Skewness and Kurtosis in real data samples

Parametric statistics are based on the assumption of normality. Recent findings suggest that Type I error and power can be adversely affected when data are non-normal. This paper aims to assess the distributional shape of real data by examining the values of the third and fourth central moments as a...

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Autores: Blanca Mena, M. José, Arnau Gras, Jaume, López Montiel, Dolores, Bono Cabré, Roser, Bendayan, Rebecca
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2013
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/153945
Acceso en línea:https://hdl.handle.net/2445/153945
Access Level:acceso abierto
Palabra clave:Estadística
Distribució (Teoria de la probabilitat)
Statistics
Distribution (Probability theory)
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spelling Skewness and Kurtosis in real data samplesBlanca Mena, M. JoséArnau Gras, JaumeLópez Montiel, DoloresBono Cabré, RoserBendayan, RebeccaEstadísticaDistribució (Teoria de la probabilitat)StatisticsDistribution (Probability theory)Parametric statistics are based on the assumption of normality. Recent findings suggest that Type I error and power can be adversely affected when data are non-normal. This paper aims to assess the distributional shape of real data by examining the values of the third and fourth central moments as a measurement of skewness and kurtosis in small samples. The analysis concerned 693 distributions with a sample size ranging from 10 to 30. Measures of cognitive ability and of other psychological variables were included. The results showed that skewness ranged between −2.49 and 2.33. The values of kurtosis ranged between −1.92 and 7.41. Considering skewness and kurtosis together the results indicated that only 5.5% of distributions were close to expected values under normality. Although extreme contamination does not seem to be very frequent, the findings are consistent with previous research suggesting that normality is not the rule with real data.European Association of Methodology2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/153945Articles publicats en revistes (Psicologia Social i Psicologia Quantitativa)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1027/1614-2241/a000057Methodology. European Journal of Research Methods tor the Behavioral and Social Sciences, 2013, num. 9, p. 78-84https://doi.org/10.1027/1614-2241/a000057(c) Hogrefe, 2013info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1539452026-05-27T06:46:51Z
dc.title.none.fl_str_mv Skewness and Kurtosis in real data samples
title Skewness and Kurtosis in real data samples
spellingShingle Skewness and Kurtosis in real data samples
Blanca Mena, M. José
Estadística
Distribució (Teoria de la probabilitat)
Statistics
Distribution (Probability theory)
title_short Skewness and Kurtosis in real data samples
title_full Skewness and Kurtosis in real data samples
title_fullStr Skewness and Kurtosis in real data samples
title_full_unstemmed Skewness and Kurtosis in real data samples
title_sort Skewness and Kurtosis in real data samples
dc.creator.none.fl_str_mv Blanca Mena, M. José
Arnau Gras, Jaume
López Montiel, Dolores
Bono Cabré, Roser
Bendayan, Rebecca
author Blanca Mena, M. José
author_facet Blanca Mena, M. José
Arnau Gras, Jaume
López Montiel, Dolores
Bono Cabré, Roser
Bendayan, Rebecca
author_role author
author2 Arnau Gras, Jaume
López Montiel, Dolores
Bono Cabré, Roser
Bendayan, Rebecca
author2_role author
author
author
author
dc.subject.none.fl_str_mv Estadística
Distribució (Teoria de la probabilitat)
Statistics
Distribution (Probability theory)
topic Estadística
Distribució (Teoria de la probabilitat)
Statistics
Distribution (Probability theory)
description Parametric statistics are based on the assumption of normality. Recent findings suggest that Type I error and power can be adversely affected when data are non-normal. This paper aims to assess the distributional shape of real data by examining the values of the third and fourth central moments as a measurement of skewness and kurtosis in small samples. The analysis concerned 693 distributions with a sample size ranging from 10 to 30. Measures of cognitive ability and of other psychological variables were included. The results showed that skewness ranged between −2.49 and 2.33. The values of kurtosis ranged between −1.92 and 7.41. Considering skewness and kurtosis together the results indicated that only 5.5% of distributions were close to expected values under normality. Although extreme contamination does not seem to be very frequent, the findings are consistent with previous research suggesting that normality is not the rule with real data.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/153945
url https://hdl.handle.net/2445/153945
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1027/1614-2241/a000057
Methodology. European Journal of Research Methods tor the Behavioral and Social Sciences, 2013, num. 9, p. 78-84
https://doi.org/10.1027/1614-2241/a000057
dc.rights.none.fl_str_mv (c) Hogrefe, 2013
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Hogrefe, 2013
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv European Association of Methodology
publisher.none.fl_str_mv European Association of Methodology
dc.source.none.fl_str_mv Articles publicats en revistes (Psicologia Social i Psicologia Quantitativa)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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