Skewness and Kurtosis in Real Data Samples

Blanca, María J.; Arnau, Jaume; López‐Montiel, Dolores; Bono, Roser; Bendayan, Rebecca

doi:10.1027/1614-2241/a000057

Cited by 332 publications

(228 citation statements)

References 72 publications

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“…The other two distributions analyzed had a fixed skewness, γ 1 = 0.8, and two values of kurtosis, γ 2 = 2.4 and γ 2 = 5.4. These values are well within the ranges of skewness and kurtosis that are observed in real-world settings (Blanca et al, 2013;Lei & Lomax, 2005), and they are also the values used in the study by Arnau et al (2012).…”

Section: Study Variablessupporting

confidence: 72%

“…Among the strongly biased distributions, a number of simulation studies have analyzed the log-normal distribution Keselman, Kowalchuk, & Boik, 2000;and Kowalchuk et al, 2004, among others). The distributions used in the present study had positive values of skewness and kurtosis, given that such values are used in simulation studies and are also the most common found in distributions of psychological variables (Blanca et al, 2013). Regarding the degree of contamination, the extreme values chosen were γ 1 = 1.75 and γ 2 = 5.9, which correspond to the log-normal distribution, one of the most widely studied.…”

Section: Study Variablesmentioning

confidence: 99%

“…By means of simulation it is possible to generate not only normally distributed data but also data that reflect what is commonly found in real-world settings (Blanca, Arnau, López-Montiel, Bono, & Bendayan, 2013;Micceri, 1989). Thus, various Monte Carlo simulation studies have analyzed the fixed effects associated with time (repeated measures variable) using normally or nonnormally distributed data (Arnau, Bono, Blanca, & Bendayan, 2012;Arnau, Bono, & Vallejo, 2009;Kowalchuk, Keselman, Algina, & Wolfinger, 2004;Vallejo & Ato, 2006, among others).…”

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confidence: 99%

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Sphericity estimation bias for repeated measures designs in simulation studies

et al. 2015

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In this study, we explored the accuracy of sphericity estimation and analyzed how the sphericity of covariance matrices may be affected when the latter are derived from simulated data. We analyzed the consequences that normal and nonnormal data generated from an unstructured population covariance matrix-with low (ε = .57) and high (ε = .75) sphericity-can have on the sphericity of the matrix that is fitted to these data. To this end, data were generated for four types of distributions (normal, slightly skewed, moderately skewed, and severely skewed or log-normal), four sample sizes (very small, small, medium, and large), and four values of the within-subjects factor (K = 4, 6, 8, and 10). Normal data were generated using the Cholesky decomposition of the correlation matrix, whereas the Vale-Maurelli method was used to generate nonnormal data. The results indicate the extent to which sphericity is altered by recalculating the covariance matrix on the basis of simulated data. We concluded that bias is greater with spherical covariance matrices, nonnormal distributions, and small sample sizes, and that it increases in line with the value of K. An interaction was also observed between sample size and K: With very small samples, the observed bias was greater as the value of K increased.

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Section: Study Variablessupporting

confidence: 72%

Section: Study Variablesmentioning

confidence: 99%

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confidence: 99%

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Sphericity estimation bias for repeated measures designs in simulation studies

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“…ANOVA) require that the assumption of normality be fulfilled, in other words, the dependent variable must be distributed according to the normal curve. However, the variables encountered in the field of health and social sciences often do not follow a normal distribution (Blanca, Arnau, Bono, López-Montiel & Bendayan, 2013;Limpert, Stahel & Abbt, 2001;Micceri, 1989). Examples of such variables in the health sciences are survival times for certain types of cancer (Claret et al, 2009;Qazi, DuMez & Uckun, 2007) or the age at onset of Alzheimer's disease (Horner, 1987), while in the social sciences it is the case of variables such as social support (Matud, Carballeira, Lopez, Marrero & Ibáñez, 2002), physical and verbal aggression in couple relationships (Soler, Vinyak & Quadagno, 2000), certain psychosocial aspects of addictions (Deluchi & Bostrom, 2004), post-traumatic stress (Sullivan & Holt, 2008), reaction times or response latency (ShangWen & Ming-Hua, 2010;Ulrich & Miller, 1993; Van der Linden, 2006), certain attentional skills (Brown, Weatherholt & Burns, 2010) and variables of a psychophysiological nature (Keselman, Wilcox & Lix, 2003).…”

Section: Introductionmentioning

confidence: 99%

“…The criteria used to evaluate this include how long the process takes (Afflerbach, 1990), its replicability (Ripley, 1990) and the degree to which the generated distribution fits the theoretical model (Bang, Shumacker & Schlieve, 1998), with this latter criterion being of particular interest for determining the accuracy of the procedure. In this context, it is especially important to evaluate the suitability of data generators for generating non-normal distributions, both known and unknown (Demirtas, 2007), as these types of distributions are commonly encountered in real data (Blanca et al, 2013;Limpert et al, 2001;Micceri, 1989).…”

Section: Introductionmentioning

confidence: 99%

Comparación de los procedimientos de Fleishman y Ramberg et al. para generar datos no normales en estudios de simulación

et al. 2014

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Título: Comparación de los procedimientos de Fleishman y Ramberg et al. para generar datos no normales en estudios de simulación. Resumen: Las técnicas de simulación deben posibilitar la generación adecuada de las distribuciones más frecuentes en la realidad como son las distribuciones no normales. Entre los procedimientos para la generación de datos no normales destacan el método de transformaciones lineales propuesto por Fleishman y el método basado en la generalización de la distribución lambda de Tukey propuesto por Ramberg et al. Este estudio compara los procedimientos en función del ajuste de las distribuciones generadas a sus respectivos modelos teóricos y del número de simulaciones necesarias para dicho ajuste. Con este objetivo se seleccionan, junto con la distribución normal, una serie de distribuciones no normales frecuentes en datos reales, y se analiza el ajuste según el grado de violación de la normalidad y del número de simulaciones realizadas. Los resultados muestran que ambos procedimientos de generación de datos tienen un comportamiento similar. A medida que aumenta el grado de contaminación de la distribución teórica hay que aumentar el número de simulaciones a realizar para asegurar un mayor ajuste a la generada. Los dos procedimientos son más precisos para generar distribuciones normales y no normales a partir de 7000 simulaciones aunque cuando el grado de contaminación es severo (con valores de asimetría y curtosis de 2 y 6, respectivamente), se recomienda aumentar el número de simulaciones a 15000. Palabras clave: Simulación; Monte Carlo; generadores de datos; datos no normales; número de simulaciones.Abstract: Simulation techniques must be able to generate the types of distributions most commonly encountered in real data, for example, nonnormal distributions. Two recognized procedures for generating nonnormal data are Fleishman's linear transformation method and the method proposed by Ramberg et al. that is based on generalization of the Tukey lambda distribution. This study compares these procedures in terms of the extent to which the distributions they generate fit their respective theoretical models, and it also examines the number of simulations needed to achieve this fit. To this end, the paper considers, in addition to the normal distribution, a series of non-normal distributions that are commonly found in real data, and then analyses fit according to the extent to which normality is violated and the number of simulations performed. The results show that the two data generation procedures behave similarly. As the degree of contamination of the theoretical distribution increases, so does the number of simulations required to ensure a good fit to the generated data. The two procedures generate more accurate normal and non-normal distributions when at least 7000 simulations are performed, although when the degree of contamination is severe (with values of skewness and kurtosis of 2 and 6, respectively) it is advisable to perform 15000 simulations.

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Within‐Case Designs: Distribution‐Free Methods

Lix¹

2018

Wiley StatsRef: Statistics Reference Online

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In within‐case designs, individuals are measured repeatedly over time or across multiple experimental conditions. Univariate and multivariate parametric procedures for testing within‐case effects may lose statistical power under departures from a multivariate normal distribution. Nonparametric procedures based on rank scores or bootstrapping are useful alternatives for testing within‐case effects when the data are skewed or have heavy tails. We consider these methods when there are missing observations and for complex designs.

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Skewness and Kurtosis in Real Data Samples

Cited by 332 publications

References 72 publications

Sphericity estimation bias for repeated measures designs in simulation studies

Sphericity estimation bias for repeated measures designs in simulation studies

Comparación de los procedimientos de Fleishman y Ramberg et al. para generar datos no normales en estudios de simulación

Within‐Case Designs: Distribution‐Free Methods

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