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Anomaly detection attempts to learn models from data that can detect anomalous examples in the data. However, naturally occurring variations in the data impact the model that is learned and thus which examples it will predict to be anomalies. Ideally, an anomaly detection method should be robust to such small changes in the data. Hence, this paper introduces a ranking stability measure that quantifies the robustness of any anomaly detector’s predictions by looking at how consistently it ranks examples in terms of their anomalousness. Our experiments investigate the performance of this stability measure under different data perturbation schemes. In addition, they show how the stability measure can complement traditional anomaly detection performance measures, such as area under the ROC curve or average precision, to quantify the behaviour of different anomaly detection methods.