Category:Examples of Chi-Squared Test for Goodness of Fit

This category contains examples of Chi-Squared Test for Goodness of Fit.

The chi-squared test for goodness of fit is a test of goodness of fit of observations to some theoretical probability distribution.

Let $n \in \Z_{>0}$.

Let a value $x_i$ for $i \in \set {1, 2, \ldots, n}$ be expected to occur $E_i$ times.

Let $x_i$ actually occur $O_i$ times.

Then the statistic:

$\ds \chi^2 = \sum_i \dfrac {\paren {O_i - E_i}^2} {E_i}$

has a $\chi$-squared distribution with $n - p$ degrees of freedom where $p$ is the number of distribution parameters estimated from the data and used to compute the $E_i$.

Significantly high values of $\chi^2$ lead to the rejection of the hypothesised distribution.