Impact of sample size allocation when using stratified random sampling to estimate accuracy and area of land-cover change

The ground reference data obtained to assess map accuracy can be simultaneously used to estimate area (extent). This dual-purpose use of ground reference data is examined for the special case of a two-class map of 'change' and 'no change'. To assess the accuracy of a change map, stratified sampling is often implemented with a disproportionately larger sample size allocated to the map change stratum. But this allocation targeting user's accuracy of change is not necessarily effective for the competing objective of estimating the area of change. Sampling theory provides the basis for deciding a sample size allocation to strata when multiple, but competing estimation objectives are of interest. Neyman optimal allocation is preferred for estimating the area of change as well as overall accuracy, whereas equal allocation is effective for estimating user's accuracy. The results and recommendations developed in this article extend to any dichotomous classification in which one class is relatively rare.