A finite pool correction reduced mean squared concentration error for five uniformly selected posterior EEG windows in the first session of 60 adults

We tested a finite pool correction for spectral concentration in OpenNeuro ds004148 version 1.0.1. The primary test used both eye states in the first session of 60 adults. It used eight posterior channels, an average reference, and frequencies from 2 to 30 Hz. Each window was normalized before averaging. Five different windows were selected uniformly from each fixed accepted pool. The target was the concentration of the complete pool. Exact mean squared sampling error was 0.000125676 for the conventional estimate and 0.0000959512 for the corrected estimate. The ratio was 0.763, with a paired 95 percent person bootstrap interval from 0.727 to 0.796. Error was lower in all 120 primary records. All seven planned checks had lower mean error. A proof gives zero bias under the stated selection rule. An exact counterexample shows that the correction can increase error in other pools. Early chronological windows had greater error than uniform samples. The expected conventional eye-state contrast exceeded the full pool contrast by 13.6 percent. The package preserves all 360 spectral inputs, code, source hashes, results, bootstrap draws, the local plan, and reproduction commands. Two source signals were downloaded again and reproduced all arrays exactly. The result does not establish an unbiased estimate of a new recording or a causal brain effect.

electroencephalography · EEG · spectral concentration · finite pool · sampling error · uniform sampling · without replacement · U-statistics · posterior channels · risk · mean squared error · OpenNeuro · test-retest dataset