Experimenters assume that participants of an experimental group have learned an artificial grammar if they classify test items with significantly higher accuracy than does a control group without training. The validity of such a comparison, however, depends on an additivity assumption: Learning is superimposed on the action of non-specific variables—for example, repetitions of letters, which modulate the performance of the experimental group and the control group to the same extent. In two experiments we were able to show that this additivity assumption does not hold. Grammaticality classifications in control groups without training (Experiments 1 and 2) depended on non-specific features. There were no such biases in the experimental groups. Control groups with training on randomized strings (Experiment 2) showed fewer biases than did control groups without training. Furthermore, we reanalysed published research and demonstrated that earlier experiments using control groups without training had produced similar biases in control group performances, bolstering the finding that using control groups without training is methodologically unsound.