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Activity Number:
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320
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Type:
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Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #303950 |
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Title:
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Greenhouse-Geisser Adjustment and the ANOVA-Type Statistic: Distant Cousins or Twins?
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Author(s):
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Arne C. Bathke*+ and Oliver Schabenberger and Randall Tobias and Laurence V. Madden
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Companies:
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University of Kentucky and SAS Institute Inc. and SAS Institute Inc. and The Ohio State University
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Address:
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Department of Statistics, Lexington, KY, 40506-0027,
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Keywords:
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analysis of variance ; repeated measures ; dependent data
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Abstract:
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Geisser and Greenhouse (1959) described a method for repeated measures ANOVA that has become an important part of statistical tradition. Their method is based on Box's (1954) epsilon adjustment. In separate work on deriving small sample approximations for linear rank statistics in factorial designs, Brunner et al. (1997, 1999) proposed an F approximation with estimated degrees of freedom that is also motivated by Box's approximation. We show that these two descendent lines of research, while apparently divergent, actually converge for important special cases. This convergence indicates close theoretical and practical relationships between ANOVA-type statistic and Greenhouse-Geisser F adjustment. As a useful consequence, software implementations of the latter can be used to calculate the former. Furthermore, improvements in each area may be useful in the other.
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