The SPP Procedure

Quadrat Count Test for CSR

The quadrat test is a test of complete spatial randomness (CSR) that uses the $\chi ^{2}$ statistic based on quadrat counts. In the quadrat test, the study area window W is divided into subregions called quadrats ( $W_1$ , $W_2$ ,.... $W_ m$ ) of equal area. The test counts the number of points that fall in each quadrat $n_ j = n(X\cap W_ j)$ for $j=1,...,m$ . Under the null hypothesis of CSR, the $n_ j$ are iid Poisson random variables. The following Pearson $\chi ^{2}$ test statistic assesses whether there is a departure from the homogeneous poisson process:

$\chi ^{2} = \frac{\sum _ j(n_ j - n/m)}{n/m}$

A significant p-value indicates that the underlying point pattern is not CSR.