The stationarity of a texture can be considered a fundamental property of images, although the property of stationarity is difficult to define precisely. We propose a stationarity test based on multiscale, locally stationary, 2D wavelets. Three separate experiments were performed to evaluate the capabilities and the limitations of this test. The experiments comprised a chessboard stationarity analysis, two classification tasks, and a psychophysical experiment. The classification tasks were performed on 110 texture images from a texture database. In one subtask, five texture feature vectors were extracted from each image and the classification accuracy of two classical methods compared, whereas in the second subtask, the classification accuracy of several methods was compared to the descriptors defined for each image within the database. In the psychophysical experiment, the correlation between the classification results and observer judgements of texture similarity were determined. It was found that a combination of wavelet shrinkage and rotation-invariant local binary pattern best predicted the observer response. The results show that the proposed stationarity test is able to provide relevant information for texture analysis.