Discussiones Mathematicae Probability and Statistics 24(2) (2004) 183-195

SOME INFERENTIAL QUESTIONS IN REGARD TO ANALYSING TWO-WAY LAYOUTS AND ASSOCIATED LINEAR MODEL THEORY AND PRACTICE

Brenton R. Clarke

Mathematics and Statistics
Division of Science and Engineering
Murdoch University, Murdoch, W.A., 6150, Australia

Antony G. Monaco

Department of Health, Government of Western Australia
W.A. 6004, Australia

Abstract

In analysing a well known data set from the literature which can be thought of as a two-way layout it transpires that a robust adaptive regression approach for identifying outliers fails to be sensitive enough to detect the possible interchange of two observations. On the other hand if one takes the classical approach of diagnostic checking one may also stop too early and be satisfied with a model that falls short of a more detailed analysis that takes account of heteroscedasticity in the data. An exact F-test for heteroscedasticity in the two way layout is compared with various more general tests proposed by Shukla. In conclusion it is noted that when modelling the particular form of heteroscedasticity countenanced here, the estimated column effects are unchanged from those estimated from the model assuming homogeneous error variance structure. It is only the estimated variances of these column effects that changes.

Keywords: outlier; two-way layout; adaptive estimation; heteroscedaticity.

2000 Mathematics Subject Classification: 62J10, 2F05.

References

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Received 17 December 2003
Revised 28 June 2004