2. Relation to TFCE

TFCE, referring to Threshold-Free Cluster Enhancement[1] is a widely used method, developed by Steven Smith and Tom Nichols and first made available as part of FSL. Like pTFCE, TFCE also boosts belief in large areas of signals and in its main concept, it is very similar to pTFCE.

Both TFCE and pTFCE are based on the integration of cluster-forming height threshold (h₁, h₂, …, h_n) and the supporting section or cluster size (c₁, c₂, …, c_n) at that given height. The difference is that, while TFCE combines raw measures of height and cluster size to an arbitrary unit, pTFCE realises the integration by constructing the conditional probability p(h|c) based on Bayes’ rule, thereby providing a natural adjustment for various signal topologies. Aggregating this probability across height thresholds provides enhanced p-values directly, without the need of permutation testing. Since a p(h_i|c__i) value is the "cluster-enhanced" version of the actual threshold h_i and not the actual voxel value v_x, a special equidistant incremental logarithmic probability aggregation method is needed to construct the enhanced probability.

With the aid of this novel aggregation technique, pTFCE, in contrast to TFCE, can directly output p-values (or -log(p) values or Z-scores), without the need for permutation testing. pTFCE is therfore computationally inexpensive and can be easily fit into any neuroimaging analysis pipeline.