A hybrid method for improved critical points for multiple comparisons
Titel:
A hybrid method for improved critical points for multiple comparisons
Auteur:
McCann, Melinda Edwards, Don
Verschenen in:
Communications in statistics
Paginering:
Jaargang 29 (2000) nr. 3 pagina's 703-722
Jaar:
2000
Inhoud:
We present new methods for computing conservative critical points for simultaneous confidence intervals and bounds in the normal-theoretic fixed effects general linear model. The methods use a representation of the joint error probability attributed to Uusipaikka (unpublished manuscript, 1984), and popularized by Naiman (Annals of Statistics, 14, 1986, 896-906). This representation expresses the joint error probability of the confidence bounds as an expectation of surface areas of unions of disks with random radii on the sphere. The representation can be used to compute critical points by most well-known conservative methods; these can be regarded as using different upper bounds for the surface area of the union of disks. Our new hybrid methods compute the critical points using the minimum of several of these existing upper bounds, as well as some new bounds, and so improve upon all such methods included in the minimum expression. The new methods are a substantial improvement over the Hunter-Worsley and Sidak methods. Over 216 test cases the sample size savings of the new methods to the Hunter-Worsley method ranged from a worst-case loss of 3% to savings as large as 65%. Compared to the Sidak method, sample size savings ranged from a worst-case loss of 2% to savings as large as 95%. Savings of 5-10% were typical against both existing methods. One of the new methods, the “capped tubes” critical point, can be computed relatively cheaply without a large sacrifice in relative efficiency.
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