# Probability waves: adaptive cluster-based correction by convolution of p-value series from mass univariate analysis

## Description

dataset and Octave/MatLab codes/scripts for data analysis Background: Methods for p-value correction are criticized for either increasing Type II error or improperly reducing Type I error. This problem is worse when dealing with thousands or even hundreds of paired comparisons between waves or images which are performed point-to-point. This text considers patterns in probability vectors resulting from multiple point-to-point comparisons between two event-related potentials (ERP) waves (mass univariate analysis) to correct p-values, where clusters of signiticant p-values may indicate true H0 rejection. New method: We used ERP data from normal subjects and other ones with attention deficit hyperactivity disorder (ADHD) under a cued forced two-choice test to study attention. The decimal logarithm of the p-vector (p') was convolved with a Gaussian window whose length was set as the shortest lag above which autocorrelation of each ERP wave may be assumed to have vanished. To verify the reliability of the present correction method, we realized Monte-Carlo simulations (MC) to (1) evaluate confidence intervals of rejected and non-rejected areas of our data, (2) to evaluate differences between corrected and uncorrected p-vectors or simulated ones in terms of distribution of significant p-values, and (3) to empirically verify rate of type-I error (comparing 10,000 pairs of mixed samples whit control and ADHD subjects). Results: the present method reduced the range of p'-values that did not show covariance with neighbors (type I and also type-II errors). The differences between simulation or raw p-vector and corrected p-vectors were, respectively, minimal and maximal for window length set by autocorrelation in p-vector convolution. Comparison with existing methods: Our method was less conservative while FDR methods rejected basically all significant p-values for Pz and O2 channels. The MC simulations, gold-standard method for error correction, presented 2.78±4.83% of difference (all 20 channels) from p-vector after correction, while difference between raw and corrected p-vector was 5,96±5.00% (p = 0.0003). Conclusion: As a cluster-based correction, the present new method seems to be biological and statistically suitable to correct p-values in mass univariate analysis of ERP waves, which adopts adaptive parameters to set correction.