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Chi-Squared Test of Independence

The $\chi^2$ statistics measures the lack of independence between $f$ and $y$ and can be compared to $\chi^2$ with one degree of freedom

it's zero when $f$ and $y$ are independent

$\chi^2$ measures how the results of an observation differs from the result expected according to the null hypothesis

- lower values indicate less dependency
- so for $\chi^2$ we want to take biggest values