A supplemental indicator of high-value or low-value spatial clustering

Most test statistics for detecting spatial clustering cannot distinguish between low-value spatial clustering and high-value spatial clustering, and none is designed to explicitly detect high-value clustering, low-value clustering, or both. To fill this void in practice, we introduce an adjustment procedure that can supplement common two-sided spatial clustering tests so that a one-sided conclusion can be reached. The procedure is applied to Moran's I and Tango's C-G in both simulated and real-world spatial patterns. The results show that the adjustment procedure can account for the influence of low-value clusters on high-value clustering and vice versa. The procedure has little effect on the original global testing methods when there is no clustering. When there is a clustering tendency, the procedure can unambiguously distinguish the existence of high-value clusters or low-value clusters or both.