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The study of bias in Machine Learning is receiving a lot of attention in recent years, however, few only papers deal explicitly with the problem of race bias in face anti-spoofing. In this paper, we present a systematic study of race bias in face anti-spoofing with three key characteristics: the focus is on analysing potential bias in the bona fide errors, where significant ethical and legal issues lie; the analysis is not restricted to the final binary outcomes of the classifier, but also covers the classifier's scalar responses and its latent space; the threshold determining the operating point of the classifier is considered a variable. We demonstrate the proposed bias analysis process on a VQ-VAE based face anti-spoofing algorithm, trained on the Replay Attack and the Spoof in the Wild (SiW) databases, and analysed for bias on the SiW and Racial Faces in the Wild (RFW), databases. The results demonstrate that race bias is not necessarily the result of different mean response values among the various populations. Instead, it can be better understood as the combined effect of several possible characteristics of the response distributions: different means; different variances; bimodal behaviour; existence of outliers.