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A New Interpretation of the F Statistic

John W. Pratt and Robert Schlaifer
The American Statistician
Vol. 52, No. 2 (May, 1998), pp. 141-143
DOI: 10.2307/2685472
Stable URL: http://www.jstor.org/stable/2685472
Page Count: 3
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A New Interpretation of the F Statistic
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Abstract

A new interpretation of the F statistics appearing in the ANOVA of a balanced fixed-effect model permits them to be used, not only to test null hypotheses which assert that certain effects or contrasts of effects are zero, but also to help one decide whether relations or patterns observed in estimates of three or more effects can be reasonably assumed to hold for the effects themselves. And whether or not a design is balanced, the underlying mathematical arguments hold and yield formulas for near-optimal uniform shrinkage of estimates.

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