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Quality control measures for ocean waves observations are necessary to give confidence of their accuracy. It is common practice to detect anomalies or outliers in surface displacement observations by applying a standard deviation threshold. Besides being a purely statistical method, this quality control procedure is likely to flag extreme wave events erroneously, thereby impacting higher-order descriptions of the wave field. In this paper we extend the use of the statistical phase-space threshold, an established outlier detection method in the field of turbulence, to detect anomalies in a wave record. We show that a wave record in phase space (here defined as a diagram of displacement against acceleration) can be enclosed by a predictable ellipse where the major and minor axes are defined by the spectral properties of the wave field. By using the parameterized ellipse in phase space as a threshold to identify wave anomalies, this is a semiphysical filtering method. Wave buoy data obtained from a mooring deployed near King George Island, Antarctica [as part of the Antarctic Modeling Observation System (ATMOS)], and laser altimeter data obtained at the Northwest Shelf of Australia were used to demonstrate the functioning of the filtering methodology in identifying wave anomalies. Synthetic data obtained using a high-order spectral model are used to identify how extreme waves are positioned in phase space. [ABSTRACT FROM AUTHOR]