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education/statistics/Hypothesis Tests.md
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@ -70,6 +70,8 @@ Reliable investigators test their conclusions on an independent batch of data
## Goodness of fit tests ($\chi ^2$)
This test is used when you have one qualitative variable with many categories, eg the (color, size, shape) of an (item).
$$ \chi ^2 = sum(\frac{(obs_{freq} - exp_{freq})^2}{exp_{freq}}) $$
The $\chi^2$ curve does not follow the normal curve. It has a long right hand tail. As the degrees of freedom go up, the curves flatten out, and the hump moves out to the right.
$$ df = num_{terms} - 1 $$