= Variance-stabilizing transformation
{title2=$g'(\mu)\propto V(\mu)^{-1/2}$}
{wiki}
If a response has mean $\mu$ and <variance> $V(\mu)$, the <delta method> gives $\operatorname{Var}(g(Y))\approx g'(\mu)^2V(\mu)$. Choosing $g'(\mu)$ proportional to $V(\mu)^{-1/2}$ makes this first-order <variance> independent of $\mu$. For $V(\mu)=k\mu^2$ on positive means, the resulting transformation is the <natural logarithm>. This is a local approximation and requires the transformation to be defined on the observations; it does not make arbitrary normal responses positive or preserve an exact <normal distribution>.
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