Geodesic
Calculation of power measures of Grabbs' criterion for checking for one outlier
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 141-154

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We obtain recurrences for calculating five measures of the David power of Grabbs' criterion in the case that a normally distributed sample contains an outlier. We show that the power measures are functions of the parameters of the outlier, the sample volume, and the critical values of the Grabbs statistics. We proved that all power measures, except for the fourth, are nonincreasing functions of the critical values of the Grabbs statistics, while the fourth power measure always has a local maximum. Using our formulas we ran model simulations of the power measures in the case of a normally distributed sample of 20 observations including one outlier. The results of the simulations turn out close to those expected theoretically. 
@article{SJIM_2010_13_4_a12,
     author = {L. K. Shiryaeva},
     title = {Calculation of power measures of {Grabbs'} criterion for checking for one outlier},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {141--154},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a12/}
}
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L. K. Shiryaeva. Calculation of power measures of Grabbs' criterion for checking for one outlier. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 141-154. http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a12/