Small areas refer to small geographic areas, a more literal meaning of the phrase, as well as small domains (e.g., small sub-populations), a more figurative meaning of the phrase. With post-stratification, even with big data, either case can encounter the problem of small local sample sizes, which tend to inflate local uncertainty and undermine otherwise sound statistical analyses. This condition is the opposite of that afflicting statistical significance in the context of big data. These two definitions can also occur jointly, such as during the standardization of data: small geographic units may contain small populations, which in turn have small counts in various age cohorts. Accordingly, big spatial data can become not-so-big spatial data after post-stratification by geography and, for example, by age cohorts. This situation can be ameliorated to some degree by the large volume of and high velocity of big spatial data. However, the variety of any big spatial data may well exacerbate this situation, compromising veracity in terms of bias, noise, and abnormalities in these data. The purpose of this paper is to establish deeper insights into big spatial data with regard to their uncertainty through one of the hallmarks of georeferenced data, namely spatial autocorrelation, coupled with small geographic areas. Impacts of interest concern the nature, degree, and mixture of spatial autocorrelation. The cancer data employed (from Florida for 2001-2010) represent a data category that is beginning to enter the realm of big spatial data; its volume, velocity, and variety are increasing through the widespread use of digital medical records.
Keywords: big data; big spatial data; cancer; small area; small geographic area.