1.4 Sample size and autocorrelation

Determination of sample size:
The presence of SA in a dataset of length N implies that the number of independent observations is fewer than N. Essentially, the data is not random in space, and the information in each observation is not totally separate from the information in other observations. Reduction in the number of independent observations has implications for hypothesis testing. The presence of positive spatial auto-correlation indicates the presence of redundant information in data values, with this redundancy being attributable to the relative locations of the values. Sample size \cite{Dale2002,Griffith2005} is the equivalent number of independent values (the classical statistics situation). As spatial auto-correlation increases from 0 to 1, the effective sample size decreases from n to 1.
For computing “effective” sample size, for second order simultaneous autoregressive process, the “Effective” sample size is given by \cite{Griffith2003}