Human randomness perception is commonly described as biased. This is because when generating random sequences humans tend to systematically underand over-represent certain sub-sequences relative to the number expected from an unbiased random process. In a purely theoretical analysis we have previously suggested that common misperceptions of randomness may actually reflect genuine aspects of the statistical environment, once cognitive constraints are taken into account which impact on how that environment is actually experienced. In the present study we provide a preliminary test of this account, comparing human-generated against unbiased process-generated binary sequences. Crucially we apply metrics to both sets of sequences that reflect constraints on human experience. In addition, sequences are compared using statistics that are shown to be more appropriate than a standard expected value analysis. We find preliminary evidence in support of our theoretical account and challenge the notion of bias in human randomness perception.