The analysis of ranked data in blocked factorial experiments.
The analysis of ranked data in blocked factorial experiments.
A non-parametric method for the analysis of blocked factorial experiments, based on ranking within blocks, is proposed and shown to be equivalent to partitioning Friedman's test statistic into a set of contrasts reflecting polynomial components of the main effects and interaction. A slightly modified version of the procedure is suggested to partially overcome the problem of loss of power to detect one component when the model includes other components. This alternative procedure is shown to be equivalent to applying a standard normal theory analysis of variance to the ranks. The null distributions and power comparisons are investigated using simulation methods, and it is shown that the non-parametric methods are almost as powerful as the analysis of variance.
analysis of variance, blocking in factorial experiments, friedman's test, orthogonal contrasts, ranking
37-54
Prescott, Philip
cf0adfdd-989b-4f15-9e60-ef85eed817b2
Shahlaee, Rahim
54494243-e229-4683-9980-ec4a2afac67b
1999
Prescott, Philip
cf0adfdd-989b-4f15-9e60-ef85eed817b2
Shahlaee, Rahim
54494243-e229-4683-9980-ec4a2afac67b
Prescott, Philip and Shahlaee, Rahim
(1999)
The analysis of ranked data in blocked factorial experiments.
Metrika, 50 (1), .
(doi:10.1007/s001840050034).
Abstract
A non-parametric method for the analysis of blocked factorial experiments, based on ranking within blocks, is proposed and shown to be equivalent to partitioning Friedman's test statistic into a set of contrasts reflecting polynomial components of the main effects and interaction. A slightly modified version of the procedure is suggested to partially overcome the problem of loss of power to detect one component when the model includes other components. This alternative procedure is shown to be equivalent to applying a standard normal theory analysis of variance to the ranks. The null distributions and power comparisons are investigated using simulation methods, and it is shown that the non-parametric methods are almost as powerful as the analysis of variance.
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Published date: 1999
Keywords:
analysis of variance, blocking in factorial experiments, friedman's test, orthogonal contrasts, ranking
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Statistics
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Local EPrints ID: 29982
URI: http://eprints.soton.ac.uk/id/eprint/29982
PURE UUID: 676dcf2e-a8fd-42f1-a78e-570e25daf01a
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Date deposited: 16 Mar 2007
Last modified: 15 Mar 2024 07:36
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Author:
Rahim Shahlaee
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