Using a spatial data set generator in an empirical analysis of aggregation effects on univariate statistics

The resistance of the modifiable area unit problem (MAUP) to analytical solution requires that it be investigated by empirical studies that have the potential to lay the foundations for analytical approaches. The use of synthetic spatial data sets, whose spatial autocorrelation, mean and variance of individual variables, and Pearson correlation between variables, can be controlled, greatly enhances the ability of the analyst to study the MAUP in this manner. This paper explores the effects of spatial aggregation on the variance and three univariate spatial autocorrelation statistics using a synthetic 400-region data set. The relationship between the relative change in variance and a modified version of the G-statistic that was first proposed by Amrhein and Reynolds is explored in more detail. These results are compared favorably to results generated from the Lancashire data set of Amrhein and Reynolds.