Cerebral hemispheric specialization has traditionally been described using a lateralization index (LI). Such an index, however, shows a very severe threshold dependency and is prone to be influenced by statistical outliers. Reliability of this index thus has been inherently weak, and the assessment of this reliability is as yet not possible as methods to detect such outliers are not available. Here, we propose a new approach to calculating a lateralization index on functional magnetic resonance imaging data by combining a bootstrap procedure with a histogram analysis approach. Synthetic and real functional magnetic resonance imaging data was used to assess performance of our approach. Using a bootstrap algorithm, 10,000 indices are iteratively calculated at different thresholds, yielding a robust mean, maximum and minimum LI and thus allowing to attach a confidence interval to a given index. Taking thresholds into account, an overall weighted bootstrapped lateralization index is calculated. Additional histogram analyses of these bootstrapped values allow to judge reliability and the influence of outliers within the data. We conclude that the proposed methods yield a robust and specific lateralization index, sensitively detect outliers and allow to assess the underlying data quality.