Repeated Measures ANOVA with Huynh and Feldt Epsilon Correction

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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 ith of n_j observations in the jth 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 jth 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.[1]


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

See also

References

  1. Huynh, H., & Feldt, L.S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomised block and split-plot designs. Journal of Educational Statistics, 1, 69-82.
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