Judging the conformity of binary events in macroeconomics and finance has often been done with indices that measure synchronization. In recent years, the use of Receiver Operating Characteristic (ROC) curve has become popular for this task. This paper shows that the ROC and synchronization approaches are closely related, and each can be represented as a weighted average of correlation coefficients between a set of binary indicators and the target event. An advantage of such a representation is that inferences on the degree of conformity can be made robust to serial dependence in the underlying series in the standard framework of a linear regression model. Such serial correlation is common in macroeconomic and financial data.