Quantification of statistical type I and II errors in correlation analysis of simulated functional magnetic resonance imaging data

The potential of statistical analyses of functional magnetic resonance images using various threshold strategies in combination with correlation analysis was studied by simulating brain activation. Differences in statistical Type I (α) and II (β) errors are substantial for the various thresholds. Absolute thresholds and individualized thresholds based on the assumption of a gaussian noise distribution are producing constant α-errors and thus do not sufficiently improve discrimination of 'truly' activated pixels even for very high contrast-to-noise ratios (CNR). Only relative threshold strategies related to the maximum correlation coefficient and thus the individual data quality and activation level, i.e., a data-driven approach, can perfectly discriminate true positives, at least for CNR > 2.5. To further improve discrimination of activated and non-activated pixel in studies with lower CNR, additional prior knowledge would be necessary. From the data presented, one would also expect that the best performing threshold strategy in this simulation study would perform best under in vivo conditions.