Reducing type II error: Sample size affects fMRI cluster-extent threshold to correct for multiple comparisons

Many procedures to correct for multiple comparisons in functional magnetic resonance imaging (fMRI) analysis require a minimum cluster-extent threshold; however, sample size is often not modeled. In the present study, a series of simulations was conducted where sample size was varied to determine whether this parameter affected cluster threshold. The primary hypothesis was that modeling sample size in the simulations would reduce cluster thresholds. A secondary hypothesis was that this reduction in cluster size was due to between-subject variability, which was tested by eliminating the corresponding standard error term. Whole-brain acquisition volume parameters were fixed, while the following key parameters were varied to reflect commonly employed ranges: sample size (N = 10, 20, or 30), corrected p-value (.05, .01, or .001), individual-voxel p-value (.01, .005, or .001), FWHM (3, 5, or 7 mm), and voxel resolution (2 or 3 mm). Each simulation consisted of 100 iterations repeated 100 times, with a total of 4,860,000 iterations and 66,420,000 simulated subjects. There was a significant effect of condition; clusters were approximately 18% smaller with versus without N modeled (and there was a significant increase in cluster thresholds for larger sample sizes). Bayesian analysis provided very strong support for the secondary hypothesis. The present findings indicate that sample size should be incorporated into all methods to provide the most accurate thresholds possible and reduce type II error. A broader range of topics is discussed including balancing type I and type II error along with the fallacy that non-task fMRI activity reflects null data.