Test statistic

The test statistic is defined as:

$$X^2 = \sum_{i = 1}^{m}\frac{(n_{i,obs} - n_{i,exp})^2}{n_{i,exp}}$$

It follows a Chi-square distribution under the null hypothesis, i.e. under CSR.

$$X_{CSR}^2 \sim \chi_{m-1}^2$$