Geodesic
On computable estimates for accuracy of approximation for the Bartlett--Nanda--Pillai statistic
Matematičeskie trudy, Tome 19 (2016) no. 2, pp. 109-118

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For the Bartlett-Nanda-Pillai statistic, we find computable estimates for accuracy of approximation, i.e., we describe explicitly the dependence on all parameters of the distributions that occur in the inequalities. For the other two classical statistics traditionally used in multivariate analysis of variance, i.e., the likelihood-ratio and Lawley–Hotelling statistics, similar computable estimates were found earlier. 
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     author = {A. A. Lipatev and V. V. Ulyanov},
     title = {On computable estimates for accuracy of approximation for the {Bartlett--Nanda--Pillai} statistic},
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A. A. Lipatev; V. V. Ulyanov. On computable estimates for accuracy of approximation for the Bartlett--Nanda--Pillai statistic. Matematičeskie trudy, Tome 19 (2016) no. 2, pp. 109-118. http://geodesic.mathdoc.fr/item/MT_2016_19_2_a3/