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Educational and Psychological Measurement
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A Comparison of the Bootstrap-F, Improved General Approximation, and Brown-Forsythe Multivariate Approaches in a Mixed Repeated Measures Design

Guillermo Vallejo Seco

Universidad de Oviedo, gvallejo{at}correo.uniovi.es

Marcelino Cuesta Izquierdo

Universidad de Oviedo

M. Paula Fernández García

Universidad de Oviedo

F. Javier Herrero Díez

Universidad de Oviedo

The authors compare the operating characteristics of the bootstrap-F approach, a direct extension of the work of Berkovits, Hancock, and Nevitt, with Huynh’s improved general approximation (IGA) and the Brown-Forsythe (BF) multivariate approach in a mixed repeated measures design when normality and multisample sphericity assumptions do not hold. The results of the simulation show that the three approaches adequately control Type I error when data are generated from normal or slightly nonnormal distributions. However, when data are generated from distributions with moderate or severe skewness, the approaches tend to produce conservative Type I error rates, except the IGA test of the main effect, which has liberal Type I error rates in some conditions. With regard to power, it was found that the bootstrap-F approach can compete with the IGA approach but not with the BF approach: The power differences favoring the bootstrap-F approach are generally small, whereas those favoring the BF approach are substantial.

Key Words: multisample sphericity • theoretical critical values • bootstrap resampling • sensitivity

Educational and Psychological Measurement, Vol. 66, No. 1, 35-62 (2006)
DOI: 10.1177/0013164404273943
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