Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 3, pp. 338--350

A USEFUL STATISTIC FOR STUDYING OUTLIERS IN EXPERIMENTAL DESIGNS

By

LALMOHAN BHAR and V.K.GUPTA, *Indian Agricultural Statistics Research Institute, New Delhi*

SUMMARY. For testing outliers in the linear model (**y**, **X**(theta), (sigma)²**I**)
for experimental designs, the Cook-statistic (Cook, 1977) is appropriately modified.
Special emphasis is given to the case of a single outlier in block designs.
This newly developed statistic is applied to a data set obtained from a
randomized complete block design. A new cirterion for robustness of
experimental designs against the presence of a single outlier is proposed.
This new criterion is based on average Cook-statistic. A number of designs
for one-way elimination of heterogeneity are identified that are robust
against the presence of a single outlier.

*AMS subject classification.* 62K10.

*Key words and phrases.* Outlier, linear model, Cook-statistic,
robustness.