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Analysis of distributions in factorial experiments

Analysis of distributions in factorial experiments
Analysis of distributions in factorial experiments
The Cramer-von Mises statistic provides a useful goodness of fit test of whether a random sample has been drawn from some given null distribution. Its use in comparing several samples has also been studied, but not systematically. We show that the statistic is capable of significant generalization. In particular we consider the comparison of the distributions of observations arising from factorial experiments.
Provided that observations are replicated, we show that our generalization yields a test statistic capable of decomposition like the sum of squares used in ANOVA. The statistic is calculated using ranked data rather than original observations. We give the asymptotic theory. Unlike ANOVA, the asymptotic distributional properties of the statistic can be obtained without the assumption of normality. Further, the statistic enables differences in distribution other than the mean to be detected.
Because it is distribution free, Monte-Carlo sampling can be used to directly generate arbitrarily accurate critical test null values in online analysis irrespective of sample size. The statistic is thus easy to implement in practice. Its use is illustrated with an example based on a man-in-the-loop simulation trial where operators carried out self assessment of the workload that they experienced under different operating conditions.
cramer-von Mises statistic, distribution free, factorial experiment, homoscedasticity, rank based, simulation experiment
1017-0405
1085-1103
Cheng, R.C.H.
a4296b4e-7693-4e5f-b3d5-27b617bb9d67
Jones, O.D.
d5046a34-1cd1-4404-95be-39fa10adc806
Cheng, R.C.H.
a4296b4e-7693-4e5f-b3d5-27b617bb9d67
Jones, O.D.
d5046a34-1cd1-4404-95be-39fa10adc806

Cheng, R.C.H. and Jones, O.D. (2004) Analysis of distributions in factorial experiments. Statistica Sinica, 14 (4), 1085-1103.

Record type: Article

Abstract

The Cramer-von Mises statistic provides a useful goodness of fit test of whether a random sample has been drawn from some given null distribution. Its use in comparing several samples has also been studied, but not systematically. We show that the statistic is capable of significant generalization. In particular we consider the comparison of the distributions of observations arising from factorial experiments.
Provided that observations are replicated, we show that our generalization yields a test statistic capable of decomposition like the sum of squares used in ANOVA. The statistic is calculated using ranked data rather than original observations. We give the asymptotic theory. Unlike ANOVA, the asymptotic distributional properties of the statistic can be obtained without the assumption of normality. Further, the statistic enables differences in distribution other than the mean to be detected.
Because it is distribution free, Monte-Carlo sampling can be used to directly generate arbitrarily accurate critical test null values in online analysis irrespective of sample size. The statistic is thus easy to implement in practice. Its use is illustrated with an example based on a man-in-the-loop simulation trial where operators carried out self assessment of the workload that they experienced under different operating conditions.

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Published date: 2004
Keywords: cramer-von Mises statistic, distribution free, factorial experiment, homoscedasticity, rank based, simulation experiment
Organisations: Operational Research

Identifiers

Local EPrints ID: 29730
URI: http://eprints.soton.ac.uk/id/eprint/29730
ISSN: 1017-0405
PURE UUID: 60f0e1a7-e6de-4eb9-bca6-882a9648b91c

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Date deposited: 12 May 2006
Last modified: 15 Mar 2024 07:34

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Contributors

Author: R.C.H. Cheng
Author: O.D. Jones

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