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This article identifies a critical incompatibility between European notions of discrimination and existing statistical measures of fairness. First, we review the evidential requirements to bring a claim under EU non-discrimination law. Due to the disparate nature of algorithmic and human discrimination, the EU's current requirements are too contextual, reliant on intuition, and open to judicial interpretation to be automated. Second, we show how the legal protection offered by non-discrimination law is challenged when AI, not humans, discriminate. Humans discriminate due to negative attitudes (e.g. stereotypes, prejudice) and unintentional biases (e.g. organisational practices or internalised stereotypes) which can act as a signal to victims that discrimination has occurred. Finally, we examine how existing work on fairness in machine learning lines up with procedures for assessing cases under EU non-discrimination law. We propose "conditional demographic disparity" (CDD) as a standard baseline statistical measurement that aligns with the European Court of Justice's "gold standard." Establishing a standard set of statistical evidence for automated discrimination cases can help ensure consistent procedures for assessment, but not judicial interpretation, of cases involving AI and automated systems. Through this proposal for procedural regularity in the identification and assessment of automated discrimination, we clarify how to build considerations of fairness into automated systems as far as possible while still respecting and enabling the contextual approach to judicial interpretation practiced under EU non-discrimination law. N.B. Abridged abstract