Correlation Ratio

$\backslash overline\{y\}\_x=\backslash frac\{\backslash sum\_i\; y\_\{xi\}\}\{n\_x\}$ and $\backslash overline\{y\}=\backslash frac\{\backslash sum\_x\; n\_x\; \backslash overline\{y\}\_x\}\{\backslash sum\_x\; n\_x\}$

$\backslash eta^2\; =\; \backslash frac\{\backslash sum\_x\; n\_x\; (\backslash overline\{y\}\_x-\backslash overline\{y\})^2\}\{\backslash sum\_\{xi\}\; (y\_\{xi\}-\backslash overline\{y\})^2\}$

$\backslash frac\{\backslash sigma\_\{\backslash overline\{y\}\}^2\}\{\backslash sigma\_\{y\}^2\}.$

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