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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.
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
0167-9473
393-401
Hayter, A.J.
d09cb9d1-c4ca-45fb-b8e3-e63c08f1bd4f
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, A.J.
d09cb9d1-c4ca-45fb-b8e3-e63c08f1bd4f
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 & Data Analysis, 30 (4), 393-401. (doi:10.1016/S0167-9473(99)00005-5).

Record type: Article

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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More information

Published date: 1999
Keywords: analysis of variance, order restricted inference, simultaneous confidence intervals, umbrella ordering
Organisations: Statistics, Mathematical Sciences

Identifiers

Local EPrints ID: 30095
URI: http://eprints.soton.ac.uk/id/eprint/30095
ISSN: 0167-9473
PURE UUID: 13af207f-73f3-4230-9c22-73d39672015b
ORCID for W. Liu: ORCID iD orcid.org/0000-0002-4719-0345

Catalogue record

Date deposited: 14 Mar 2007
Last modified: 20 Jul 2019 01:23

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