A new test against an umbrella alternative and the associated simultaneous confidence intervals.
A new test against an umbrella alternative and the associated simultaneous confidence intervals.
For the usual balanced one-way fixed effects analysis of variance (ANOVA) model, a new test of the null hypothesis H[0]: ?[1] = … = ?[k] against the umbrella alternative H[h]: ?[1] ? …? ?[h] ? …? ?[k] with at least one strict inequality is proposed. More usefully, this new test can be easily inverted to produce a set of one-sided simultaneous confidence intervals (SCIs) for all the ordered pairwise differences ?[j]-? for 1 ? i < j ? h and h ? j < i ? k, and therefore enables the experimenter to infer which ?[j]'s are different when H[0] is rejected. A table of critical values is provided to allow immediate and simple implementation of this new inference procedure.
analysis of variance, order restricted inference, simultaneous confidence intervals, umbrella ordering
393-401
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
1999
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, A.J. and Liu, W.
(1999)
A new test against an umbrella alternative and the associated simultaneous confidence intervals.
Computational Statistics and Data Analysis, 30 (4), .
(doi:10.1016/S0167-9473(99)00005-5).
Abstract
For the usual balanced one-way fixed effects analysis of variance (ANOVA) model, a new test of the null hypothesis H[0]: ?[1] = … = ?[k] against the umbrella alternative H[h]: ?[1] ? …? ?[h] ? …? ?[k] with at least one strict inequality is proposed. More usefully, this new test can be easily inverted to produce a set of one-sided simultaneous confidence intervals (SCIs) for all the ordered pairwise differences ?[j]-? for 1 ? i < j ? h and h ? j < i ? k, and therefore enables the experimenter to infer which ?[j]'s are different when H[0] is rejected. A table of critical values is provided to allow immediate and simple implementation of this new inference procedure.
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Published date: 1999
Keywords:
analysis of variance, order restricted inference, simultaneous confidence intervals, umbrella ordering
Organisations:
Statistics, Mathematical Sciences
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Local EPrints ID: 30095
URI: http://eprints.soton.ac.uk/id/eprint/30095
ISSN: 0167-9473
PURE UUID: 13af207f-73f3-4230-9c22-73d39672015b
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Date deposited: 14 Mar 2007
Last modified: 16 Mar 2024 02:42
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Author:
A.J. Hayter
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