# What is the relationship between effect size and sample size ? - when the effect size is small large sample are needed, -when the effect size is large,large samples are needed, -regardless of effect size,large sample are generally necessary, -effect size and sample size are dependent on level power

What is the relationship between effect size and sample size ?
- when the effect size is small large sample are needed
- when the effect size is large,large samples are needed
- regardless of effect size,large sample are generally necessary
- effect size and sample size are dependent on level power
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Brooklyn Mcintyre
Put: $X=\mathrm{log}\left(\frac{\alpha }{\alpha +\beta }\right)=\mathrm{log}\left(\frac{1}{1+\frac{\beta }{\alpha }}\right)$
Then working in terms of X will ensure that the logarithm is always well defined. You then need to define another independent variable Y such that a linarization of Y in terms of small changes in $\alpha$ and $\beta$ does not become almost linearly dependent on the way the change in X depends on small changes in $\alpha$ and $\beta$. Since X depends on the ratio of $\alpha$ and $\beta$, you can choose Y to be a function of the product of $\alpha$ and $\beta$, so:
$Y=\alpha \beta$
might work well, at least you'll have elminated two potential problems with Newton-Raphson.