Dependence between the sensitivities or specificities of pairs of tests affects the sensitivity and specificity of tests when used in combination. Compared with values expected if tests are conditionally independent, a positive dependence in test sensitivity reduces the sensitivity of parallel test interpretation and a positive dependence in test specificity reduces the specificity of serial interpretation. We calculate conditional covariances as a measure of dependence between binary tests and show their relationship to kappa (a chance-corrected measure of test agreement). We use published data for toxoplasmosis and brucellosis in swine, and Johne's disease in cattle to illustrate calculation methods and to indicate the likely magnitude of the dependence between serologic tests used for diagnosis and surveillance of animal diseases.