Repeated Measures ANOVA with Greenhouse & Geisser Epsilon Correction

The test statistics is:

$F=\frac{\sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij}(\bar{x}_j - \bar{x})^2 / (j-1)} {\sum^s_{j=1} \sum^{n_j}_{i=1} w_{ij}(\bar{x}_j - x_{ij})^2 / ((\sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij}-1) (j - 1))}$

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 $\sum^s_{j=1} x_{ij} = 0\forall i$,

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

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

$w_{ij}$ is the calibrated weight,

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

$\epsilon$ is computed using the Greenhouse-Geisser method.

See also

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