Synthetic aperture radar (SAR) images are subject to intrinsic 'noise', called speckle, over and above any spatial variability due to variations in the properties of the scene. Many noise-reduction techniques have been employed to reduce the effects of this phenomenon. In this note we review the statistical effects of one of the simplest such techniques, the median filter. This filter can be performed almost as rapidly as the mean (box average) filter but has significantly better edge-preserving properties. It is, however, unsuited to images containing significant point- or small-target features. Use of the median filter can introduce significant biases into the data, for example a 25 per cent reduction in an intensity image after 3 by 3 median filtering. This note presents calculations of the size of these biases for the case of homogeneous target areas, fully-developed speckle, and statistically independent looks in multi-look images.