The main objective of this paper is to elucidate the characteristics of a new spatial association statistic,Si, in comparison with local Moran's I, local Geary's c, and Getis-Ord's G. Si as a new local statistic measures how much (and in what direction) a local set contributes to an overall variance reduction resulting from the smoothing effect which occurs when an original variable is represented by its spatial moving average; the presence of a strong positive spatial autocorrelation in a local set results in a higher Si and vice versa. The main findings of a comparison of the four local spatial association statistics on the basis of four main concepts (spatial clusters, spatial outliers, spatial regimes, and local stability) and two additional criteria are two fold. First, they are largely divided into two distinct categories, I and c as more association-centered ones, and and as more clusteringcentered ones. Second, Si can be seen as a substitute for Gi in the sense that the former satisfies the two conditions for a LISA and its distributional properties are better known. A regular tessellation analysis is conducted to examine the feasible ranges and distributional properties of the local spatial association statistics. Major findings are as follows. First, correlations among the local statistics are much smaller in amount and their feasible ranges are much narrower when compared to their global counterparts. Second, the feasible ranges and distributional properties vary in accordance to the number and shape of spatial units, the number of neighboring spatial units, and the specification of spatial proximity matrix. Third, both the skewness and kurtosis are much more pronounced when compared to those from global SAS such that normal approximation is proved to be much less reliable for significance testing. Fourth, differences in spatial configuration of the 7 largest cities in South Korea dictate differences in the feasible ranges and distributional characteristics. This study can be viewed as one of the most comprehensive studies to address different pros and cons of the local statistics and is expected to help researchers choose a statistic suitable for their empirical studies.