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.