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I'm no expert in the bootstrap, but I anticipate that using fewer samples in your bootstrap means that the uncertainty in mean will be inflated. The standard error of the sampling distribution is inversely proportional to the square root of the sample size. A smaller sample size thus means larger uncertainty in your estimates. Its easy to see evidence of ...

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In terms of power against the overall null hypothesis in an ANOVA (all groups same), the most efficient design for $5n$ subjects in 5 groups is to have $n$ subjects per group. The most sensible departure from this balanced design that I have seen is to put slightly more subjects in the control group because, among ad hoc comparisons, the most important are ...

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I was not able to reproduce the results you got from WebPower using the pilot data you supplied. I was able to reproduce your R code however. You are correct that you can't use the $\eta^2$ for Cohen's f, but $f^2 = \frac{\eta^2}{1-\eta^2}$ "However, how should I compute the effect size from the pilot study" - use the $\eta^2$ from the pilot ...

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