Variability of Statistics in Generalizability Theory

  • Robert L. Brennan
Part of the Statistics for Social Sciences and Public Policy book series (SSBS)


Estimates of variance components, error variances, generalizability coefficients, and so on, like all statistics, are subject to sampling variability. Traditionally, such variability is quantified through estimated standard errors and/or confidence intervals. Cronbach et al. (1972) recognized the importance of this topic for generalizability analyses and gave it more than passing attention, although at that time statistical methodologies for addressing the topic were limited. Subsequently, in the generalizability theory literature, Smith (1978, 1982) considered standard errors of estimated variance components, Brennan (1992a) summarized some procedures for establishing standard errors and confidence intervals, Brennan et al. (1987) considered bootstrap and jackknife procedures, Betebenner (1998) examined a relatively new procedure for establishing confidence intervals, Wiley (2000) studied the bootstrap, and Gao and Brennan (2001) provided examples from the performance assessment literature.


Variance Component Bootstrap Procedure Multivariate Normal Distribution Notational Convention Estimate Variance Component 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Robert L. Brennan
    • 1
  1. 1.Iowa Testing ProgramsUniversity of IowaIowa CityUSA

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