This study investigates the relation between two common localisation methods in ensemble Kalman filter (EnKF) systems: covariance localisation and local analysis. Both methods are popular in large-scale applications with the EnKF. The case of local observations with non-correlated errors is considered. Both methods are formulated in terms of tapering of ensemble anomalies, which provides a framework for their comparison. Based on analytical considerations and experimental evidence, we conclude that in practice the two methods should yield very similar results, so that the choice between them should be based on other criteria, such as numerical effectiveness and scalability.