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2004 | 24 | 2 | 183-195
Tytuł artykułu

Some inferential questions in regard to analysing two-way Layouts and associated linear model theory and practice

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
24
Numer
2
Strony
183-195
Opis fizyczny
Daty
wydano
2004
otrzymano
2003-12-17
poprawiono
2004-06-28
Twórcy
  • Mathematics and Statistics, Division of Science and Engineering, Murdoch University, Murdoch, W.A., 6150, Australia
  • Department of Health, Government of Western Australia, W.A. 6004, Australia
Bibliografia
  • [1] B.R. Clarke, An adaptive method of estimation and outlier detection in regression applicable for small to moderate sample sizes, Discussiones Mathematicae Probability and Statistics 20 (2000), 25-50.
  • [2] B.R. Clarke, A representation of orthogonal components in analysis of variance, International Mathematical Journal 1 (2002), 133-147.
  • [3] B.R. Clarke and E.J. Godolphin, Uncorrelated residuals and an exact test for two variance components in experimental design, Communications in Statistics, Part A - Theory and Methods 21 (1992), 2501-2526.
  • [4] C. Daniel, Applications of Statistics to Industrial Experimentation, Wiley, New York 1976.
  • [5] R.A. Fisher, Design of Experiments, 5th ed., Oliver and Boyd, Edinburgh 1949.
  • [6] P.J. Huber, Robust Statistical Procedures, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia 1996.
  • [7] S. Puntanen and G.P.H. Styan, The equality of the ordinary least squares estimator and the best linear unbiased estimator, (with discussion) The American Statistician 43 (1989), 153-164.
  • [8] T.S. Russell and R.A. Bradley, One-way variances in a two-way classification, Biometrika 45 (1958), 111-129.
  • [9] H. Scheffé, The Analysis of Variance, Wiley, New York 1959.
  • [10] G.K. Shukla, An invariant test for the homogeneity of variances in a two-way classification, Biometrics 28 (1972), 1063-1072.
  • [11] G.K. Shukla, Testing the homogeneity of variances in a two-way classification, Biometrika 69 (1982), 411-416.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1052
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