Repeated Measures ANOVA with Greenhouse & Geisser Epsilon Correction

The test statistics is:

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

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

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

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

$w_{ij}$ is the calibrated weight,

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

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

See also

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