Repeated Measures ANOVA with Huynh and Feldt Epsilon Correction

The test statistics is:

$F=\frac{\sum _{j=1}^s\sum _{i=1}^{n_j}{w}_{ij}({\overline{x}}_j-\overline{x}{)}^2/(j-1)}{\sum _{j=1}^s\sum _{i=1}^{n_j}{w}_{ij}({\overline{x}}_j-x_{ij}{)}^2/((\sum _{j=1}^s\sum _{i=1}^{n_j}{w}_{ij}-1)(j-1))}$

where:

$x_{ij}$ is the value of the $i$th of $n_j$ observations in the $j$th of $s$ groups, where $x_{ij}$ has been 'centered' such that $\sum _{j=1}^s{x}_{ij}=0\mathrm{\forall }i$,

${\overline{x}}_j$ is the average in the $j$th group,

$\overline{x}$ is the overall average,

$w_{ij}$ is the calibrated weight,

$p\approx \mathrm{Pr}(F_{(s-1)ϵ,(\sum _{j=1}^s\sum _{i=1}^{n_j}{w}_{ij}-1)(s-1))ϵ}\ge F)$, and

$ϵ$ is computed using the Greenhouse-Geisser method.

and $F$ is evaulated using the F-distribution with $(j-1)ϵ$ and $((\sum _{j=1}^s\sum _{i=1}^{n_j}{w}_{ij}-1)(j-1))ϵ$ degrees of freedom, where $ϵ=1/(j-1)$.

See also

• ANOVA-Type Tests - Comparing Three or More Groups
• Planned ANOVA-Type Test