Estimating area and map accuracy for stratified random sampling when the strata are different from the map classes

The results of an accuracy assessment are typically organized using an error matrix that displays the proportion of area correctly mapped for each class and the proportion of area misclassified. Stratified random sampling is commonly implemented to obtain the reference data used to estimate the error matrix. When the strata correspond exactly to the map classes, the formulas for estimating accuracy and area are well known. Nevertheless, applications arise in which the strata are different from the map classes, as for example when the stratification is based on the map class labels of one map but the sample is subsequently used to assess the accuracy of other maps. In this paper, the estimators required when the stratum label and map label do not match for all pixels are presented for the proportion of area of each class based on the reference classification and for overall, user’s, and producer’s accuracies. Standard error formulas are also presented. A numerical example is provided to illustrate the computations.