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Title: Sphericity estimation bias for repeated measures designs in simulation studies
Author: Bono Cabré, Roser
Arnau Gras, Jaume
Blanca Mena, M. José
Alarcón Postigo, Rafael
Keywords: Anàlisi de variància
Mètode de Montecarlo
Analysis of variance
Monte Carlo method
Issue Date: 2016
Publisher: Springer Verlag
Abstract: 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.
Note: Versió postprint del document publicat a:
It is part of: Behavior Research Methods, 2016, vol. 48, num. 4, p. 1621-1630
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ISSN: 1554-351X
Appears in Collections:Articles publicats en revistes (Psicologia Social i Psicologia Quantitativa)

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