A New Interpretation of the F Statistic

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.

Key Words:

• ANOVA
• Average variance
• Linear hypotheses
• Mean squared effect
• Shrinkage estimation