A residual test kept its 5% pair level after common average reference in Gaussian models with known covariance and 88 public EEG power profiles

We tested pair inference after common average reference. The model used 19 independent input channels. The inputs were proper complex Gaussian vectors with a known zero mean. Fixed channel powers came from 88 public EEG records in OpenNeuro ds004504 v1.0.9. At 10 Hz, each generated record had 100 vectors. We generated 5,000 records per profile. A zero-coherence test at a 5% pair level rejected 10.82% of pairs. A residual test that used the known reference covariance rejected 5.00%. Bonferroni graph alarm rates were 29.26% and 4.89%. The proof gives an exact pair level under the stated Gaussian assumptions. All five planned model checks are reported. The package supplies the test tool, proof, fixed powers, spectra, source hashes, seeds, and full results. Three fresh source replays and a full simulation repeat passed. Reference effects and Gaussian residual tests are established methods. This work adds a benchmark with public power profiles and reusable code. It does not measure brain connections. The exact test requires known covariance fixed independently of the tested samples.

common average reference · complex Gaussian model · EEG · exact inference · pairwise coherence · Monte Carlo benchmark · known covariance · Bonferroni correction