title: A NewFApproximation for the Pillai-Bartlett Trace underH0.
abstract: Pillai suggested two approximations for the Pillai-Bartlett trace statistic in the null case. The first one matches one moment of a β1random variable, and corresponds to anFrandom variable, and the second matches four moments in the Pearson system. Although intuitively appealing and widely used in current statistical packages, the first lacks accuracy even with moderate sample size. The second matches two moment ratios in the Pearson system and provides much greater accuracy. Two new approximations match two moments of a β1random variable, and hence correspond to anFrandom variable, yet achieve most of the accuracy of Pillai's second approximation. The second of the two new approximations provides the best combination of logical properties and numerical accuracy.
authors.affiliation: Department of Biostatistics CB #7400, University of North Carolina, Chapel Hill, NC 27599-7400 ( Keith_Muller@UNC.EDU ).
authors.forename: Keith E
authors.initials: KE
authors.lastname: Muller
keywords: Multivariate linear models; Repeated measures
references.citation: J Am Stat Assoc. 1992 Dec 1;87(420):1209-1226
references.pmid: 24790282