Variance approximations for assessments of classification accuracy

Variance approximations are derived for the weighted and unweighted kappa statistics, the conditional kappa statistic, and conditional probabilities. These statistics are useful to assess classification accuracy, such as accuracy of remotely sensed classifications in thematic maps when compared to a sample of reference classifications made in the field. Published variance approximations assume multinomial sampling errors, which implies simple random sampling where each sample unit is classified into one and only one mutually exclusive category with each of two classification methods. The variance approximations in this paper are useful for more general cases, such as reference data from multiphase or cluster sampling. As an example, these approximations are used to develop variance estimators for accuracy assessments with a stratified random sample of reference data.