Is there any alternative (like Cohen's d in t-test) to report about effect sizes for post-hoc paired comparisons in a one-way ANOVA (3 factor levels, correlated samples)?.

Many thanks!!

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#### Best Answer

You can test a contrast, which gives you a $t$-ratio:

$t=displaystylefrac{hat{Psi}_j}{hat{sigma}_psi} = frac{displaystylesum_{j=1}^{p}c_jbar{Y}_j}{sqrt{MS_{error}displaystylesum_{j=1}^{p}frac{c^2_j}{} }}$,

where $p$ is the number of levels in your categorical variable and $c_j$ is the contract weight for the $j^{th}$ level. Then convert the $t$ to $Cohen's;d$.

Alternatively, you can test a contrast $bar{Y}_{Max} – bar{Y}_{Min}$ and compute $d_{Max}$.