Variation in count data transferred from a set of irregular zones to a set of regular zones through the point-in-polygon method

This paper deals with variation in transferred data from a set of irregular zones (called source zones) to a set of regular zones (called target zones) through the point-in-polygon method (i.e., the method that transfers the attribute value of a source zone to a target zone if a representative point of the source zone is included in the target zone). First,the variation is written as a mathematical equation. Second, it is shown that among regular lattices of target zones, a regular hexagonal lattice gives the minimum variation. However, the difference in variation between a square lattice and a regular hexagonal lattice is very small. Third, under the condition that an allowable variation is less than 5 per cent (which is usually acceptable in practice), the safest (the most conservative) rule supported by a theory is that the point-in-polygon method should be used when the diameter of every source zone is less than 4 per cent of the length of the edge of a square cell. Last, a practical rule based upon empirical data is that the point-in-polygon method should be used when the perimeter of every source zone is less than around 20 per cent of the length of the edge of a square cell.