the Royal Society of London A, 185, 71-110. https://doi.org/10.1098/rsta.1894.0003.Poncet, P. (2022). Package ‘modeest’. Mode estimation. https://cran.r-project.org/web/packages/modeest/modeest.pdf.Ruzankin, P. S. (2022). A class of nonparametric mode estimators. Communications in Statistics - Simulation and Computation, 51(6), 3291-3304. https://doi.org/10.1080/03610918.2019.1711410.Sarka, D. (2021). Descriptive statistics. In: Advanced Analytics with Transact-SQL (pp. 3-29). Berkeley, CA: Apress. https://doi.org/10.1007/978-1-4842-7173-5_1.Scott, D. W. (1979). On optimal and data-based histograms. Biometrika, 66(3), 605-610. https://doi.org/10.1093/biomet/66.3.605.Sheather, S. J. & Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological), 53(3), 683-690. https://doi.org/10.1111/j.2517-6161.1991.tb01857.x.Shi, J., Luo, D., Wan, X., Liu, Y., Liu, J., Bian, Z. & Tong, T. (2020). Detecting the skewness of data from the sample size and the five-number summary. arXiv, article 2010.05749. https://doi.org/10.48550/arXiv.2010.05749.Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall.info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.http://creativecommons.org/licenses/by-nc-sa/4.0https://revistas.usb.edu.co/index.php/Psychologia/article/view/6542Simetríaestimación de la modabootstrapinferencia estadísticaDos medidas de asimetría basadas en la moda: cálculo y normas interpretativasTwo measures of skewness based on mode: calculation and interpretative rulesArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Textinfo:eu-repo/semantics/articleJournal articleinfo:eu-repo/semantics/publishedVersionPublicationOREORE.xmltext/xml2537https://bibliotecadigital.usb.edu.co/bitstreams/a1fb293a-0852-4d6d-95f1-2ccd6c6d241c/download5428c8c068d07ce5cc6837f701f19ef5MD5110819/29335oai:bibliotecadigital.usb.edu.co:10819/293352025-08-25 16:59:48.764http://creativecommons.org/licenses/by-nc-sa/4.0https://bibliotecadigital.usb.edu.coRepositorio Institucional Universidad de San Buenaventura Colombiabdigital@metabiblioteca.com

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