Voice anti-spoofing aims at classifying a given utterance either as a bonafide human sample, or a spoofing attack (e.g. synthetic or replayed sample). Many anti-spoofing methods have been proposed but most of them fail to generalize across domains (corpora)-and we do not know why. We outline a novel interpretative framework for gauging the impact of data quality upon anti-spoofing performance. Our within-and betweendomain experiments pool data from seven public corpora and three anti-spoofing methods based on Gaussian mixture and convolutive neural network models. We assess the impacts of long-term spectral information, speaker population (through xvector speaker embeddings), signal-to-noise ratio, and selected voice quality features.