Early Post-Stimulus Activity and P300 Amplitude in the Auditory Oddball: Decomposition into Mean and Variance Components at Fz and Pz

The P300 event-related potential is a core index of attention and context updating, but the trial-by-trial factors that shape its amplitude remain incompletely characterized. Within-trial root mean square (RMS) amplitude is often used as a summary of "early activity," yet RMS is algebraically a sum of mean and variance components (RMS{superscript 2} = mean{superscript 2} + variance) and so cannot, on its own, distinguish amplitude-driven from variability-driven coupling. Using single-trial EEG from the ERP CORE auditory oddball dataset (N = 27 retained from 40 after a {+/-}100 {micro}V peak-to-peak rejection criterion; 1,084 trials, 52.2% targets), we decomposed early-window (0-150 ms) activity at Fz and Pz into mean and standard-deviation components and modelled their associations with P300 amplitude (300-600 ms at Pz) using linear mixed-effects regression. Three findings emerge. First, early-window RMS at Fz showed only a small negative association with P300 amplitude ({beta} = -0.074, p = 0.006, marginal R{superscript 2} {approx} 0.01), three times smaller than the originally reported effect and accounting for [~]1% of P300 variance. Second, when RMS was decomposed, the early-window mean amplitude at Fz competed against the within-trial standard deviation; only the mean carried predictive weight, and its sign was positive ({beta} = +0.107, p = 2x10-{square}), the opposite sign of the RMS effect. Third, a per-electrode mixed-effects model identified Pz as the site where early activity was most strongly coupled to the P300, and at Pz the early-window mean was a powerful positive predictor of P300 amplitude ({beta} = +0.568, p < 10-{superscript 1}{square}, marginal R{superscript 2} {approx} 0.31), with a slope similar across target and standard trials and robust to baseline-window subtraction ({beta} = +0.538, p < 10-{superscript 1}{square}). Exploratory information-theoretic complexity measures (permutation entropy, sample entropy, Lempel-Ziv) showed no Bonferroni-significant association. The same-electrode parietal coupling is interpreted as evidence for a continuous parietal generator whose pre-300 ms leading edge is captured by the early window; we therefore frame this as a substantive observation about parietal cortical dynamics rather than a methodological artifact, while acknowledging that it constrains causal inference.