Measuring the spatial balance of a sample: A new measure based on the Moran's I index

TL;DR

This paper introduces a new absolute measure for assessing the spatial spreading of a sample by normalizing Moran's I index, enabling meaningful interpretation of spatial balance in sampling.

Contribution

The paper proposes a normalized Moran's I-based measure for spatial balance, addressing the interpretability limitations of existing indices.

Findings

The new measure effectively quantifies spatial spreading in absolute terms.

Simulation experiments demonstrate the measure's properties and behavior.

Application to real data shows practical usefulness.

Abstract

Measuring the degree of spatial spreading of a sample can be of great interest when sampling from a spatial population. The commonly used spatial balance index by Grafstr\"om et al. (2012) is particularly effective in comparing the level of spatial spreading of different samples from the same population. However, its unbounded and uninterpretable scale of measurement does not allow to assess the level of spatial spreading in absolute terms and confines its use to only raw comparisons. In this paper, we introduce a new absolute measure of the spatial spreading of a sample using a normalized version of the Moran's $I$ index. The properties and behaviour of the proposed measure are analysed through two simulation experiments, one based on artificial populations and the other on a population of real business units located in the province of Siena (Italy).