To gain insight into today's large data resources, data mining provides automatic aggregation techniques. Clustering aims at grouping data such that objects within groups are similar while objects in different groups are dissimilar. In scenarios with many attributes or with noise, clusters are often hidden in subspaces of the data and do not show up in the full dimensional space. For these applications, subspace clustering methods aim at detecting clusters in any subspace. Existing subspace clustering approaches fall prey to an effect we call dimensionality bias. As dimensionality of subspaces varies, approaches which do not take this effect into account fail to separate clusters from noise. We give a formal definition of dimensionality bias and analyze consequences for subspace clustering. A dimensionality unbiased subspace clustering (DUSC) definition based on statistical foundations is proposed. In thorough experiments on synthetic and real world data, we show that our approach outperforms existing subspace clustering algorithms.