Independence, Stationarity, Categorical Spatial Data and the Chi-Squared Test

This paper presents a correction to the simple chi-squared test for spatial data. The paper commences with an outline of the temporal analogue before giving a proof for a deflating factor appropriate to a square lattice sampling scheme. The effects of varying degrees of spatial autocorrelation are illustrated, though the correction is designed to require only minimum assumptions about the nature of the autocorrelation mechanism.