Limitations of the rank transform procedure: A study of repeated measures designs, part I

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Abstract

The applicability of the rank transform procedure to two-way repeated measures designs with equicorrelated errors is examined. All of the common testing problems with these models are examined. It is demonstrated that, with the exception of one testing problem, the rank transform procedure is not generally applicable. This complements the findings in Akritas (1990) for models with independent errors. The one valid rank transform statistic presented here does have the interesting feature that it allows the covariance of the equicorrelated errors to depend on the column treatment. This is due to the robustness of the corresponding F statistic to this kind of departure from the assumption of a common covariance matrix. It is shown, however, that the efficacy of this rank transform procedure has the undesirable property of depending on the model parameters.

Original languageEnglish (US)
Pages (from-to)457-460
Number of pages4
JournalJournal of the American Statistical Association
Volume86
Issue number414
DOIs
StatePublished - Jan 1 1991

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Repeated Measures Design
Transform
F-statistics
Testing
Exception
Covariance matrix
Statistic
Efficacy
Complement
Model
Valid
Robustness
Repeated measures
Statistics

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "The applicability of the rank transform procedure to two-way repeated measures designs with equicorrelated errors is examined. All of the common testing problems with these models are examined. It is demonstrated that, with the exception of one testing problem, the rank transform procedure is not generally applicable. This complements the findings in Akritas (1990) for models with independent errors. The one valid rank transform statistic presented here does have the interesting feature that it allows the covariance of the equicorrelated errors to depend on the column treatment. This is due to the robustness of the corresponding F statistic to this kind of departure from the assumption of a common covariance matrix. It is shown, however, that the efficacy of this rank transform procedure has the undesirable property of depending on the model parameters.",
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AB - The applicability of the rank transform procedure to two-way repeated measures designs with equicorrelated errors is examined. All of the common testing problems with these models are examined. It is demonstrated that, with the exception of one testing problem, the rank transform procedure is not generally applicable. This complements the findings in Akritas (1990) for models with independent errors. The one valid rank transform statistic presented here does have the interesting feature that it allows the covariance of the equicorrelated errors to depend on the column treatment. This is due to the robustness of the corresponding F statistic to this kind of departure from the assumption of a common covariance matrix. It is shown, however, that the efficacy of this rank transform procedure has the undesirable property of depending on the model parameters.

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