A simulation study comparing two approximations for a quasi t-quantile, used in repeated measures ANOVA

Area of Science:

• Statistics
• Statistical Methods

Background:

• In analysis of variance, denominators for t-statistics often use linear combinations of mean squares.
• This occurs in problems like Behrens-Fisher and repeated measures ANOVA.

Purpose of the Study:

• To compare the bias of Satterthwaite's approximation and Cochran's approximation for determining degrees of freedom.
• To provide guidance on choosing between these two approximation methods.

Main Methods:

• Computer simulations were used to evaluate the bias of both approximations.
• The magnitude of bias for Satterthwaite's and Cochran's approximations was compared across various scenarios.

Main Results:

• Satterthwaite's approximation exhibited less bias than Cochran's approximation in 68 out of 75 simulated cases.
• When Cochran's approximation had less bias, Satterthwaite's estimated bias was minimal (≤0.5%).

Conclusions:

• Satterthwaite's approximation is generally less biased for combining mean squares.
• Performing Satterthwaite's calculations is recommended, particularly when one mean square has ≤12 degrees of freedom.