Early Post-Stimulus Activity Negatively Predicts P300 Amplitude: A Single-Trial Analysis of the Auditory Oddball Task

Early Post-Stimulus Activity Negatively Predicts P300 Amplitude: A Single-Trial Analysis of the Auditory Oddball Task | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Early Post-Stimulus Activity Negatively Predicts P300 Amplitude: A Single-Trial Analysis of the Auditory Oddball Task Erkan Biber This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8657074/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract The P300 event-related potential is a core index of attention and context updating, yet the trial-by-trial factors that modulate its amplitude remain incompletely characterized. This study tested whether early post-stimulus signal magnitude (0–150 ms) predicts subsequent P300 amplitude (300–600 ms) at the single-trial level. Using data from the ERP CORE auditory oddball dataset (N = 40 participants; 1,661 trials), early activity was quantified as root mean square (RMS) amplitude at electrode Fz. A linear mixed-effects model with full model diagnostics and post-hoc power analysis revealed a statistically reliable negative association between early RMS and P300 amplitude (β = −0.064, SE = 0.0245, z = − 2.61, p = 0.0085, 95% CI [− 0.112, − 0.016]). However, the effect size was minimal (R² = 0.0042), explaining less than 0.5% of trial-level variance. Notably, the stimulus condition effect (Target vs. Standard) was approximately 13 times larger, indicating that early signal magnitude provides modest modulation rather than decisive control over P300 generation. Model diagnostics confirmed adequate assumptions (Shapiro-Wilk W = 0.9995, p = 0.97; achieved power = 0.85). Exploratory complexity measures (Permutation Entropy, Lempel–Ziv) were non-predictive, suggesting amplitude-dependent rather than complexity-based coupling. The most conservative interpretation is that early RMS reflects momentary neural state that weakly biases P300 amplitude, possibly through resource competition or refractory-like effects. These findings establish a quantitative constraint on early–late ERP coupling, demonstrate that P300 is predominantly endogenously driven, and highlight the importance of distinguishing amplitude-based measures from trial-to-trial variability. Future work should decompose these components and incorporate pre-stimulus state covariates to clarify mechanisms. P300 event-related potential single-trial analysis linear mixed-effects models neural state state-dependent processing Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction The P300 event-related potential (ERP) is a core electrophysiological marker of attention and context updating in cognitive neuroscience, reflecting the neural response to task-relevant, unpredictable stimuli within working memory (Donchin, 1981; Polich, 2007). At the group level, P300 morphology and topography are well characterized; however, trial-by-trial dynamics underlying P300 amplitude variability remain incompletely understood. A key unresolved question is whether the neural state during early post-stimulus processing (0–150 ms) meaningfully constrains the magnitude of the subsequent P300 response (300–600 ms), and if so, whether this reflects amplitude-dependent or variability-dependent mechanisms. Recent computational and empirical work has reconceptualized the P300 as a build-to-threshold decision variable that accumulates evidence toward a response criterion (Twomey et al., 2015). Under this framework, trial-to-trial P300 amplitude variation reflects fluctuations in evidence-accumulation dynamics, including drift rate and baseline excitability (Murphy et al., 2016). This perspective raises a mechanistic question: does the momentary neural state reflected in early post-stimulus signal magnitude modulate the initial conditions or gain of this accumulation process? 1.1 Competing Theoretical Predictions Four theoretical frameworks make distinct predictions about early–late ERP coupling: 1.1.1. State-Dependent Processing (Primary Interpretation) State-dependent or gain control perspectives propose that early post-stimulus neural activity indexes a momentary processing state that biases downstream cognitive computations (Churchland et al., 2010; Arazi et al., 2017). Specifically, the amplitude and stability of early sensory responses (N1, ~ 100 ms; P2, ~ 200 ms) may set the gain or baseline excitability for subsequent context-updating operations. Trials with moderate early activity may reflect optimal neural states for robust P300 generation, while excessively high or low early activity may reflect suboptimal states, slightly dampening subsequent processing. This interpretation is consistent with recent findings that pre-stimulus alpha amplitude, a proxy for neural state stability, predicts both trial-by-trial variability quenching and downstream ERP components (Studenova et al., 2023; Lago et al., 2023). A state-dependent account predicts a U-shaped or non-monotonic relationship between early activity and P300, or more conservatively, a modest linear coupling reflecting state-dependent biasing. 1.1.2. Resource Competition (Alternative Mechanism) The resource competition account posits that neural processing capacity is finite (Kok, 2001; Polich, 2007; Lavie & Torralbo, 2010). Under this view, if early sensory processing consumes substantial metabolic or computational resources, fewer resources remain for subsequent P300 generation, predicting a negative correlation between early and late amplitudes. This mechanism aligns with perceptual load theory and extends to ERP components. A strong resource competition model would predict substantial negative coupling (large effect sizes). 1.1.3. Refractory-Like Effects Neural populations that participate in both early sensory and late P300 processing may exhibit transient refractoriness. Strong early activation (large N1/P2) may leave overlapping neural populations temporarily less excitable, dampening the subsequent P300 (Neville et al., 1986; Johannsen et al., 2014). This predicts a negative relationship, mechanistically distinct from resource competition but observationally similar. 1.1.4. Facilitation / Positive Coupling Conversely, high-fidelity early sensory representation (large N1/P2) may more effectively trigger downstream context-updating cascades, predicting a positive correlation between early and late amplitudes (gain control in the classical sense). 1.2. The Variability-Amplitude Measurement Ambiguity A critical methodological issue complicates mechanistic interpretation: most univariate measures of "early activity," including root mean square (RMS) amplitude, conflate mean signal deflection with within-trial signal variability (Luck, 2014). RMS reflects overall signal energy (i.e., \(\:\sqrt{\frac{1}{N}\sum\:{x}^{2}\left(t\right)}\) ) rather than pure dispersion after mean removal. This ambiguity creates interpretive challenges. Recent neuroscience literature on neural variability quenching proposes that stimulus onset reduces ongoing neural noise, stabilizing representations and enhancing perceptual discrimination (Churchland et al., 2010; Arazi et al., 2017). At the trial level, individuals with larger stimulus-evoked variability reduction show better perceptual performance (Arazi et al., 2017). However, this variability-quenching effect typically operates on across-trial measures (e.g., Fano factor of neural spiking or trial-to-trial EEG power fluctuations) rather than within-trial signal energy. A within-trial RMS metric captures signal energy but does not isolate variability per se. Consequently, a negative early RMS–P300 relationship could reflect: Amplitude-dependent mechanisms: Resource competition or refractory effects driven by signal magnitude Variability-related mechanisms: Higher early signal energy correlated with lower within-trial noise, reflecting a more stable neural state favorable to P300 generation State-dependent gain effects: Early neural state (reflected in both amplitude and variability) biasing the gain of downstream processing Distinguishing these mechanisms requires rigorous single-trial quantification and, ideally, complementary measures that separately quantify amplitude and variability. 1.3. Single-Trial Approaches and Mixed-Effects Modeling Modern ERP research increasingly employs single-trial analysis with mixed-effects models (LMM) to account for hierarchical data structure, trials nested within subjects, with unbalanced trial counts, and to quantify individual differences in early–late coupling (Twomey et al., 2015; Hoy et al., 2021; Heise et al., 2022). LMMs provide several advantages over traditional averaging approaches: (1) retain trial-level resolution, (2) properly handle unbalanced designs and subject-level variability, (3) provide uncertainty estimates for individual regression slopes, and (4) enable formal comparison of competing random-effects structures via information criteria (Baayen et al., 2008). Recent reviews emphasize that LMMs are now the recommended approach for hierarchical ERP data (Heise et al., 2022), particularly when testing trial-by-trial predictors. 1.4. Study Aims and Hypotheses This study addresses three primary questions: Directional relationship : Is there a statistically reliable single-trial association between early post-stimulus signal magnitude (RMS at 0–150 ms, electrode Fz) and subsequent P300 amplitude (300–600 ms, electrode Pz)? Effect magnitude and mechanism : What is the magnitude of this relationship? Does it support state-dependent, resource-based, or refractory hypotheses? Critically, how much trial-level P300 variance does early RMS explain? Amplitude versus variability : Does the observed coupling reflect amplitude-dependent mechanisms (resource/refractory) or variability-related state effects? We analyzed single-trial EEG data from the ERP CORE auditory oddball dataset (Kappenman et al., 2021), a large, standardized, openly available resource, using linear mixed-effects regression to quantify early–late coupling while properly accounting for subject-level random effects and individual differences in coupling strength. We report full model diagnostics (residual normality, homoscedasticity, convergence) consistent with current transparency and reproducibility standards (Paul et al., 2021; Clayson et al., 2022). We interpret findings cautiously, acknowledging that (1) RMS reflects signal energy rather than pure variability, (2) the exploratory nature of this single-trial analysis requires independent replication, and (3) small effect sizes, while statistically reliable, may require multivariate or network-level approaches for practical prediction. Our primary contribution is to establish a precise lower bound on how much a simple univariate early-window amplitude measure can explain P300 trial-to-trial variability, a methodologically valuable constraint regardless of effect size. 2. Methods 2.1 Participants Data were obtained from the publicly available ERP CORE database (Kappenman et al., 2021), which provides standardized ERP paradigms with high quality pre-processing. The P300 dataset included 40 healthy young adults (25 female, 15 male; mean age = 21.5 years, SD = 2.1) recruited from the University of California, Davis community. All participants provided informed consent in accordance with institutional review board approval. Participants had normal hearing and no history of neurological or psychiatric disorders. 2.2 Stimuli and Procedure Participants completed an active auditory oddball task with the following parameters: Standard tones: 1000 Hz, 80% probability Target ("oddball") tones: 2000 Hz, 20% probability Both stimuli were presented binaurally at 75 dB SPL with 100 ms duration (10 ms rise/fall times). Inter stimulus interval varied randomly between 1100 and 1500 ms. Participants pressed a button on a gamepad with their dominant hand whenever they detected a target tone. Each session comprised 200 trials (160 standard, 40 target) presented in a single ~ 6 minute block. 2.3 EEG Recording and Pre-processing Continuous EEG was recorded using a Biosemi ActiveTwo system with 30 active Ag/AgCl electrodes positioned according to the international 10–20 system. Data were digitized at 1024 Hz. Pre-processing was performed using MNE-Python v1.x (Gramfort et al., 2013) following standardized ERP analysis procedures: Filtering : Bandpass filter 0.1–30 Hz (FIR design, zero phase) Artifact correction : Independent Component Analysis (ICA) to identify and remove blink and saccade artifacts Referencing : Re-referenced to average of all scalp electrodes Epoching : Segmentation from − 200 to 800 ms relative to stimulus onset Baseline correction : Subtraction of pre-stimulus baseline (− 200 to 0 ms) Rejection : Epochs with peak-to-peak amplitude > 100 µV in any channel were excluded After pre-processing, an average of 41.5 trials per participant (range: 22–79) were retained, yielding 1,661 trials across all participants. The wide range in retained trials reflects individual differences in artifact rates; five participants contributed < 30 trials. 2.4 Single-Trial Metrics 2.4.1.Early Signal Magnitude (0–150 ms): Early post-stimulus activity was quantified as the root mean square (RMS) amplitude at electrode Fz in the 0–150 ms window $$\:RMS=\sqrt{\frac{1}{N}{\sum\:}_{t=1}^{N}{x}^{2}\left(t\right)}$$ where x(t) is the voltage at time point t, and N is the number of time points in the window (75 samples at 512 Hz). This window captures early sensory components (N1 ~ 100 ms, P2 ~ 200 ms) and reflects initial cortical responses. RMS values were log-transformed to reduce skewness $$\:{RMS}_{log}=\text{l}\text{o}\text{g}(RMS+{10}^{-12})$$ Note on Interpretation As shown in the equation, RMS amplitude reflects overall signal energy and is influenced by both the mean deflection (DC offset) and within-trial fluctuation (AC variance). RMS therefore captures signal magnitude rather than pure dispersion after mean removal. We interpret early RMS primarily as an early-window signal magnitude proxy rather than a pure measure of neural variability or trial-to-trial variance. This measurement ambiguity is discussed extensively in the Discussion. 2.4.2. Late P300 Amplitude (300–600 ms): P300 amplitude was calculated as the mean voltage at electrode Pz in the 300–600 ms window. Pz was selected as the canonical site for the parietal P300b component (Polich, 2007). P300 amplitudes were z-scored within each participant to facilitate interpretation of standardized effect sizes. 2.5 Statistical Analysis Linear mixed-effects models (LMMs) were used to predict single-trial P300 amplitude. LMMs are increasingly recognized as the recommended approach for hierarchical ERP data (Heise et al., 2022), appropriately handling hierarchical data structure (trials nested within participants), unbalanced trial counts across participants, and individual differences in predictor effects (Baayen et al., 2008). Recent work employing single-trial LMM approaches includes computational modeling of trial-by-trial P300 dynamics (Twomey et al., 2015) and decomposition of overlapping ERP components (Hoy et al., 2021).. 2.5.1.Primary model specification $$\:{P300}_{trial}\sim1+Condition+{RMS}_{log,z}+(1+⟨{RMS}_{early,log,z}|Subject⟩)$$ This specification includes: Fixed effects: Stimulus condition (Target vs. Standard) and log-transformed, z scored early RMS Random effects: Random intercepts and random slopes for RMS by participant, allowing individual differences in baseline P300 and the strength of early-late coupling All continuous variables were z scored within participants prior to analysis to facilitate interpretation. Analysis was performed using the statsmodels v0.14 library in Python with restricted maximum likelihood (REML) estimation. To justify the random effects structure, we compared three nested models: Random intercept only: ( 1 | Subject ) Random intercept + slope: ( 1 + RMS_log,z | Subject ) Interaction model: Added Condition × RMS_log,z interaction term Model comparison was based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), with lower values indicating better fit. (See Results Table 1 ) Table 1 Model Comparison for Random Effects Structure Model Random Effects AIC BIC Δ AIC Δ BIC 1 Intercept Only 4,321.8 4,361.4 + 17.2 + 12.3 2 Intercept + Slope 4,304.6 4,349.1 0 (reference) 0 (reference) 3 Intercept + Slope + Interaction 4,306.4 4,356.3 + 1.8 + 7.2 Note: Model 2 (random intercept + slope) shows best fit based on lower AIC and BIC. Model 3 includes Condition × RMS interaction but does not improve fit 2.5.2.Interaction model: We also tested whether the early RMS effect differed between Target and Standard trials by adding a Condition × RMS interaction term to the primary model. 2.6 Model Diagnostics Model assumptions were evaluated through: Residual normality : Q-Q plots and Shapiro-Wilk test on standardized residuals Homoscedasticity : Visual inspection of residuals vs. fitted values Convergence : Verification of successful REML convergence Diagnostic plots were generated using matplotlib and scipy libraries in Python. Full diagnostic results are reported in Results section 3.6 , consistent with transparent reporting standards (Paul et al., 2021; Clayson et al., 2022). 2.7 Post-Hoc Power Analysis Post-hoc power analysis was conducted for the primary effect using the statsmodels power module, assuming α = 0.05, the observed effect size (β = −0.064), and sample characteristics (N = 1,661 trials, 40 participants). 2.8 Exploratory Complexity Analysis As supplementary exploratory analyses, we computed two information-theoretic complexity measures on the early window (0–150 ms at Fz): Permutation Entropy (PE) : Quantifies the complexity of time series patterns by analyzing ordinal patterns in sequential data (Bandt & Pompe, 2002) Lempel-Ziv (LZ) complexity : Measures sequence compressibility as a proxy for algorithmic complexity (Lempel & Ziv, 1976) These measures were included to assess whether information-theoretic complexity (rather than simple signal magnitude) predicted P300 amplitude. Both metrics were z-scored within participants and included as predictors in separate LMMs. We note that these analyses are exploratory and that complexity measures may have limited reliability when applied to short signal segments (~ 75 samples); null results should be interpreted cautiously (Bai et al., 2015; Lau et al., 2022). 3. Results 3.1 P300 Task Effects Grand average ERPs confirmed canonical P300 responses (Fig. 1 A). Target stimuli elicited a large positive deflection at Pz peaking around 350–450 ms, substantially larger than Standard stimuli. Both conditions showed clear N1 (~ 100 ms) and P2 (~ 200 ms) components, with characteristic P300 enhancement for targets. This pattern validates data quality and confirms participant task engagement. Mean reaction time to target tones was 432 ± 68 ms with 98.2% accuracy, indicating excellent task performance. 3.2 Model Comparison: Justification for Random Effects Structure Table 1 presents the model comparison results. The random intercept + slope model showed the best fit based on AIC (4,304.6) compared to the intercept-only model (AIC = 4,321.8, Δ = 17.2), justifying the inclusion of random slopes for early RMS by participant. BIC also favored the intercept + slope model (4,349.1 vs. 4,361.4, Δ = 12.3), indicating that participants varied meaningfully in the strength of early–late coupling. The interaction model (Condition × RMS) did not improve fit (AIC = 4,306.4, Δ = +1.8), indicating the early RMS effect does not significantly differ between Target and Standard trials. Therefore, the random intercept + slope model without interaction was selected as the primary model. 3.3 Primary Analysis: Early RMS and P300 Amplitude Table 2 presents the primary linear mixed-effects model results. Early RMS (0–150 ms at F z ) showed a statistically reliable negative association with P300 amplitude (300–600 ms at P z ): β = −0.064, SE = 0.0245, z = − 2.61, p = 0.0085, 95% CI [− 0.112, − 0.016]. Table 2 Linear Mixed Effects Model predicting single-trial P300 amplitude (z-scored) from stimulus condition and log-transformed, z-scored early RMS (0–150 ms at Fz). N = 1,661 trials from 40 participants. Predictor β SE z p 95% CI Intercept 0.000 0.052 0.00 1.000 [− 0.102, 0.102] Condition [Target] 0.821 0.048 17.10 < 0.001 [0.727, 0.915] Early RMS (log, z) −0.064 0.0245 −2.61 0.0085 [− 0.112, − 0.016] Random Effects: • Subject Intercept (SD): 0.285 • Subject Slope (SD): 0.152 • Residual (SD): 0.952 Model Fit: • R² (early RMS alone): 0.0042 • Log-Likelihood: −2,145.3 • AIC: 4,304.6 • BIC: 4,349.1 • Convergence: Yes (REML) This indicates that trials with higher early signal energy tended to show slightly smaller P300 amplitudes. However, the incremental variance explained by early RMS at the trial level was very small (R² = 0.0042), accounting for only 0.42% of P300 variance. To contextualize this magnitude: the stimulus condition effect (Target vs. Standard) in the same model yielded β = 0.821, representing an effect approximately 13 times larger than that of early RMS. This comparison underscores that early signal magnitude is a modest modulator rather than a primary driver of P300 amplitude. Analysis of the random effects structure revealed an intraclass correlation coefficient (ICC) of approximately 0.08, indicating that subject-level differences accounted for ~ 8% of the total variance in P300 amplitude, while the vast majority (> 90%) was trial-to-trial variability. The marginal R² (variance explained by fixed effects alone) and conditional R² (variance explained by both fixed and random effects) for the early RMS predictor were both low (< 1%), confirming that the effect, while statistically reliable, is small in magnitude. The random slope standard deviation (SD = 0.152) indicated that individual subjects varied in the strength of the coupling, but the negative direction held robustly across participants . Figure 1 B visualizes this relationship: each dot represents a single trial, color-coded by condition (blue = Standard, red = Target). The black regression line shows the overall negative slope. Trials with low early signal magnitude (left side of the plot, representing quieter initial states) tend to have higher P300 amplitudes (upper part of Y-axis). The substantial scatter around the regression line reflects the modest effect size and the dominance of other unmeasured factors in determining P300 amplitude. 3.4 Sensitivity Analysis: Trial Count In order to assess whether the effect was driven by participants with few trials, we conducted a sensitivity analysis excluding the 5 participants with < 30 retained trials. Results remained virtually identical: β = −0.066, SE = 0.026, p = 0.011, indicating the effect is not an artifact of unbalanced trial counts and is robust to variations in per-participant sample size. 3.5 Interaction Analysis The Condition × Early RMS interaction was not significant (β = −0.012, SE = 0.026, z = − 0.46, p = 0.65), indicating the negative association between early RMS and P300 is similar in magnitude for Target and Standard trials. This suggests the early–late coupling mechanism operates consistently across both trial types. 3.6 Model Diagnostics Residual diagnostics revealed adequate satisfaction of model assumptions: Normality of residuals : The Q-Q plot (Fig. 2 ) showed residuals closely aligned with the theoretical normal line across the full range, with minimal deviation. The Shapiro-Wilk test confirmed normality: W = 0.9995, N = 1,661, p = 0.9690 (p > 0.05), indicating residuals are approximately normally distributed. Homoscedasticity : The residuals vs. fitted values plot (Fig. 3 ) showed no systematic pattern or funnel shape. The cloud of residuals was symmetrically distributed around the zero line across the range of fitted values, indicating homogeneous variance (constant error variance assumption satisfied). Residual distribution : The histogram of standardized residuals (Fig. 4 ) revealed an approximately normal distribution centered at zero with slight departures at extreme tails, consistent with the large sample size (N = 1,661). Convergence : REML estimation converged successfully with no warnings or singularity issues. We conclude that these diagnostics support the validity of model assumptions and statistical inferences from the linear mixed-effects analysis. Full diagnostic plots are provided in Figs. 2 – 4 , consistent with transparent reporting standards (Paul et al., 2021; Clayson et al., 2022). 3.7 Power Analysis Post-hoc power analysis indicated achieved power of 0.85 for detecting the observed effect (β = −0.064, α = 0.05, N = 1,661 trials, 40 participants), suggesting adequate statistical power despite the small effect size. This high power estimate confirms that the small observed effect is unlikely to be a Type II error (false negative) and reflects a genuine, if modest, early–late coupling. 3.8 Exploratory Complexity Measures Neither Permutation Entropy (PE) nor Lempel-Ziv (LZ) complexity in the early window (0–150 ms) significantly predicted P300 amplitude: PE: β = 0.031, SE = 0.025, z = 1.24, p = 0.21 LZ: β = −0.018, SE = 0.025, z = − 0.72, p = 0.47 These null results may reflect the challenge of reliably estimating information-theoretic complexity from short signal segments (~ 75 samples at 512 Hz effective sampling; Bai et al., 2015; Lau et al., 2022). Alternatively, they suggest the observed RMS effect is more closely tied to signal magnitude (amplitude/energy) than to complexity or entropy per se. The contrast between the significant RMS effect and null complexity effects supports an amplitude-dependent interpretation (resource competition or refractory mechanisms) rather than a complexity-based or variability-quenching mechanism (see Discussion 4.1 for detailed interpretation). 4. Discussion This study examined whether early post-stimulus signal magnitude predicts later P300 amplitude at the single-trial level in an auditory oddball paradigm. A linear mixed-effects analysis of 1,661 trials from 40 participants revealed a small but statistically reliable negative association : trials with higher early RMS (0–150 ms at Fz) showed slightly smaller P300 amplitudes (300–600 ms at Pz; β = −0.064, SE = 0.0245, z = − 2.61, p = 0.0085, 95% CI [− 0.112, − 0.016]). The effect size was very small (R² = 0.0042), indicating that early RMS accounts for less than 0.5% of trial-level P300 variance. This finding is best interpreted as establishing a precise quantitative constraint on how much a simple univariate early-window signal magnitude measure can explain trial-to-trial P300 variability under well-controlled conditions. 4.1 Interpretation: State-Dependent Processing as Primary Mechanism The primary finding, higher early signal energy predicts slightly smaller P300 amplitude, admits several mechanistic interpretations. Following the theoretical framework developed in the Introduction, we interpret this coupling conservatively as reflecting state-dependent processing , wherein early post-stimulus signal magnitude indexes a momentary neural state that modestly biases subsequent context-updating operations. 1. State-Dependent Processing (Primary Interpretation) Early RMS likely reflects a composite of stimulus-evoked amplitude and the background neural state (e.g., ongoing oscillatory power, network excitability) at the moment of stimulus onset. This interpretation aligns with recent evidence that pre-stimulus alpha amplitude , a canonical marker of neural state, predicts both trial-by-trial variability quenching and downstream ERP component amplitude (Studenova et al., 2023; Lago et al., 2023). Trials with moderate early activity may correspond to optimal neural states for robust P300 generation, reflecting balanced excitability and effective sensory-to-cognitive signal propagation. In contrast, excessively high or low early activity may mark suboptimal states : high early activity could reflect noisy or over-reactive sensory processing that interferes with downstream integration, while very low early activity might indicate insufficient sensory registration or subthreshold arousal. This state-dependent account is conceptually distinct from deterministic feedforward models (wherein P300 amplitude would be a simple function of early sensory strength) and instead positions early RMS as an index of processing state that sets the gain or baseline excitability for evidence accumulation. Critically, this interpretation predicts modest, not dominant, coupling , consistent with the observed small effect size. The P300, as a marker of endogenous context updating and decision-related processing (Twomey et al., 2015), should be primarily driven by higher-order cognitive factors; stimulus meaning, task relevance, expectation violations, rather than by low-level sensory magnitude alone. 2. Resource Competition (Alternative Amplitude-Based Mechanism) Resource competition accounts propose that early sensory processing and late P300 generation draw on partially shared neural or metabolic resources (Kok, 2001; Polich, 2007; Lavie & Torralbo, 2010; de Ron et al., 2023). Under this view, trials with larger early responses may transiently deplete attentional or metabolic capacity available for subsequent P300 assembly, producing amplitude trade-offs. The observed negative coupling is consistent with this framework; however, the very small effect size (R² = 0.0042) suggests that any such resource-based trade-offs are subtle. Modern resource-allocation models predict effect sizes in the range of 15–30% variance explained when resources are genuinely limiting (de Ron et al., 2023), far exceeding the < 0.5% observed here. This discrepancy suggests that resource competition, if operative, is a minor modulator rather than a primary constraint on P300 generation in this paradigm. 3. Refractory-Like Effects Neural populations participating in both early sensory (N1, P2) and late P300 processing may exhibit transient refractoriness following strong early activation (Neville et al., 1986; Johannsen et al., 2014). Large early deflections might leave overlapping populations temporarily less excitable, reducing subsequent P300 amplitude. This mechanism predicts a negative relationship similar in sign to resource competition but grounded in local excitability dynamics rather than global capacity limits. The small effect size is consistent with partial, rather than complete, overlap between early sensory and late P300 neural generators, and with relatively rapid recovery times (on the order of 100–200 ms; Johannsen et al., 2014) that minimize sustained refractory effects by the P300 window. 4. Variability Quenching and Noise Suppression (Conceptually Related but Methodologically Distinct) Although RMS is not a pure variability measure , the negative coupling is directionally consistent with variability-quenching frameworks, which propose that stimulus-evoked stabilization (i.e., reduction of ongoing neural noise) enhances information processing and perceptual performance (Churchland et al., 2010; Arazi et al., 2017). However, critical methodological distinctions must be acknowledged: Churchland et al. (2010) and Arazi et al. (2017) quantified variability quenching as reductions in across-trial variance (e.g., Fano factor of neural spiking, trial-to-trial EEG power fluctuations). The present RMS metric reflects within-trial energy (i.e., \(\:\sqrt{\frac{1}{N}\sum\:{x}^{2}\left(t\right)}\) ), which conflates mean amplitude (DC component) and within-trial fluctuation (AC variance). These are conceptually and mathematically distinct . Recent work has emphasized the importance of separating mean signal amplitude from dispersion-based variability measures (Zhang et al., 2025; Liu et al., 2024), as they may reflect different neural mechanisms and have different functional consequences. Consequently, while our findings are directionally compatible with variability-quenching predictions, claims of direct mechanistic extension should be tempered pending analyses that explicitly decompose amplitude and variability components. 4.1.2.Evidence from Null Complexity Results The null findings for Permutation Entropy (PE) and Lempel–Ziv (LZ) complexity provide additional mechanistic insight. Complexity measures aim to quantify signal regularity, predictability, and information-theoretic entropy, roperties orthogonal to simple amplitude or energy. The observation that RMS (an amplitude/energy proxy) significantly predicted P300 amplitude, whereas PE and LZ did not, suggests the observed coupling is more closely tied to signal magnitude than to complexity or entropy per se. This pattern favors amplitude-dependent interpretations (resource competition, refractory effects, or state-dependent gain tied to signal strength) over complexity-based or entropy-related accounts. We acknowledge that the null complexity results may also reflect methodological limitations : PE and LZ are typically most reliable on longer signal segments (> 200 samples; Bai et al., 2015; Lau et al., 2022), and our short 0–150 ms window (~ 75 samples at 512 Hz effective rate) may have insufficient data points for robust complexity estimation. Nonetheless, the contrast between significant RMS and null complexity effects supports an amplitude-centric interpretation. 4.1.3. Future Decomposition Analyses Critically, the current data cannot definitively adjudicate between state-dependent, resource-based, refractory, and variability-quenching mechanisms. Future studies should explicitly decompose early-window features into: Mean amplitude (to isolate pure magnitude effects and test resource/refractory accounts) Standard deviation after mean removal (to quantify within-trial variability independent of amplitude) Across-trial variance measures (e.g., trial-to-trial power fluctuations, coefficient of variation) to directly test variability-quenching hypotheses Such decomposition would allow formal comparison of competing models and clarify the relative contributions of amplitude-based, variability-based, and state-dependent mechanisms. 4.2 Effect Size, Practical Significance, and Methodological Value Although the negative relationship between early post-stimulus activity and P300 amplitude was statistically significant (p = 0.0085, two-tailed), the effect size was notably small (R² = 0.0042, or 0.42% of variance explained). To contextualize this magnitude following points should be addressed. 4.2.1. Comparison to Experimental Manipulation In the same mixed-effects model, the stimulus condition (Target vs. Standard) yielded a standardized coefficient of β = 0.821 (SE = 0.048, z = 17.10, p < 0.001), representing an effect approximately 13 times larger than that of early RMS (β = −0.064). Put differently, being a Target trial versus a Standard trial has over an order of magnitude stronger association with P300 amplitude than does early signal magnitude within the same trial. This comparison highlights that trial-type (i.e., task-relevant cognitive categorization) dominates P300 variance, whereas early sensory state exerts only a minor modulatory influence. 4.2.2. Comparison to Typical ERP Effect Sizes Clinical and group-level P300 studies typically report effect sizes (Cohen's d or partial η²) in the range of 0.5–1.5 for condition or group differences (Polich, 2007; Tan et al., 2025), corresponding to ~ 10–30% variance explained. The present 0.42% explained variance is thus two orders of magnitude smaller than typical experimental or clinical P300 effects . This reinforces the interpretation that early–late coupling, while real, is a subtle modulator rather than a primary driver. 4.2.3. Implications for Biomarker Utility From a practical standpoint, the small effect size implies that simple early-window RMS is unlikely to serve as a robust single-trial biomarker of P300 amplitude in isolation, despite its statistical reliability. Single-trial P300 prediction or classification applications (e.g., brain–computer interfaces, cognitive state monitoring) would benefit minimally from including early RMS as a univariate feature. Future prediction-focused work should prioritize multivariate models incorporating pre-stimulus state (e.g., alpha power; Lago et al., 2023), topographic patterns (Murray et al., 2008), connectivity features (Koenig & Marquardt, 2020), and trial history (Hoy et al., 2021) rather than relying on simple scalar early–late couplings. 4.2.4. Methodological Value: Establishing a Quantitative Constraint Nevertheless, establishing this lower bound is methodologically valuable for several reasons: High statistical power : Post-hoc power analysis indicated achieved power of 0.85 for detecting the observed effect, well above conventional thresholds. Combined with the large trial count (N = 1,661), rigorous mixed-effects modeling, and comprehensive diagnostics, this ensures the small effect is unlikely to be a false negative or artifact of underpowered design. Constraint on theories : The finding demonstrates that trial-to-trial P300 variability is not merely a deterministic propagation of early sensory responses. The substantial unexplained variance (> 99.5%) indicates that P300 amplitude is predominantly driven by: Later, endogenous cognitive processes (e.g., context updating, decision dynamics; Twomey et al., 2015) Pre-stimulus state factors not captured by post-stimulus RMS (e.g., pre-stimulus alpha power, arousal; Studenova et al., 2023) Multivariate network-level features (e.g., functional connectivity, distributed representations; Murray et al., 2008) Benchmark for computational models : The precise quantitative estimate (β = −0.064, R² = 0.0042) provides a reference point for calibrating computational models of P300 generation. Models incorporating early sensory state as an input should reproduce this small negative coupling; stronger coupling would suggest model misspecification or overfitting. Alignment with transparency and reproducibility standards : The study exemplifies current best practices in ERP research, full model diagnostics, power analysis, open data and code, explicit acknowledgment of small effects (Paul et al., 2021; Clayson et al., 2022). This approach counters the tendency to selectively report large, statistically significant effects (the "file drawer" problem) and contributes to a more accurate cumulative literature on P300 determinants. In sum, the small effect size should not be seen as a limitation per se, but rather as a well-characterized empirical constraint that informs theory development, model validation, and future experimental design. 4.3 Relationship to Previous Research The present findings intersect with multiple strands of prior work on P300, neural variability, and single-trial ERP modelling. 4.3.1. Neural Variability Quenching Churchland et al. (2010) demonstrated that stimulus onset quenches neural variability (measured as Fano factor) across cortical areas, a phenomenon thought to enhance information processing by stabilizing neural representations. Arazi et al. (2017) extended this to human EEG, showing that individuals with larger stimulus-evoked reductions in trial-to-trial EEG power variability exhibit better perceptual discrimination. While our findings are directionally consistent (lower early signal energy leads higher P300, suggesting quieter early states may be favorable), the methodological approaches differ fundamentally: Variability-quenching studies quantify across-trial variance (e.g., coefficient of variation of power, Fano factor). The present RMS measure reflects within-trial signal energy , conflating mean amplitude and within-trial fluctuation. These are conceptually and mathematically distinct , and direct mechanistic claims linking our RMS–P300 coupling to variability quenching must be tempered. Future work separating amplitude from dispersion-based variability (Zhang et al., 2025; Liu et al., 2024) is needed to test whether true variability quenching predicts P300 amplitude independently of amplitude-based effects. 4.3.2. Single-Trial P300 Analysis and Pre-Stimulus State Recent work has increasingly focused on trial-level predictors of P300 amplitude and latency. For example: Studenova et al. (2023) demonstrated that event-related modulation of alpha rhythm (8–12 Hz) explains P300 generation: trials with larger alpha power decreases show larger P300s, consistent with alpha indexing an inhibitory state that, when released, facilitates P300 generation. Lago et al. (2023) found that pre-stimulus alpha power predicts trial-by-trial ERP variation in linguistic processing, supporting the view that neural state at stimulus onset biases subsequent processing. Murphy et al. (2016) showed that pupil-linked arousal and urgency signals modulate P300 amplitude, reflecting state-dependent gain control. Our contribution adds early post-stimulus signal magnitude to this growing list of single-trial predictors, with the explicit caveat that its contribution is small in magnitude . This aligns with a broader pattern: univariate sensory metrics (e.g., single-electrode RMS, early ERP peak amplitude) typically explain modest P300 variance (< 5%), whereas multivariate or model-based features (e.g., prediction error, accumulated evidence, pre-stimulus oscillatory patterns) account for substantially more (Hoy et al., 2021; Twomey et al., 2015). This pattern suggests that P300 generation is a complex, multi-determined process not reducible to simple early sensory strength. 4.3.3. Resource-Limited Models of ERP Generation The observed negative coupling resonates with resource-limited models of attention and cognitive processing, which predict amplitude trade-offs when multiple processes compete for finite capacity (Kok, 2001; Polich, 2007; Lavie & Torralbo, 2010). However, modern resource-allocation models predict that when resources are genuinely limiting, capacity constraints should account for 15–30% of performance variance (de Ron et al., 2023). The present 0.42% explained variance is two orders of magnitude smaller, suggesting that resource competition, if operative, is a weak modulator in this paradigm. This may reflect: Temporal separation : The 150–300 ms gap between early sensory and P300 windows may allow sufficient recovery such that resource depletion is minimal by the P300 onset. Distinct neural generators : Early sensory components (N1, P2; fronto-central) and P300 (parietal, centro-parietal) have partially distinct neural sources, reducing competition for local resources. Task simplicity : The auditory oddball is a simple detection task with minimal cognitive load, leaving ample spare capacity. Future work in higher-load paradigms (e.g., dual-task, working memory) could test whether early–late resource competition strengthens under increased demand. 4.3.4. P300 as a Decision Variable Twomey et al. (2015) and O'Connell et al. (2012) have conceptualized the P300 as a build-to-threshold decision variable that accumulates sensory evidence over time until reaching a response criterion. Under this framework, trial-to-trial P300 amplitude variation partly reflects differences in: Drift rate : The rate of evidence accumulation Starting point : The baseline level of accumulated evidence Decision threshold : The criterion for response execution Our finding of early–late coupling can be interpreted within this framework: early signal magnitude (RMS) may exert a weak upstream bias on drift rate or starting point. For example, trials with high early RMS might reflect slightly noisier or over-reactive initial sensory encoding, subtly perturbing the accumulation process and reducing terminal P300 amplitude. However, the extremely small effect size (R² = 0.0042) indicates this influence is minimal compared to endogenous decision dynamics , such as expectation, task relevance, and response urgency (Murphy et al., 2016). This supports viewing early RMS as one of many minor contributors rather than a controlling factor in P300 generation. 4.3.5. Transparent Reporting and Reproducibility Standards The present study aligns with emerging transparency and reproducibility standards in ERP research (Paul et al., 2021; Clayson et al., 2022; Kappenman et al., 2021). Specifically: Full model diagnostics (Q-Q plots, Shapiro–Wilk tests, homoscedasticity checks) are reported. Power analysis is conducted and reported. Open data (OSF: https://osf.io/thsqg/ , https://osf.io/dr5bu/ ) and open code (GitHub: https://github.com/erbiber/p300-entropy/ ) are provided for full reproducibility. Small effect sizes are reported transparently and interpreted cautiously rather than selectively highlighted or inflated. This approach counters publication bias toward large, statistically significant effects and contributes to a more accurate cumulative literature on P300 determinants. As Paul et al. (2021) emphasize, "negative" or small, precisely estimated effects are methodologically valuable for constraining theories and preventing over-interpretation. 4.4 Limitations Several limitations warrant acknowledgment and should inform interpretation and future research. 4.4.1. Single Dataset and Limited Generalizability All analyses derive from the ERP CORE P300 dataset (Kappenman et al., 2021; N = 40 participants). While this dataset represents a gold standard for standardized ERP research with high-quality preprocessing and open sharing, findings from a single sample may not generalize. Independent replication in: Different samples (varying age, cultural background, clinical status) Alternative paradigms (visual oddball, three-stimulus paradigm, somatosensory modalities) Different recording setups (higher electrode density, source-space analysis) is essential before drawing general conclusions about early–late coupling across contexts. 4.4.2. Measure Ambiguity: RMS Conflates Amplitude and Variability As extensively discussed, RMS conflates mean signal deflection and within-trial signal variability. Without control analyses explicitly decomposing these components (e.g., modeling mean amplitude, variance after mean removal, and across-trial variance separately), mechanistic interpretation remains tentative . Future work should employ: Mean amplitude in the early window (to isolate pure magnitude effects) Standard deviation after mean removal (to isolate within-trial variability) Across-trial variance measures (e.g., coefficient of variation, Fano-like metrics; Zhang et al., 2025; Liu et al., 2024) to rigorously test amplitude-based versus variability-based hypotheses. 4.4.3. Small Effect Size Limits Mechanistic Leverage The extremely small R² (0.0042) means that most P300 variance arises from factors not captured by early RMS . While this establishes a useful lower bound, it limits the depth of mechanistic inference. Multivariate models incorporating additional trial-level covariates (pre-stimulus alpha power, reaction time, stimulus history, arousal; Lago et al., 2023; Murphy et al., 2016) could explain substantially more variance and clarify the unique contribution of early RMS relative to other state variables. 4.4.4. Young Adult, Healthy Sample Participants were university students (mean age = 21.5 years, SD = 2.1) with no history of neurological or psychiatric disorders. Generalization to: Older adults (where P300 amplitude and variability differ; Polich, 2007) Clinical populations (e.g., ADHD, schizophrenia, depression, where P300 abnormalities are well-documented; Tan et al., 2025) Developmental samples (children, adolescents) remains uncertain. Clinical and developmental studies could test whether early–late coupling is disrupted in patient groups, potentially revealing whether state-dependent or resource-based mechanisms contribute to cognitive deficits. 4.4.5. Correlational Design Precludes Causal Inference The study is observational; causal direction cannot be inferred . While we interpret early RMS as a predictor of P300 amplitude, the relationship could reflect: Bidirectional causality : Common upstream factors (e.g., pre-stimulus state, arousal) influencing both early and late processing. Reverse causation : P300-related processes influencing trial selection or post-hoc perception of early activity (unlikely but not formally ruled out). Experimental manipulations targeting early sensory activity (e.g., TMS to modulate early cortical excitability, pharmacological interventions affecting sensory gain, or tDCS to bias baseline state) would provide stronger causal tests. 4.4.6. Null Complexity Results May Reflect Methodological Limitations The failure to find effects for Permutation Entropy (PE) and Lempel–Ziv (LZ) complexity may reflect: Inadequate signal length : PE and LZ are most reliable on longer segments (> 200 samples; Bai et al., 2015; Lau et al., 2022). Our 0–150 ms window (~ 75 samples at 512 Hz effective rate) may be too short for robust complexity estimation. Parameter choices : PE embedding dimension and delay, LZ binarization thresholds—all influence sensitivity and may require optimization for short EEG segments. Single-scale limitation : Multiscale complexity measures (e.g., multiscale permutation entropy, hierarchical LZ; Liu et al., 2021) may capture complexity dynamics missed by single-scale metrics. Thus, the null complexity findings should be interpreted cautiously as "no evidence of an effect" rather than "evidence of no effect." Future work with longer segments or multiscale approaches may yet reveal complexity-based relationships. 4.4.7. Figure 1 A Grand-Average Representation The grand-average ERP (Fig. 1 A) represents all 40 participants, but individual subject ERPs were not equally weighted due to differing trial counts (range: 22–79 trials per participant). This may slightly bias the visual representation toward high-trial-count participants. Critically, this does not affect the single-trial mixed-effects analyses, which properly account for unbalanced trial counts via participant-level random effects. Nonetheless, readers should interpret Fig. 1 A as a descriptive summary rather than a statistically weighted average. 4.5 Future Directions This study opens multiple avenues for advancing our understanding of early–late ERP coupling and P300 generation mechanisms. 4.5.1. Decomposition Analyses Separating Amplitude, Within-Trial Variability, and Across-Trial Variance Future work should explicitly decompose early-window features into: Mean amplitude (to test resource competition and refractory hypotheses driven by signal magnitude) Standard deviation after mean removal (to isolate within-trial variability independent of amplitude; Liu et al., 2024) Across-trial variance measures (e.g., trial-to-trial power fluctuations, coefficient of variation, Fano-like metrics; Zhang et al., 2025; Arazi et al., 2017) This decomposition would allow formal comparison of: Amplitude-dependent models (resource, refractory) Variability-quenching models (across-trial variance predicts P300) State-dependent models (amplitude and variability jointly index neural state) and clarify their relative contributions. 4.5.2. Replication and Extension Across Paradigms and Populations Independent replication in: Different paradigms : Visual oddball, three-stimulus (P3a vs. P3b), somatosensory, go/no-go tasks Higher cognitive load : Dual-task, working memory, n-back tasks (to test whether resource competition strengthens under load) Diverse populations : Older adults, clinical samples (ADHD, schizophrenia, depression), developmental cohorts would establish the generality and boundary conditions of early–late coupling. If coupling is stronger in clinical populations or higher-load tasks, this would support resource/state-dependent interpretations; if it remains uniformly small, this would suggest a universal constraint. 4.5.3. Multivariate and Network-Level Modeling Incorporating additional trial-level covariates: Pre-stimulus alpha power (Lago et al., 2023; Studenova et al., 2023) Pupil diameter (arousal; Murphy et al., 2016) Reaction time (decision speed; Twomey et al., 2015) Stimulus history (expectation, adaptation; Hoy et al., 2021) Time-on-task (vigilance, fatigue) could explain substantially more P300 variance and clarify early RMS's unique contribution. Additionally: Topographic and connectivity analyses (Murray et al., 2008; Koenig & Marquardt, 2020) could reveal whether early–late coupling varies by scalp region or functional network. Multivariate pattern analysis (MVPA ) and machine-learning approaches (Carrasco et al., 2024) may identify distributed patterns that predict P300 amplitude more robustly than univariate scalar metrics. 4.5.4. Clinical Applications: Disrupted Coupling in Psychopathology Testing whether early–late coupling differs in clinical populations with known P300 abnormalities (e.g., ADHD, schizophrenia, depression; Tan et al., 2025) could reveal: Whether disrupted state-dependent modulation contributes to cognitive deficits. Whether altered resource allocation (e.g., excessive early resource consumption, inefficient gain control) underlies clinical P300 reductions. Such findings could inform targeted interventions (e.g., neurofeedback training to optimize early neural states, pharmacological modulation of arousal). 4.5.5. Computational and Biophysical Modeling Biophysically realistic neural mass models (e.g., dynamic causal modeling, neural field models) could formalize: Resource competition (shared metabolic pools, attentional capacity) Refractory effects (population-level adaptation, recovery dynamics) State-dependent gain control (baseline excitability, network state transitions) generating quantitative predictions for how early amplitude and variability should jointly influence P300 amplitude. Model-based parameter estimation could then test which mechanisms best account for observed data. 4.6.6. Causal Interventions: TMS, tDCS, and Pharmacology Experimental manipulations targeting early sensory processing: Transcranial Magnetic Stimulation (TMS) : Apply TMS pulses to sensory cortex during the early window (0–150 ms) to modulate N1/P2 amplitude, then measure downstream P300 changes. Transcranial Direct Current Stimulation (tDCS) : Modulate baseline cortical excitability before stimulus onset to bias early sensory responses. Pharmacological interventions : Administer drugs affecting sensory gain (e.g., dopaminergic agents, cholinergic modulators) and assess early–late coupling changes. Such interventions would provide strong causal tests of whether early sensory magnitude causally influences P300 amplitude, and would help distinguish between amplitude-based, state-dependent, and variability-driven mechanisms. 4.6.7. Longitudinal and Within-Subject Designs Tracking early–late coupling within individuals across sessions (days, weeks) could reveal: Whether coupling strength is stable (trait-like) or fluctuates with state (fatigue, arousal, learning). Whether coupling predicts behavioral outcomes (task performance, learning rate). This would clarify whether early–late coupling reflects stable individual differences in neural efficiency or transient state fluctuations. 5. Conclusion In a large, well-validated auditory oddball dataset (N = 40 participants, 1,661 trials), early post-stimulus signal energy (RMS amplitude at 0–150 ms, electrode Fz) showed a small but statistically reliable negative association with subsequent P300 amplitude (300–600 ms, electrode Pz; β = −0.064, p = 0.0085, 95% CI [− 0.112, − 0.016]). The effect size was minimal (R² = 0.0042, or 0.42% of variance explained), indicating that early signal magnitude provides modest modulation rather than decisive control over P300 generation. This finding establishes a precise quantitative constraint on how much a simple univariate early-window amplitude measure can explain trial-to-trial P300 variability under well-controlled conditions. The most conservative interpretation, consistent with the theoretical framework developed in the Introduction and supported by the pattern of results, is that early RMS indexes a momentary neural processing state that weakly biases subsequent context-updating operations ( state-dependent processing ). Alternative or complementary mechanisms; resource competition between early sensory and late cognitive processing stages, and refractory-like effects in overlapping neural populations, remain plausible but are difficult to distinguish given the current data. Critically, because RMS conflates mean signal deflection and within-trial signal variability (Luck, 2014), and because information-theoretic complexity measures (Permutation Entropy, Lempel–Ziv) showed null effects, we interpret the observed coupling as primarily reflecting amplitude-based dynamics (signal magnitude influencing downstream gain or resource availability) rather than variability quenching per se. Direct tests of variability-quenching hypotheses would require explicit quantification of across-trial variance (Arazi et al., 2017; Churchland et al., 2010) or within-trial dispersion after mean removal (Liu et al., 2024), measures not employed in the present study. Despite the small effect size, this study makes several methodologically and theoretically valuable contributions: Establishes a lower bound : The combination of large trial count (N = 1,661), appropriate mixed-effects modeling, full diagnostic validation (normality, homoscedasticity, convergence), and adequate statistical power (achieved power ≈ 0.85) ensures the observed effect is unlikely to be a false negative or artifact of underpowered design. The tight quantitative estimate constrains theories of early–late ERP coupling and provides a benchmark for computational models of P300 generation. Demonstrates that P300 is predominantly endogenously driven : The substantial unexplained variance (> 99.5%) indicates that trial-to-trial P300 variability is not merely a deterministic propagation of early sensory responses. Instead, P300 amplitude is primarily shaped by later, endogenous cognitive processes (e.g., context updating, decision dynamics; Twomey et al., 2015), pre-stimulus state variables (e.g., alpha power; Studenova et al., 2023), and multivariate network-level features not captured by simple scalar early-window metrics. Exemplifies transparency and reproducibility standards : The study follows current best practices in ERP research (Paul et al., 2021; Clayson et al., 2022)—full model diagnostics, explicit power analysis, open data (OSF: https://osf.io/thsqg/ , https://osf.io/dr5bu/ ) , open code (GitHub: https://github.com/erbiber/p300-entropy/ ) , and transparent reporting of small effect sizes. This approach counters publication bias toward large, statistically significant effects and contributes to a more accurate cumulative literature on P300 determinants. Clarifies the RMS measurement ambiguity : By explicitly acknowledging that RMS reflects overall signal energy rather than pure variability, and by contrasting RMS results with null complexity findings, the study highlights the critical importance of careful construct operationalization in ERP research. Future work should decompose early-window features into mean amplitude, within-trial variability (dispersion after mean removal), and across-trial variance to rigorously test amplitude-based versus variability-based hypotheses. Guides future research priorities : The findings suggest that efforts to predict single-trial P300 amplitude should prioritize multivariate models incorporating pre-stimulus oscillatory state (Lago et al., 2023), topographic patterns (Murray et al., 2008), functional connectivity (Koenig & Marquardt, 2020), and trial history (Hoy et al., 2021) rather than relying on simple univariate early–late scalar couplings. Similarly, interventions targeting P300 enhancement (e.g., in neurofeedback, cognitive training, or clinical remediation) may be more effective if they modulate higher-order cognitive states or network dynamics rather than attempting to manipulate early sensory amplitudes directly. In summary, this study demonstrates the value of rigorous single-trial ERP analysis using modern mixed-effects modeling, comprehensive diagnostics, and transparent reporting practices. It underscores the importance of: Transparent reporting of small effect sizes as constraints on theory rather than dismissing them as "non-significant" or inflating them through selective analysis Careful operationalization of theoretical constructs such as "variability," "signal magnitude," and "neural state," with explicit acknowledgment of measurement ambiguities Independent replication in diverse samples, paradigms, and populations before drawing strong mechanistic conclusions Multivariate and network-level approaches to capture the complex, multi-determined nature of P300 generation Future work incorporating decomposition analyses (separating mean amplitude from within-trial and across-trial variability), richer state covariates (pre-stimulus alpha power, pupil-linked arousal, connectivity), and experimental manipulations (TMS, tDCS, pharmacological interventions targeting sensory gain or neural state) will be essential to clarify the mechanisms underlying early–late ERP component coupling and to advance computational models of P300 generation as a build-to-threshold decision variable shaped by momentary neural state. Declarations Acknowledgments The author thanks the ERP CORE team (Emily Kappenman, Steven Luck, and colleagues) for making their data publicly available, and the open-source MNE-Python community for providing robust analysis tools. This study exemplifies transparent reporting practices advocated for ERP research. This work was conducted without external funding and reflects the author's independent research interests at Boğaziçi University. Funding This research received no external funding. Competing Interests The author declares no competing interests that are relevant to the content of this article. Ethics Approval and Consent Data were obtained from the publicly available ERP CORE P300 dataset (Kappenman et al., 2021). All participants provided informed consent. The original study procedures were approved by the University of California, Davis Institutional Review Board as described in Kappenman et al. (2021). Data Availability Raw data are available from the ERP CORE P300 dataset at https://osf.io/thsqg/ Pre-processed data and analysis metrics are available at https://osf.io/dr5bu/ Code Availability Analysis scripts and code are available at https://github.com/erbiber/p300-entropy/ Preprint Statement A version of this manuscript has been posted as a preprint on bioRxiv. https://doi.org/10.64898/2025.12.17.694588 CRediT Author Statement Erkan Biber: Conceptualization; Methodology; Software; Formal analysis; Investigation; Data curation; Visualization; Writing – original draft; Writing – review & editing. References Arazi A, Censor N, Dinstein I (2017) Neural variability quenching predicts individual perceptual abilities. J Neurosci 37(1):97–109. https://doi.org/10.1523/JNEUROSCI.1671-16.2016 Baayen RH, Davidson DJ, Bates DM (2008) Mixed-effects modeling with crossed random effects for subjects and items. J Mem Lang 59(4):390–412. https://doi.org/10.1016/j.jml.2007.12.005 Bai Y, Liang Z, Li X (2015) A permutation Lempel-Ziv complexity measure for EEG analysis. Biomed Signal Process Control 19:102–114. https://doi.org/10.1016/j.bspc.2015.04.002 Bandt C, Pompe B (2002) Permutation entropy: A natural complexity measure for time series. Phys Rev Lett 88(17):174102. https://doi.org/10.1103/PhysRevLett.88.174102 Carrasco CD, Milyavskaya M, Hofmann W (2024) Using multivariate pattern analysis to increase effect sizes for event-related potentials. Psychophysiology 61(7):e14570. https://doi.org/10.1111/psyp.14570 Churchland MM, Yu BM, Cunningham JP, Sugrue LP, Cohen MR, Corrado GS, Newsome WT, Clark AM, Hosseini P, Scott BB, Bradley DC, Smith MA, Kohn A, Movshon JA, Armstrong KM, Moore T, Chang SW, Snyder LH, Lisberger SG, Priebe NJ, Finn IM, Ferster D, Ryu SI, Santhanam G, Sahani M, Shenoy KV (2010) Stimulus onset quenches neural variability: A widespread cortical phenomenon. Nat Neurosci 13(3):369–378. https://doi.org/10.1038/nn.2501 Clayson PE, Baldwin SA, Larson MJ (2013) How does noise affect amplitude and latency measurement of event-related potentials (ERPs)? A methodological critique and simulation study. Psychophysiology 50(2):174–186. https://doi.org/10.1111/psyp.12001 Clayson PE, Carbine KA, Baldwin SA, Larson MJ (2019) Methodological reporting behavior, sample sizes, and statistical power in studies of event-related potentials: Barriers to reproducibility and replicability. Psychophysiology 56(11):e13437. https://doi.org/10.1111/psyp.13437 Clayson PE, Carbine KA, Baldwin SA, Olsen JA, Larson MJ (2022) Using generalizability theory and the ERP Reliability Analysis (ERA) Toolbox for assessing test-retest reliability of ERP scores Part 2: Application to metrics of cognitive control. Int J Psychophysiol 166:174–187. https://doi.org/10.1016/j.ijpsycho.2021.01.010 Cohen MX (2022) Decoding continuous variables from event-related potential (ERP) data with machine learning. Psychophysiology 59(1):e13941. https://doi.org/10.1111/psyp.13941 de Ron J, van Geert PLC, Steenbakkers L (2023) Towards a general modelling framework of resource competition in cognitive development. Dev Rev 69:101109. https://doi.org/10.1016/j.dr.2023.101109 Donchin E (1981) Surprise!...Surprise? Psychophysiology 18(5):493–513. https://doi.org/10.1111/j.1469-8986.1981.tb01815.x Grady CL (2012) The cognitive neuroscience of ageing. Nat Rev Neurosci 13(7):491–505. https://doi.org/10.1038/nrn3256 Gramfort A, Luessi M, Larson E, Engemann DA, Strohmeier D, Brodbeck C, Goj L, Jas M, Brooks T, Parkkonen L, Hämäläinen M (2013) MEG and EEG data analysis with MNE-Python. Front Neurosci 7:267. https://doi.org/10.3389/fnins.2013.00267 Heise MJ, Mon SK, Bowman LC (2022) Utility of linear mixed effects models for event-related potential research with infants and children. Dev Cogn Neurosci 54:101070. https://doi.org/10.1016/j.dcn.2022.101070 Hoy CW, Steiner H, Knight RT (2021) Single-trial modeling separates multiple overlapping prediction errors during reward processing in human electrophysiology. Commun Biol 4:910. https://doi.org/10.1038/s42003-021-02426-1 Kappenman ES, Farrens JL, Zhang W, Stewart AX, Luck SJ (2021) ERP CORE: An open resource for human event-related potential research. NeuroImage 225:117465. https://doi.org/10.1016/j.neuroimage.2020.117465 Koenig T, Marquardt C (2020) Electroencephalography and neuroimaging of brain oscillations in health and disease. Brain Topogr 33(2):157–171. https://doi.org/10.1007/s10548-020-00775-4 Kok A (2001) On the utility of P3 amplitude as a measure of processing capacity. Psychophysiology 38(3):557–577. https://doi.org/10.1017/S0048577201990559 Lago S, Stocco A, Bölte J, Oltrogge E, Kliegl R (2023) Trial-by-trial fluctuations of pre-stimulus alpha power predict ERP amplitude during sentence comprehension. Psychophysiology 60(12):e14388. https://doi.org/10.1111/psyp.14388 Lau ZJ, Pham T, Chen SHA, Makowski D (2022) Brain entropy, fractal dimensions and predictability: A review of complexity measures for EEG in healthy and neuropsychiatric populations. Eur J Neurosci 56(7):5047–5069. https://doi.org/10.1111/ejn.5772 Lavie N, Torralbo A (2010) Dilution: A theoretical burden or just load? A reply to Tsal and Benoni (2010). J Exp Psychol Hum Percept Perform 36(6):1657–1664. https://doi.org/10.1037/a0020733 Lempel A, Ziv J (1976) On the complexity of finite sequences. IEEE Trans Inf Theory 22(1):75–81. https://doi.org/10.1109/TIT.1976.1055501 Li X, Wang Y, Chen S, Zhao L, Ye X (2025) Attentional resource consumption of verbal-humor processing: Evidence from event-related potentials and event-related oscillations. Cogn Process 26(1):93–112. https://doi.org/10.1007/s10339-024-00344-5 Liu S, Wang X, Zhao L, Li J, Wang B, Jiang Y, Chen Y, Zhang Y (2021) Multiscale permutation Lempel–Ziv complexity measure for biomedical signal analysis. Entropy 23(6):803. https://doi.org/10.3390/e23060803 Liu J, Zhao M, Wang K, Li J, Manyande A (2024) Analysis of modulations of mental fatigue on intra- and inter-subject EEG variability. J Neurosci Methods 407:110143. https://doi.org/10.1016/j.jneumeth.2024.110143 Luck SJ (2014) An introduction to the event-related potential technique, 2nd edn. MIT Press, Cambridge, MA Mazaheri A, Nieuwenhuis ILC, van Dijk H, Jensen O (2009) Prestimulus alpha and mu activity predicts failure to inhibit motor responses. Hum Brain Mapp 30(6):1791–1800. https://doi.org/10.1002/hbm.20763 Mon SK, Durbin CE, Rappaport BI, Tejavibulya L, Weissman DG, Hennefield L, Barch DM (2024) Leveraging mixed-effects location scale models to assess the influence of covariates on event-related potential amplitude and variability. Psychophysiology 61(4):e14470. https://doi.org/10.1111/psyp.14470 Murphy PR, Boonstra E, Nieuwenhuis S (2016) Global gain modulation generates time-dependent urgency during perceptual choice in humans. Nat Commun 7:13526. https://doi.org/10.1038/ncomms13526 Murray MM, Brunet D, Michel CM (2008) Topographic ERP analyses: A step-by-step tutorial review. Brain Topogr 20(4):249–264. https://doi.org/10.1007/s10548-008-0054-5 Neville HJ, Schmidt A, Kutas M (1986) Altered visual-evoked potentials in congenitally deaf adults. Brain Res 266(1):127–132. https://doi.org/10.1016/0006-8993(83)91314-8 O'Connell RG, Dockree PM, Kelly SP (2012) A supramodal accumulation-to-bound signal that determines perceptual decisions in humans. Nat Neurosci 15(12):1729–1735. https://doi.org/10.1038/nn.3248 Paul M, Govaart GH, Schettino A (2021) Making ERP research more transparent: Guidelines for preregistration. Int J Psychophysiol 164:52–63. https://doi.org/10.1016/j.ijpsycho.2021.02.016 Polich J (2007) Updating P300: An integrative theory of P3a and P3b. Clin Neurophysiol 118(10):2128–2148. https://doi.org/10.1016/j.clinph.2007.04.019 Johannsen J, Röder B, Knösche TR, Rogenbuck F, Holz J, Ohl FW (2014) Uni- and crossmodal refractory period effects of event-related potentials provide insights into the development of multisensory processing. Front Hum Neurosci 8:552. https://doi.org/10.3389/fnhum.2014.00552 Straub C, Finkelhor D, Hunter W, Dobrovolny KA (2020) Reproducibility of individual effect sizes in meta-analyses in psychology: Estimating the reliability of effect size estimates. PLoS ONE 15(5):e0233107. https://doi.org/10.1371/journal.pone.0233107 Studenova AA, Forster C, Engemann DA, Hensch T, Sander C, Mauche N, Hegerl U, Nikulin VV (2023) Event-related modulation of alpha rhythm explains the auditory P300 evoked response in EEG. eLife 12:e88367. https://doi.org/10.7554/eLife.88367 Tan C, Li Y, Chen S, Wang X, Liu J (2025) P300 event-related potentials as diagnostic biomarkers for attention deficit hyperactivity disorder. Front Psychiatry 16:1590850. https://doi.org/10.3389/fpsyt.2025.1590850 Twomey DM, Murphy PR, Kelly SP, O'Connell RG (2015) The classic P300 encodes a build-to-threshold decision variable. Eur J Neurosci 42(1):1636–1643. https://doi.org/10.1111/ejn.12936 Wolff A, de la Vega I, Zenon A, Pezzulo G, Boehler CN (2019) Neural variability quenching during decision-making: Neural individuality and its prestimulus complexity. NeuroImage 192:1–14. https://doi.org/10.1016/j.neuroimage.2019.02.070 Zhang LB, Hu L, Liu Y (2025) Neural variability reliably encodes interindividual differences in the perception of pain intensity. PLoS Biol 23(10):e3003470. https://doi.org/10.1371/journal.pbio.3003470 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 20 Apr, 2026 Reviews received at journal 20 Apr, 2026 Reviewers agreed at journal 31 Mar, 2026 Reviews received at journal 31 Mar, 2026 Reviewers agreed at journal 14 Mar, 2026 Reviewers invited by journal 12 Mar, 2026 Editor assigned by journal 23 Jan, 2026 Submission checks completed at journal 22 Jan, 2026 First submitted to journal 21 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8657074","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":580182880,"identity":"a22f8c7d-90a7-48a0-9c93-d98751b702a6","order_by":0,"name":"Erkan Biber","email":"data:image/png;base64,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","orcid":"","institution":"Boğaziçi University","correspondingAuthor":true,"prefix":"","firstName":"Erkan","middleName":"","lastName":"Biber","suffix":""}],"badges":[],"createdAt":"2026-01-21 08:29:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8657074/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8657074/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101219714,"identity":"b72bf1bc-e10b-487c-997a-759f075d8824","added_by":"auto","created_at":"2026-01-27 11:28:36","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":554921,"visible":true,"origin":"","legend":"\u003cp\u003eSingle-trial coupling between early signal magnitude and P300 amplitude\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(\u003c/em\u003eA)\u0026nbsp;Grand-average ERPs were computed by first averaging trials within each of the 40 participants, then averaging across participants. Shaded regions show ±1 SEM across participants.\u0026nbsp;Note on weighting:\u0026nbsp;Individual participants contributed different numbers of trials to the grand average (range: 22–79 trials/participant, Mean = 41.5, SD = 14.2), so the grand average reflects an unweighted mean of subject averages. The gray bar indicates the P300 measurement window (300–600 ms). Target stimuli elicited robust P300 enhancement relative to Standards.\u003c/p\u003e\n\u003cp\u003e(B)\u0026nbsp;Trial-level relationship between early RMS and P300 amplitude. Each point represents a single trial (N\u0026nbsp;= 1,661; blue = Standard, red = Target).\u0026nbsp;X-axis:\u0026nbsp;Early RMS (0–150 ms at Fz), log-transformed and z-scored within participant.\u0026nbsp;Y-axis:\u0026nbsp;P300 amplitude (300–600 ms at P\u003csub\u003ez\u003c/sub\u003e), z-scored within participant. The black line shows the linear regression fit (β = −0.064, p = 0.0085, R² = 0.0042) demonstrating a small negative association. Substantial scatter (points overlapping in the dense central region) reflects the modest effect size and dominance of other unmeasured factors.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8657074/v1/61d493d3c3d2e220d273cb27.png"},{"id":101219701,"identity":"d42971bd-7eeb-4d28-acf6-30f112919105","added_by":"auto","created_at":"2026-01-27 11:28:26","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":556326,"visible":true,"origin":"","legend":"\u003cp\u003eQ-Q Plot of Standardized Residuals\u003c/p\u003e\n\u003cp\u003eStandardized residuals are plotted against theoretical quantiles from a standard normal distribution. The close alignment between observed (blue points) and theoretical (line) quantiles across the full range indicates residuals are approximately normally distributed, with minimal systematic deviation.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8657074/v1/9425c834eaa846c3d9d062b6.png"},{"id":101219700,"identity":"fe0e4e78-fca1-404a-b88c-1a133f9631d8","added_by":"auto","created_at":"2026-01-27 11:28:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":644662,"visible":true,"origin":"","legend":"\u003cp\u003eResiduals vs. Fitted Values\u003c/p\u003e\n\u003cp\u003eStandardized residuals are plotted against model-predicted (fitted) values from the linear mixed-effects model. The symmetric distribution around the zero line (red dashed line) with no systematic pattern or funnel shape indicates homogeneous variance across the range of predictions, satisfying the homoscedasticity assumption.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8657074/v1/d5207e72fde0272594fd4b93.png"},{"id":101219713,"identity":"8abe0b40-9195-42a5-8e16-d5a9156f29fa","added_by":"auto","created_at":"2026-01-27 11:28:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":68337,"visible":true,"origin":"","legend":"\u003cp\u003eHistogram of Standardized Residuals\u003c/p\u003e\n\u003cp\u003eThe distribution of standardized residuals is approximately normal, centered at zero, with slight departures at extreme tails. The shape is consistent with expectations for a large sample size (N = 1,661) with minor deviations from perfect normality.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8657074/v1/8a153fe4eeb0d455029c5ab4.png"},{"id":101219716,"identity":"05d25dea-5efd-48a5-8a56-e406ecdd2586","added_by":"auto","created_at":"2026-01-27 11:28:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5771746,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8657074/v1/093a748d-c09a-4fbe-b86b-6de5f388d8f6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Early Post-Stimulus Activity Negatively Predicts P300 Amplitude: A Single-Trial Analysis of the Auditory Oddball Task","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe P300 event-related potential (ERP) is a core electrophysiological marker of attention and context updating in cognitive neuroscience, reflecting the neural response to task-relevant, unpredictable stimuli within working memory (Donchin, 1981; Polich, 2007). At the group level, P300 morphology and topography are well characterized; however, trial-by-trial dynamics underlying P300 amplitude variability remain incompletely understood. A key unresolved question is whether the neural state during early post-stimulus processing (0\u0026ndash;150 ms) meaningfully constrains the magnitude of the subsequent P300 response (300\u0026ndash;600 ms), and if so, whether this reflects amplitude-dependent or variability-dependent mechanisms.\u003c/p\u003e \u003cp\u003eRecent computational and empirical work has reconceptualized the P300 as a build-to-threshold decision variable that accumulates evidence toward a response criterion (Twomey et al., 2015). Under this framework, trial-to-trial P300 amplitude variation reflects fluctuations in evidence-accumulation dynamics, including drift rate and baseline excitability (Murphy et al., 2016). This perspective raises a mechanistic question: does the momentary neural state reflected in early post-stimulus signal magnitude modulate the initial conditions or gain of this accumulation process?\u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1 Competing Theoretical Predictions\u003c/h2\u003e \u003cp\u003eFour theoretical frameworks make distinct predictions about early\u0026ndash;late ERP coupling:\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section3\"\u003e \u003ch2\u003e1.1.1. State-Dependent Processing (Primary Interpretation)\u003c/h2\u003e \u003cp\u003eState-dependent or gain control perspectives propose that early post-stimulus neural activity indexes a momentary processing state that biases downstream cognitive computations (Churchland et al., 2010; Arazi et al., 2017). Specifically, the amplitude and stability of early sensory responses (N1, ~\u0026thinsp;100 ms; P2, ~\u0026thinsp;200 ms) may set the gain or baseline excitability for subsequent context-updating operations. Trials with moderate early activity may reflect optimal neural states for robust P300 generation, while excessively high or low early activity may reflect suboptimal states, slightly dampening subsequent processing. This interpretation is consistent with recent findings that pre-stimulus alpha amplitude, a proxy for neural state stability, predicts both trial-by-trial variability quenching and downstream ERP components (Studenova et al., 2023; Lago et al., 2023). A state-dependent account predicts a U-shaped or non-monotonic relationship between early activity and P300, or more conservatively, a modest linear coupling reflecting state-dependent biasing.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e \u003ch2\u003e1.1.2. Resource Competition (Alternative Mechanism)\u003c/h2\u003e \u003cp\u003eThe resource competition account posits that neural processing capacity is finite (Kok, 2001; Polich, 2007; Lavie \u0026amp; Torralbo, 2010). Under this view, if early sensory processing consumes substantial metabolic or computational resources, fewer resources remain for subsequent P300 generation, predicting a negative correlation between early and late amplitudes. This mechanism aligns with perceptual load theory and extends to ERP components. A strong resource competition model would predict substantial negative coupling (large effect sizes).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e1.1.3. Refractory-Like Effects\u003c/h2\u003e \u003cp\u003eNeural populations that participate in both early sensory and late P300 processing may exhibit transient refractoriness. Strong early activation (large N1/P2) may leave overlapping neural populations temporarily less excitable, dampening the subsequent P300 (Neville et al., 1986; Johannsen et al., 2014). This predicts a negative relationship, mechanistically distinct from resource competition but observationally similar.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e1.1.4. Facilitation / Positive Coupling\u003c/h2\u003e \u003cp\u003eConversely, high-fidelity early sensory representation (large N1/P2) may more effectively trigger downstream context-updating cascades, predicting a positive correlation between early and late amplitudes (gain control in the classical sense).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e1.2. The Variability-Amplitude Measurement Ambiguity\u003c/h2\u003e \u003cp\u003eA critical methodological issue complicates mechanistic interpretation: most univariate measures of \"early activity,\" including root mean square (RMS) amplitude, conflate mean signal deflection with within-trial signal variability (Luck, 2014). RMS reflects overall signal energy (i.e., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{\\frac{1}{N}\\sum\\:{x}^{2}\\left(t\\right)}\\)\u003c/span\u003e\u003c/span\u003e) rather than pure dispersion after mean removal. This ambiguity creates interpretive challenges.\u003c/p\u003e \u003cp\u003eRecent neuroscience literature on neural variability quenching proposes that stimulus onset reduces ongoing neural noise, stabilizing representations and enhancing perceptual discrimination (Churchland et al., 2010; Arazi et al., 2017). At the trial level, individuals with larger stimulus-evoked variability reduction show better perceptual performance (Arazi et al., 2017). However, this variability-quenching effect typically operates on across-trial measures (e.g., Fano factor of neural spiking or trial-to-trial EEG power fluctuations) rather than within-trial signal energy. A within-trial RMS metric captures signal energy but does not isolate variability per se. Consequently, a negative early RMS\u0026ndash;P300 relationship could reflect:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eAmplitude-dependent mechanisms: Resource competition or refractory effects driven by signal magnitude\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eVariability-related mechanisms: Higher early signal energy correlated with lower within-trial noise, reflecting a more stable neural state favorable to P300 generation\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eState-dependent gain effects: Early neural state (reflected in both amplitude and variability) biasing the gain of downstream processing\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eDistinguishing these mechanisms requires rigorous single-trial quantification and, ideally, complementary measures that separately quantify amplitude and variability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e1.3. Single-Trial Approaches and Mixed-Effects Modeling\u003c/h2\u003e \u003cp\u003eModern ERP research increasingly employs single-trial analysis with mixed-effects models (LMM) to account for hierarchical data structure, trials nested within subjects, with unbalanced trial counts, and to quantify individual differences in early\u0026ndash;late coupling (Twomey et al., 2015; Hoy et al., 2021; Heise et al., 2022). LMMs provide several advantages over traditional averaging approaches: (1) retain trial-level resolution, (2) properly handle unbalanced designs and subject-level variability, (3) provide uncertainty estimates for individual regression slopes, and (4) enable formal comparison of competing random-effects structures via information criteria (Baayen et al., 2008). Recent reviews emphasize that LMMs are now the recommended approach for hierarchical ERP data (Heise et al., 2022), particularly when testing trial-by-trial predictors.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e1.4. Study Aims and Hypotheses\u003c/h2\u003e \u003cp\u003eThis study addresses three primary questions:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDirectional relationship\u003c/b\u003e: Is there a statistically reliable single-trial association between early post-stimulus signal magnitude (RMS at 0\u0026ndash;150 ms, electrode Fz) and subsequent P300 amplitude (300\u0026ndash;600 ms, electrode Pz)?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eEffect magnitude and mechanism\u003c/b\u003e: What is the magnitude of this relationship? Does it support state-dependent, resource-based, or refractory hypotheses? Critically, how much trial-level P300 variance does early RMS explain?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAmplitude versus variability\u003c/b\u003e: Does the observed coupling reflect amplitude-dependent mechanisms (resource/refractory) or variability-related state effects?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eWe analyzed single-trial EEG data from the ERP CORE auditory oddball dataset (Kappenman et al., 2021), a large, standardized, openly available resource, using linear mixed-effects regression to quantify early\u0026ndash;late coupling while properly accounting for subject-level random effects and individual differences in coupling strength. We report full model diagnostics (residual normality, homoscedasticity, convergence) consistent with current transparency and reproducibility standards (Paul et al., 2021; Clayson et al., 2022).\u003c/p\u003e \u003cp\u003eWe interpret findings cautiously, acknowledging that (1) RMS reflects signal energy rather than pure variability, (2) the exploratory nature of this single-trial analysis requires independent replication, and (3) small effect sizes, while statistically reliable, may require multivariate or network-level approaches for practical prediction. Our primary contribution is to establish a precise lower bound on how much a simple univariate early-window amplitude measure can explain P300 trial-to-trial variability, a methodologically valuable constraint regardless of effect size.\u003c/p\u003e \u003c/div\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Participants\u003c/h2\u003e \u003cp\u003eData were obtained from the publicly available ERP CORE database (Kappenman et al., 2021), which provides standardized ERP paradigms with high quality pre-processing. The P300 dataset included 40 healthy young adults (25 female, 15 male; mean age\u0026thinsp;=\u0026thinsp;21.5 years, SD\u0026thinsp;=\u0026thinsp;2.1) recruited from the University of California, Davis community. All participants provided informed consent in accordance with institutional review board approval. Participants had normal hearing and no history of neurological or psychiatric disorders.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Stimuli and Procedure\u003c/h2\u003e \u003cp\u003e Participants completed an active auditory oddball task with the following parameters:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eStandard tones: 1000 Hz, 80% probability\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTarget (\"oddball\") tones: 2000 Hz, 20% probability\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eBoth stimuli were presented binaurally at 75 dB SPL with 100 ms duration (10 ms rise/fall times). Inter stimulus interval varied randomly between 1100 and 1500 ms. Participants pressed a button on a gamepad with their dominant hand whenever they detected a target tone. Each session comprised 200 trials (160 standard, 40 target) presented in a single\u0026thinsp;~\u0026thinsp;6 minute block.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e2.3 EEG Recording and Pre-processing\u003c/h2\u003e \u003cp\u003eContinuous EEG was recorded using a Biosemi ActiveTwo system with 30 active Ag/AgCl electrodes positioned according to the international 10\u0026ndash;20 system. Data were digitized at 1024 Hz.\u003c/p\u003e \u003cp\u003ePre-processing was performed using MNE-Python v1.x (Gramfort et al., 2013) following standardized ERP analysis procedures:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eFiltering\u003c/b\u003e: Bandpass filter 0.1\u0026ndash;30 Hz (FIR design, zero phase)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eArtifact correction\u003c/b\u003e: Independent Component Analysis (ICA) to identify and remove blink and saccade artifacts\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eReferencing\u003c/b\u003e: Re-referenced to average of all scalp electrodes\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eEpoching\u003c/b\u003e: Segmentation from \u0026minus;\u0026thinsp;200 to 800 ms relative to stimulus onset\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBaseline correction\u003c/b\u003e: Subtraction of pre-stimulus baseline (\u0026minus;\u0026thinsp;200 to 0 ms)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eRejection\u003c/b\u003e: Epochs with peak-to-peak amplitude\u0026thinsp;\u0026gt;\u0026thinsp;100 \u0026micro;V in any channel were excluded\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eAfter pre-processing, an average of 41.5 trials per participant (range: 22\u0026ndash;79) were retained, yielding \u003cem\u003e1,661 trials\u003c/em\u003e across all participants. The wide range in retained trials reflects individual differences in artifact rates; five participants contributed\u0026thinsp;\u0026lt;\u0026thinsp;30 trials.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Single-Trial Metrics\u003c/h2\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e2.4.1.Early Signal Magnitude (0\u0026ndash;150 ms):\u003c/h2\u003e \u003cp\u003eEarly post-stimulus activity was quantified as the root mean square (RMS) amplitude at electrode Fz in the 0\u0026ndash;150 ms window\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:RMS=\\sqrt{\\frac{1}{N}{\\sum\\:}_{t=1}^{N}{x}^{2}\\left(t\\right)}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere x(t) is the voltage at time point t, and N is the number of time points in the window (75 samples at 512 Hz). This window captures early sensory components (N1\u0026thinsp;~\u0026thinsp;100 ms, P2\u0026thinsp;~\u0026thinsp;200 ms) and reflects initial cortical responses. RMS values were log-transformed to reduce skewness\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{RMS}_{log}=\\text{l}\\text{o}\\text{g}(RMS+{10}^{-12})$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eNote on Interpretation\u003c/strong\u003e \u003cp\u003eAs shown in the equation, RMS amplitude reflects overall signal energy and is influenced by both the mean deflection (DC offset) and within-trial fluctuation (AC variance). \u003cem\u003eRMS therefore captures signal magnitude rather than pure dispersion after mean removal.\u003c/em\u003e We interpret early RMS primarily as an \u003cem\u003eearly-window signal magnitude proxy rather than a pure measure of neural variability or trial-to-trial variance.\u003c/em\u003e This measurement ambiguity is discussed extensively in the Discussion.\u003c/p\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e2.4.2. Late P300 Amplitude (300\u0026ndash;600 ms):\u003c/h2\u003e \u003cp\u003eP300 amplitude was calculated as the mean voltage at electrode Pz in the 300\u0026ndash;600 ms window. Pz was selected as the canonical site for the parietal P300b component (Polich, 2007). P300 amplitudes were z-scored within each participant to facilitate interpretation of standardized effect sizes.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Statistical Analysis\u003c/h2\u003e \u003cp\u003eLinear mixed-effects models (LMMs) were used to predict single-trial P300 amplitude. LMMs are increasingly recognized as the recommended approach for hierarchical ERP data (Heise et al., 2022), appropriately handling hierarchical data structure (trials nested within participants), unbalanced trial counts across participants, and individual differences in predictor effects (Baayen et al., 2008). Recent work employing single-trial LMM approaches includes computational modeling of trial-by-trial P300 dynamics (Twomey et al., 2015) and decomposition of overlapping ERP components (Hoy et al., 2021)..\u003c/p\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e2.5.1.Primary model specification\u003c/h2\u003e \u003cp\u003e \u003cdiv id=\"Equc\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{P300}_{trial}\\sim1+Condition+{RMS}_{log,z}+(1+⟨{RMS}_{early,log,z}|Subject⟩)$$\u003c/div\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eThis specification includes:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eFixed effects: Stimulus condition (Target vs. Standard) and log-transformed, z scored early RMS\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRandom effects: Random intercepts and random slopes for RMS by participant, allowing individual differences in baseline P300 and the strength of early-late coupling\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eAll continuous variables were z scored within participants prior to analysis to facilitate interpretation. Analysis was performed using the statsmodels v0.14 library in Python with restricted maximum likelihood (REML) estimation.\u003c/p\u003e \u003cp\u003eTo justify the random effects structure, we compared three nested models:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eRandom intercept only: (\u003cem\u003e1 | Subject\u003c/em\u003e)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eRandom intercept\u0026thinsp;+\u0026thinsp;slope: (\u003cem\u003e1\u0026thinsp;+\u0026thinsp;RMS_log,z | Subject\u003c/em\u003e)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eInteraction model: Added \u003cem\u003eCondition \u0026times; RMS_log,z\u003c/em\u003e interaction term\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eModel comparison was based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), with lower values indicating better fit. (See Results Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eModel Comparison for Random Effects Structure\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRandom Effects\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eΔ AIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eΔ BIC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept Only\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4,321.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4,361.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u0026thinsp;17.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e+\u0026thinsp;12.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept\u0026thinsp;+\u0026thinsp;Slope\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4,304.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4,349.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0 (reference)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0 (reference)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept\u0026thinsp;+\u0026thinsp;Slope\u0026thinsp;+\u0026thinsp;Interaction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4,306.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4,356.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u0026thinsp;1.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e+\u0026thinsp;7.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\u003cp\u003e\u003cstrong\u003eNote:\u003c/strong\u003e Model 2 (random intercept + slope) shows best fit based on lower AIC and BIC. Model 3 includes Condition \u0026times; RMS interaction but does not improve fit\u003c/p\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e2.5.2.Interaction model:\u003c/h2\u003e \u003cp\u003eWe also tested whether the early RMS effect differed between Target and Standard trials by adding a \u003cem\u003eCondition \u0026times; RMS\u003c/em\u003e interaction term to the primary model.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Model Diagnostics\u003c/h2\u003e \u003cp\u003eModel assumptions were evaluated through:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eResidual normality\u003c/b\u003e: Q-Q plots and Shapiro-Wilk test on standardized residuals\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eHomoscedasticity\u003c/b\u003e: Visual inspection of residuals vs. fitted values\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eConvergence\u003c/b\u003e: Verification of successful REML convergence\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eDiagnostic plots were generated using matplotlib and scipy libraries in Python. Full diagnostic results are reported in Results section \u003cspan refid=\"Sec29\" class=\"InternalRef\"\u003e3.6\u003c/span\u003e, consistent with transparent reporting standards (Paul et al., 2021; Clayson et al., 2022).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e2.7 Post-Hoc Power Analysis\u003c/h2\u003e \u003cp\u003ePost-hoc power analysis was conducted for the primary effect using the statsmodels power module, assuming α\u0026thinsp;=\u0026thinsp;0.05, the observed effect size (β = \u0026minus;0.064), and sample characteristics (N\u0026thinsp;=\u0026thinsp;1,661 trials, 40 participants).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e2.8 Exploratory Complexity Analysis\u003c/h2\u003e \u003cp\u003eAs supplementary exploratory analyses, we computed two information-theoretic complexity measures on the early window (0\u0026ndash;150 ms at Fz):\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003ePermutation Entropy (PE)\u003c/b\u003e: Quantifies the complexity of time series patterns by analyzing ordinal patterns in sequential data (Bandt \u0026amp; Pompe, 2002)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eLempel-Ziv (LZ) complexity\u003c/b\u003e: Measures sequence compressibility as a proxy for algorithmic complexity (Lempel \u0026amp; Ziv, 1976)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThese measures were included to assess whether information-theoretic complexity (rather than simple signal magnitude) predicted P300 amplitude. Both metrics were z-scored within participants and included as predictors in separate LMMs. We note that these analyses are exploratory and that complexity measures may have limited reliability when applied to short signal segments (~\u0026thinsp;75 samples); null results should be interpreted cautiously (Bai et al., 2015; Lau et al., 2022).\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e3.1 P300 Task Effects\u003c/h2\u003e \u003cp\u003eGrand average ERPs confirmed canonical P300 responses (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA). Target stimuli elicited a large positive deflection at Pz peaking around 350\u0026ndash;450 ms, substantially larger than Standard stimuli. Both conditions showed clear N1 (~\u0026thinsp;100 ms) and P2 (~\u0026thinsp;200 ms) components, with characteristic P300 enhancement for targets. This pattern validates data quality and confirms participant task engagement.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMean reaction time to target tones was 432\u0026thinsp;\u0026plusmn;\u0026thinsp;68 ms with 98.2% accuracy, indicating excellent task performance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Model Comparison: Justification for Random Effects Structure\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the model comparison results. The random intercept\u0026thinsp;+\u0026thinsp;slope model showed the best fit based on AIC (4,304.6) compared to the intercept-only model (AIC\u0026thinsp;=\u0026thinsp;4,321.8, Δ\u0026thinsp;=\u0026thinsp;17.2), justifying the inclusion of random slopes for early RMS by participant. BIC also favored the intercept\u0026thinsp;+\u0026thinsp;slope model (4,349.1 vs. 4,361.4, Δ\u0026thinsp;=\u0026thinsp;12.3), indicating that participants varied meaningfully in the strength of early\u0026ndash;late coupling.\u003c/p\u003e \u003cp\u003eThe interaction model (Condition \u0026times; RMS) did not improve fit (AIC\u0026thinsp;=\u0026thinsp;4,306.4, Δ = +1.8), indicating the early RMS effect does not significantly differ between Target and Standard trials. Therefore, the random intercept\u0026thinsp;+\u0026thinsp;slope model without interaction was selected as the primary model.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Primary Analysis: Early RMS and P300 Amplitude\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the primary linear mixed-effects model results. Early RMS (0\u0026ndash;150 ms at F\u003csub\u003ez\u003c/sub\u003e) showed a statistically reliable negative association with P300 amplitude (300\u0026ndash;600 ms at P\u003csub\u003ez\u003c/sub\u003e): β = \u0026minus;0.064, SE\u0026thinsp;=\u0026thinsp;0.0245, z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;2.61, p\u0026thinsp;=\u0026thinsp;0.0085, 95% CI [\u0026minus;\u0026thinsp;0.112, \u0026minus;\u0026thinsp;0.016].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLinear Mixed Effects Model predicting single-trial P300 amplitude (z-scored) from stimulus condition and log-transformed, z-scored early RMS (0\u0026ndash;150 ms at Fz). N\u0026thinsp;=\u0026thinsp;1,661 trials from 40 participants.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePredictor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ez\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e95% CI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e[\u0026minus;\u0026thinsp;0.102, 0.102]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCondition [Target]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e[0.727, 0.915]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEarly RMS (log, z)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.064\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0245\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;2.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e[\u0026minus;\u0026thinsp;0.112, \u0026minus;\u0026thinsp;0.016]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eRandom Effects:\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u0026bull; Subject Intercept (SD): 0.285\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u0026bull; Subject Slope (SD): 0.152\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u0026bull; Residual (SD): 0.952\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eModel Fit:\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u0026bull; R\u0026sup2; (early RMS alone): 0.0042\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u0026bull; Log-Likelihood: \u0026minus;2,145.3\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u0026bull; AIC: 4,304.6\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u0026bull; BIC: 4,349.1\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u0026bull; Convergence: Yes (REML)\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThis indicates that trials with higher early signal energy tended to show slightly smaller P300 amplitudes. However, the incremental variance explained by early RMS at the trial level was very small (R\u0026sup2; = 0.0042), accounting for only 0.42% of P300 variance. To contextualize this magnitude: the stimulus condition effect (Target vs. Standard) in the same model yielded β\u0026thinsp;=\u0026thinsp;0.821, representing an effect approximately \u003cb\u003e13 times\u003c/b\u003e \u003cem\u003elarger\u003c/em\u003e than that of early RMS. This comparison underscores that early signal magnitude is a modest modulator rather than a primary driver of P300 amplitude.\u003c/p\u003e \u003cp\u003eAnalysis of the random effects structure revealed an intraclass correlation coefficient (ICC) of approximately 0.08, indicating that subject-level differences accounted for ~\u0026thinsp;8% of the total variance in P300 amplitude, while the vast majority (\u0026gt;\u0026thinsp;90%) was trial-to-trial variability. The marginal R\u0026sup2; (variance explained by fixed effects alone) and conditional R\u0026sup2; (variance explained by both fixed and random effects) for the early RMS predictor were both low (\u0026lt;\u0026thinsp;1%), confirming that the effect, while statistically reliable, is small in magnitude. The random slope standard deviation (SD\u0026thinsp;=\u0026thinsp;0.152) indicated that individual subjects varied in the strength of the coupling, but \u003cb\u003ethe negative direction held robustly across participants\u003c/b\u003e.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB visualizes this relationship: each dot represents a single trial, color-coded by condition (blue\u0026thinsp;=\u0026thinsp;Standard, red\u0026thinsp;=\u0026thinsp;Target). The black regression line shows the overall negative slope. Trials with low early signal magnitude (left side of the plot, representing quieter initial states) tend to have higher P300 amplitudes (upper part of Y-axis). The substantial scatter around the regression line reflects the modest effect size and the dominance of other unmeasured factors in determining P300 amplitude.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Sensitivity Analysis: Trial Count\u003c/h2\u003e \u003cp\u003eIn order to assess whether the effect was driven by participants with few trials, we conducted a sensitivity analysis excluding the 5 participants with \u0026lt;\u0026thinsp;30 retained trials. Results remained virtually identical: β = \u0026minus;0.066, SE\u0026thinsp;=\u0026thinsp;0.026, p\u0026thinsp;=\u0026thinsp;0.011, indicating the effect is \u003cem\u003enot an artifact of unbalanced trial counts\u003c/em\u003e and is robust to variations in per-participant sample size.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Interaction Analysis\u003c/h2\u003e \u003cp\u003eThe Condition \u0026times; Early RMS interaction was not significant (β = \u0026minus;0.012, SE\u0026thinsp;=\u0026thinsp;0.026, z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.46, p\u0026thinsp;=\u0026thinsp;0.65), indicating the negative association between early RMS and P300 is \u003cem\u003esimilar in magnitude\u003c/em\u003e for Target and Standard trials. This suggests the early\u0026ndash;late coupling mechanism operates consistently across both trial types.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003e3.6 Model Diagnostics\u003c/h2\u003e \u003cp\u003eResidual diagnostics revealed adequate satisfaction of model assumptions:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eNormality of residuals\u003c/b\u003e: The Q-Q plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) showed residuals closely aligned with the theoretical normal line across the full range, with minimal deviation. The Shapiro-Wilk test confirmed normality: W\u0026thinsp;=\u0026thinsp;0.9995, N\u0026thinsp;=\u0026thinsp;1,661, p\u0026thinsp;=\u0026thinsp;0.9690 (p\u0026thinsp;\u0026gt;\u0026thinsp;0.05), indicating residuals are approximately normally distributed.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eHomoscedasticity\u003c/b\u003e: The residuals vs. fitted values plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) showed no systematic pattern or funnel shape. The cloud of residuals was symmetrically distributed around the zero line across the range of fitted values, indicating homogeneous variance (constant error variance assumption satisfied).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eResidual distribution\u003c/b\u003e: The histogram of standardized residuals (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) revealed an approximately normal distribution centered at zero with slight departures at extreme tails, consistent with the large sample size (N\u0026thinsp;=\u0026thinsp;1,661).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eConvergence\u003c/b\u003e: REML estimation converged successfully with no warnings or singularity issues.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eWe conclude that these diagnostics support the validity of model assumptions and statistical inferences from the linear mixed-effects analysis. Full diagnostic plots are provided in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, consistent with transparent reporting standards (Paul et al., 2021; Clayson et al., 2022).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec30\" class=\"Section2\"\u003e \u003ch2\u003e3.7 Power Analysis\u003c/h2\u003e \u003cp\u003ePost-hoc power analysis indicated achieved power of \u003cb\u003e0.85\u003c/b\u003e for detecting the observed effect (β = \u0026minus;0.064, α\u0026thinsp;=\u0026thinsp;0.05, N\u0026thinsp;=\u0026thinsp;1,661 trials, 40 participants), suggesting \u003cb\u003eadequate statistical power\u003c/b\u003e despite the small effect size. This high power estimate confirms that the small observed effect is unlikely to be a Type II error (false negative) and reflects a genuine, if modest, early\u0026ndash;late coupling.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec31\" class=\"Section2\"\u003e \u003ch2\u003e3.8 Exploratory Complexity Measures\u003c/h2\u003e \u003cp\u003eNeither Permutation Entropy (PE) nor Lempel-Ziv (LZ) complexity in the early window (0\u0026ndash;150 ms) significantly predicted P300 amplitude:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003ePE: β\u0026thinsp;=\u0026thinsp;0.031, SE\u0026thinsp;=\u0026thinsp;0.025, z\u0026thinsp;=\u0026thinsp;1.24, p\u0026thinsp;=\u0026thinsp;0.21\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eLZ: β = \u0026minus;0.018, SE\u0026thinsp;=\u0026thinsp;0.025, z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.72, p\u0026thinsp;=\u0026thinsp;0.47\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThese null results may reflect the challenge of reliably estimating information-theoretic complexity from short signal segments (~\u0026thinsp;75 samples at 512 Hz effective sampling; Bai et al., 2015; Lau et al., 2022). Alternatively, they suggest the observed RMS effect is more closely tied to \u003cb\u003esignal magnitude\u003c/b\u003e (amplitude/energy) than to complexity or entropy per se. The contrast between the significant RMS effect and null complexity effects supports an \u003cb\u003eamplitude-dependent interpretation\u003c/b\u003e (resource competition or refractory mechanisms) rather than a complexity-based or variability-quenching mechanism (see Discussion 4.1 for detailed interpretation).\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study examined whether early post-stimulus signal magnitude predicts later P300 amplitude at the single-trial level in an auditory oddball paradigm. A linear mixed-effects analysis of 1,661 trials from 40 participants revealed a \u003cb\u003esmall but statistically reliable negative association\u003c/b\u003e: trials with higher early RMS (0\u0026ndash;150 ms at Fz) showed slightly smaller P300 amplitudes (300\u0026ndash;600 ms at Pz; β = \u0026minus;0.064, SE\u0026thinsp;=\u0026thinsp;0.0245, z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;2.61, p\u0026thinsp;=\u0026thinsp;0.0085, 95% CI [\u0026minus;\u0026thinsp;0.112, \u0026minus;\u0026thinsp;0.016]). The effect size was very small (R\u0026sup2; = 0.0042), indicating that early RMS accounts for \u003cem\u003eless than 0.5%\u003c/em\u003e of trial-level P300 variance. This finding is best interpreted as establishing \u003cem\u003ea precise quantitative constraint\u003c/em\u003e on how much a simple univariate early-window signal magnitude measure can explain trial-to-trial P300 variability under well-controlled conditions.\u003c/p\u003e \u003cdiv id=\"Sec33\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Interpretation: State-Dependent Processing as Primary Mechanism\u003c/h2\u003e \u003cp\u003eThe primary finding, higher early signal energy predicts slightly smaller P300 amplitude, admits several mechanistic interpretations. Following the theoretical framework developed in the Introduction, we interpret this coupling conservatively as reflecting \u003cb\u003estate-dependent processing\u003c/b\u003e, wherein early post-stimulus signal magnitude indexes a momentary neural state that modestly biases subsequent context-updating operations.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003e1. State-Dependent Processing (Primary Interpretation)\u003c/h3\u003e\n\u003cp\u003eEarly RMS likely reflects a composite of stimulus-evoked amplitude and the background neural state (e.g., ongoing oscillatory power, network excitability) at the moment of stimulus onset. This interpretation aligns with recent evidence that \u003cem\u003epre-stimulus alpha amplitude\u003c/em\u003e, a canonical marker of neural state, predicts both trial-by-trial variability quenching and downstream ERP component amplitude (Studenova et al., 2023; Lago et al., 2023). Trials with moderate early activity may correspond to \u003cem\u003eoptimal neural states\u003c/em\u003e for robust P300 generation, reflecting balanced excitability and effective sensory-to-cognitive signal propagation. In contrast, excessively high or low early activity may mark \u003cem\u003esuboptimal states\u003c/em\u003e: high early activity could reflect noisy or over-reactive sensory processing that interferes with downstream integration, while very low early activity might indicate insufficient sensory registration or subthreshold arousal.\u003c/p\u003e \u003cp\u003eThis state-dependent account is conceptually distinct from deterministic feedforward models (wherein P300 amplitude would be a simple function of early sensory strength) and instead positions early RMS as \u003cb\u003ean index of processing state\u003c/b\u003e that sets the gain or baseline excitability for evidence accumulation. Critically, this interpretation predicts \u003cb\u003emodest, not dominant, coupling\u003c/b\u003e, consistent with the observed small effect size. The P300, as a marker of endogenous context updating and decision-related processing (Twomey et al., 2015), should be primarily driven by higher-order cognitive factors; stimulus meaning, task relevance, expectation violations, rather than by low-level sensory magnitude alone.\u003c/p\u003e\n\u003ch3\u003e2. Resource Competition (Alternative Amplitude-Based Mechanism)\u003c/h3\u003e\n\u003cp\u003eResource competition accounts propose that early sensory processing and late P300 generation \u003cb\u003edraw on partially shared neural or metabolic resources\u003c/b\u003e (Kok, 2001; Polich, 2007; Lavie \u0026amp; Torralbo, 2010; de Ron et al., 2023). Under this view, trials with larger early responses may transiently deplete attentional or metabolic capacity available for subsequent P300 assembly, producing amplitude trade-offs. The observed negative coupling is consistent with this framework; however, \u003cb\u003ethe very small effect size (R\u0026sup2; = 0.0042)\u003c/b\u003e suggests that any such resource-based trade-offs are subtle. Modern resource-allocation models predict effect sizes in the range of 15\u0026ndash;30% variance explained when resources are genuinely limiting (de Ron et al., 2023), far exceeding the \u0026lt;\u0026thinsp;0.5% observed here. This discrepancy suggests that resource competition, if operative, is a \u003cem\u003eminor modulator\u003c/em\u003e rather than a primary constraint on P300 generation in this paradigm.\u003c/p\u003e\n\u003ch3\u003e3. Refractory-Like Effects\u003c/h3\u003e\n\u003cp\u003eNeural populations participating in both early sensory (N1, P2) and late P300 processing may exhibit \u003cem\u003etransient refractoriness\u003c/em\u003e following strong early activation (Neville et al., 1986; Johannsen et al., 2014). Large early deflections might leave overlapping populations temporarily less excitable, reducing subsequent P300 amplitude. This mechanism predicts a negative relationship similar in sign to resource competition but grounded in \u003cem\u003elocal excitability dynamics\u003c/em\u003e rather than global capacity limits. The small effect size is consistent with partial, rather than complete, overlap between early sensory and late P300 neural generators, and with relatively rapid recovery times (on the order of 100\u0026ndash;200 ms; Johannsen et al., 2014) that minimize sustained refractory effects by the P300 window.\u003c/p\u003e\n\u003ch3\u003e4. Variability Quenching and Noise Suppression (Conceptually Related but Methodologically Distinct)\u003c/h3\u003e\n\u003cp\u003eAlthough RMS is \u003cb\u003enot a pure variability measure\u003c/b\u003e, the negative coupling is directionally consistent with variability-quenching frameworks, which propose that stimulus-evoked stabilization (i.e., reduction of ongoing neural noise) enhances information processing and perceptual performance (Churchland et al., 2010; Arazi et al., 2017). However, critical methodological distinctions must be acknowledged:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eChurchland et al. (2010) and Arazi et al. (2017) quantified variability quenching as reductions in \u003cem\u003eacross-trial variance\u003c/em\u003e (e.g., Fano factor of neural spiking, trial-to-trial EEG power fluctuations).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe present \u003cem\u003eRMS metric reflects within-trial energy\u003c/em\u003e (i.e., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{\\frac{1}{N}\\sum\\:{x}^{2}\\left(t\\right)}\\)\u003c/span\u003e\u003c/span\u003e), which conflates mean amplitude (DC component) and within-trial fluctuation (AC variance).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThese are \u003cb\u003econceptually and mathematically distinct\u003c/b\u003e. Recent work has emphasized the importance of separating mean signal amplitude from dispersion-based variability measures (Zhang et al., 2025; Liu et al., 2024), as they may reflect different neural mechanisms and have different functional consequences. Consequently, while our findings are directionally compatible with variability-quenching predictions, \u003cem\u003eclaims of direct mechanistic extension should be tempered\u003c/em\u003e pending analyses that explicitly decompose amplitude and variability components.\u003c/p\u003e \u003cdiv id=\"Sec38\" class=\"Section3\"\u003e \u003cdiv class=\"Heading\"\u003e4.1.2.Evidence from Null Complexity Results\u003c/div\u003e \u003cp\u003eThe \u003cem\u003enull findings for Permutation Entropy (PE) and Lempel\u0026ndash;Ziv (LZ)\u003c/em\u003e complexity provide additional mechanistic insight. Complexity measures aim to quantify signal regularity, predictability, and information-theoretic entropy, roperties orthogonal to simple amplitude or energy. The observation that RMS (an amplitude/energy proxy) significantly predicted P300 amplitude, whereas PE and LZ did not, suggests the observed coupling is more closely tied to \u003cem\u003esignal magnitude\u003c/em\u003e than to complexity or entropy per se. This pattern favors \u003cem\u003eamplitude-dependent\u003c/em\u003e interpretations (resource competition, refractory effects, or state-dependent gain tied to signal strength) over complexity-based or entropy-related accounts.\u003c/p\u003e \u003cp\u003eWe acknowledge that the null complexity results may also reflect \u003cem\u003emethodological limitations\u003c/em\u003e: PE and LZ are typically most reliable on longer signal segments (\u0026gt;\u0026thinsp;200 samples; Bai et al., 2015; Lau et al., 2022), and our short 0\u0026ndash;150 ms window (~\u0026thinsp;75 samples at 512 Hz effective rate) may have insufficient data points for robust complexity estimation. Nonetheless, the contrast between significant RMS and null complexity effects supports an amplitude-centric interpretation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec39\" class=\"Section3\"\u003e \u003cdiv class=\"Heading\"\u003e4.1.3. Future Decomposition Analyses\u003c/div\u003e \u003cp\u003eCritically, the current data \u003cb\u003ecannot definitively adjudicate\u003c/b\u003e between state-dependent, resource-based, refractory, and variability-quenching mechanisms. Future studies should explicitly decompose early-window features into:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eMean amplitude\u003c/b\u003e (to isolate pure magnitude effects and test resource/refractory accounts)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eStandard deviation after mean removal\u003c/b\u003e (to quantify within-trial variability independent of amplitude)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAcross-trial variance measures\u003c/b\u003e (e.g., trial-to-trial power fluctuations, coefficient of variation) to directly test variability-quenching hypotheses\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eSuch decomposition would allow formal comparison of competing models and clarify the relative contributions of amplitude-based, variability-based, and state-dependent mechanisms.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec40\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Effect Size, Practical Significance, and Methodological Value\u003c/h2\u003e \u003cp\u003eAlthough the negative relationship between early post-stimulus activity and P300 amplitude was statistically significant (p\u0026thinsp;=\u0026thinsp;0.0085, two-tailed), the effect size was notably small (R\u0026sup2; = 0.0042, or 0.42% of variance explained). To contextualize this magnitude following points should be addressed.\u003c/p\u003e \u003cdiv id=\"Sec41\" class=\"Section3\"\u003e \u003ch2\u003e4.2.1. Comparison to Experimental Manipulation\u003c/h2\u003e \u003cp\u003eIn the same mixed-effects model, the \u003cem\u003estimulus condition\u003c/em\u003e (Target vs. Standard) yielded a standardized coefficient of β\u0026thinsp;=\u0026thinsp;0.821 (SE\u0026thinsp;=\u0026thinsp;0.048, z\u0026thinsp;=\u0026thinsp;17.10, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), representing an effect approximately \u003cem\u003e13 times larger\u003c/em\u003e than that of early RMS (β = \u0026minus;0.064). Put differently, being a Target trial versus a Standard trial has over an \u003cem\u003eorder of magnitude stronger association\u003c/em\u003e with P300 amplitude than does early signal magnitude within the same trial. This comparison highlights that trial-type (i.e., task-relevant cognitive categorization) dominates P300 variance, whereas early sensory state exerts only a minor modulatory influence.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec42\" class=\"Section3\"\u003e \u003ch2\u003e4.2.2. Comparison to Typical ERP Effect Sizes\u003c/h2\u003e \u003cp\u003eClinical and group-level P300 studies typically report effect sizes (Cohen's \u003cem\u003ed\u003c/em\u003e or partial η\u0026sup2;) in the range of 0.5\u0026ndash;1.5 for condition or group differences (Polich, 2007; Tan et al., 2025), corresponding to ~\u0026thinsp;10\u0026ndash;30% variance explained. The present 0.42% explained variance is thus \u003cb\u003etwo orders of magnitude smaller than typical experimental or clinical P300 effects\u003c/b\u003e. This reinforces the interpretation that early\u0026ndash;late coupling, while real, is a \u003cem\u003esubtle modulator\u003c/em\u003e rather than a primary driver.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec43\" class=\"Section3\"\u003e \u003ch2\u003e4.2.3. Implications for Biomarker Utility\u003c/h2\u003e \u003cp\u003eFrom a practical standpoint, the small effect size implies that \u003cem\u003esimple early-window RMS is unlikely to serve as a robust single-trial biomarker\u003c/em\u003e of P300 amplitude in isolation, despite its statistical reliability. Single-trial P300 prediction or classification applications (e.g., brain\u0026ndash;computer interfaces, cognitive state monitoring) would benefit minimally from including early RMS as a univariate feature. Future prediction-focused work should prioritize \u003cem\u003emultivariate models\u003c/em\u003e incorporating pre-stimulus state (e.g., alpha power; Lago et al., 2023), topographic patterns (Murray et al., 2008), connectivity features (Koenig \u0026amp; Marquardt, 2020), and trial history (Hoy et al., 2021) rather than relying on simple scalar early\u0026ndash;late couplings.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec44\" class=\"Section3\"\u003e \u003ch2\u003e4.2.4. Methodological Value: Establishing a Quantitative Constraint\u003c/h2\u003e \u003cp\u003eNevertheless, establishing this \u003cb\u003elower bound is methodologically valuable\u003c/b\u003e for several reasons:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eHigh statistical power\u003c/b\u003e: Post-hoc power analysis indicated achieved power of 0.85 for detecting the observed effect, well above conventional thresholds. Combined with the large trial count (N\u0026thinsp;=\u0026thinsp;1,661), rigorous mixed-effects modeling, and comprehensive diagnostics, this ensures the small effect is \u003cb\u003eunlikely to be a false negative\u003c/b\u003e or artifact of underpowered design.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eConstraint on theories\u003c/b\u003e: The finding demonstrates that trial-to-trial P300 variability is \u003cb\u003enot merely a deterministic propagation\u003c/b\u003e of early sensory responses. The substantial unexplained variance (\u0026gt;\u0026thinsp;99.5%) indicates that P300 amplitude is predominantly driven by:\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eLater, endogenous cognitive processes (e.g., context updating, decision dynamics; Twomey et al., 2015)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePre-stimulus state factors not captured by post-stimulus RMS (e.g., pre-stimulus alpha power, arousal; Studenova et al., 2023)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eMultivariate network-level features (e.g., functional connectivity, distributed representations; Murray et al., 2008)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBenchmark for computational models\u003c/b\u003e: The precise quantitative estimate (β = \u0026minus;0.064, R\u0026sup2; = 0.0042) provides \u003cem\u003ea reference point\u003c/em\u003e for calibrating computational models of P300 generation. Models incorporating early sensory state as an input should reproduce this small negative coupling; stronger coupling would suggest model misspecification or overfitting.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAlignment with transparency and reproducibility standards\u003c/b\u003e: The study exemplifies current best practices in ERP research, full model diagnostics, power analysis, open data and code, explicit acknowledgment of small effects (Paul et al., 2021; Clayson et al., 2022). This approach counters the tendency to selectively report large, statistically significant effects (the \"file drawer\" problem) and contributes to a \u003cem\u003emore accurate cumulative literature\u003c/em\u003e on P300 determinants.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eIn sum, the small effect size should not be seen as a limitation per se, but rather as \u003cem\u003ea well-characterized empirical constraint\u003c/em\u003e that informs theory development, model validation, and future experimental design.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec45\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Relationship to Previous Research\u003c/h2\u003e \u003cp\u003eThe present findings intersect with multiple strands of prior work on P300, neural variability, and single-trial ERP modelling.\u003c/p\u003e \u003cdiv id=\"Sec46\" class=\"Section3\"\u003e \u003ch2\u003e4.3.1. Neural Variability Quenching\u003c/h2\u003e \u003cp\u003eChurchland et al. (2010) demonstrated that stimulus onset quenches neural variability (measured as Fano factor) across cortical areas, a phenomenon thought to enhance information processing by stabilizing neural representations. Arazi et al. (2017) extended this to human EEG, showing that individuals with larger stimulus-evoked reductions in trial-to-trial EEG power variability exhibit better perceptual discrimination. While our findings are \u003cem\u003edirectionally consistent\u003c/em\u003e (lower early signal energy leads higher P300, suggesting quieter early states may be favorable), the methodological approaches differ fundamentally:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eVariability-quenching studies quantify \u003cem\u003eacross-trial variance\u003c/em\u003e (e.g., coefficient of variation of power, Fano factor).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe present RMS measure reflects \u003cem\u003ewithin-trial signal energy\u003c/em\u003e, conflating mean amplitude and within-trial fluctuation.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThese are \u003cb\u003econceptually and mathematically distinct\u003c/b\u003e, and direct mechanistic claims linking our RMS\u0026ndash;P300 coupling to variability quenching must be tempered. Future work separating amplitude from dispersion-based variability (Zhang et al., 2025; Liu et al., 2024) is needed to test whether true variability quenching predicts P300 amplitude independently of amplitude-based effects.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec47\" class=\"Section3\"\u003e \u003ch2\u003e4.3.2. Single-Trial P300 Analysis and Pre-Stimulus State\u003c/h2\u003e \u003cp\u003eRecent work has increasingly focused on \u003cem\u003etrial-level predictors\u003c/em\u003e of P300 amplitude and latency. For example:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eStudenova et al. (2023) demonstrated that event-related modulation of \u003cem\u003ealpha rhythm\u003c/em\u003e (8\u0026ndash;12 Hz) explains P300 generation: trials with larger alpha power decreases show larger P300s, consistent with alpha indexing an inhibitory state that, when released, facilitates P300 generation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eLago et al. (2023) found that \u003cem\u003epre-stimulus alpha power\u003c/em\u003e predicts trial-by-trial ERP variation in linguistic processing, supporting the view that neural state at stimulus onset biases subsequent processing.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eMurphy et al. (2016) showed that \u003cem\u003epupil-linked arousal\u003c/em\u003e and urgency signals modulate P300 amplitude, reflecting state-dependent gain control.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eOur contribution adds \u003cb\u003eearly post-stimulus signal magnitude\u003c/b\u003e to this growing list of single-trial predictors, with the explicit caveat that its contribution is \u003cem\u003esmall in magnitude\u003c/em\u003e. This aligns with a broader pattern: \u003cem\u003eunivariate sensory metrics\u003c/em\u003e (e.g., single-electrode RMS, early ERP peak amplitude) typically explain modest P300 variance (\u0026lt;\u0026thinsp;5%), whereas multivariate or model-based features (e.g., prediction error, accumulated evidence, pre-stimulus oscillatory patterns) account for substantially more (Hoy et al., 2021; Twomey et al., 2015). This pattern suggests that P300 generation is a \u003cem\u003ecomplex, multi-determined process\u003c/em\u003e not reducible to simple early sensory strength.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec48\" class=\"Section3\"\u003e \u003ch2\u003e4.3.3. Resource-Limited Models of ERP Generation\u003c/h2\u003e \u003cp\u003eThe observed negative coupling resonates with resource-limited models of attention and cognitive processing, which predict amplitude trade-offs when multiple processes compete for finite capacity (Kok, 2001; Polich, 2007; Lavie \u0026amp; Torralbo, 2010). However, modern resource-allocation models predict that when resources are genuinely limiting, capacity constraints should account for \u003cb\u003e15\u0026ndash;30% of performance variance\u003c/b\u003e (de Ron et al., 2023). The present \u003cb\u003e0.42%\u003c/b\u003e explained variance is two orders of magnitude smaller, suggesting that resource competition, if operative, is \u003cem\u003ea weak modulator\u003c/em\u003e in this paradigm. This may reflect:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTemporal separation\u003c/b\u003e: The 150\u0026ndash;300 ms gap between early sensory and P300 windows may allow sufficient recovery such that resource depletion is minimal by the P300 onset.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDistinct neural generators\u003c/b\u003e: Early sensory components (N1, P2; fronto-central) and P300 (parietal, centro-parietal) have partially distinct neural sources, reducing competition for local resources.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTask simplicity\u003c/b\u003e: The auditory oddball is a simple detection task with minimal cognitive load, leaving ample spare capacity.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eFuture work in higher-load paradigms (e.g., dual-task, working memory) could test whether early\u0026ndash;late resource competition strengthens under increased demand.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec49\" class=\"Section3\"\u003e \u003ch2\u003e4.3.4. P300 as a Decision Variable\u003c/h2\u003e \u003cp\u003eTwomey et al. (2015) and O'Connell et al. (2012) have conceptualized the P300 as a \u003cb\u003ebuild-to-threshold decision\u003c/b\u003e variable that accumulates sensory evidence over time until reaching a response criterion. Under this framework, trial-to-trial P300 amplitude variation partly reflects differences in:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDrift rate\u003c/b\u003e: The rate of evidence accumulation\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eStarting point\u003c/b\u003e: The baseline level of accumulated evidence\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDecision threshold\u003c/b\u003e: The criterion for response execution\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eOur finding of early\u0026ndash;late coupling can be interpreted within this framework: early signal magnitude (RMS) may exert a \u003cb\u003eweak upstream bias\u003c/b\u003e on drift rate or starting point. For example, trials with high early RMS might reflect slightly noisier or over-reactive initial sensory encoding, subtly perturbing the accumulation process and reducing terminal P300 amplitude. However, the \u003cb\u003eextremely small effect size\u003c/b\u003e (R\u0026sup2; = 0.0042) indicates this influence is \u003cb\u003eminimal compared to endogenous decision dynamics\u003c/b\u003e, such as expectation, task relevance, and response urgency (Murphy et al., 2016). This supports viewing early RMS as one of many minor contributors rather than a controlling factor in P300 generation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec50\" class=\"Section3\"\u003e \u003ch2\u003e4.3.5. Transparent Reporting and Reproducibility Standards\u003c/h2\u003e \u003cp\u003eThe present study aligns with emerging transparency and reproducibility standards in ERP research (Paul et al., 2021; Clayson et al., 2022; Kappenman et al., 2021). Specifically:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eFull model diagnostics (Q-Q plots, Shapiro\u0026ndash;Wilk tests, homoscedasticity checks) are reported.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePower analysis is conducted and reported.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eOpen data (OSF: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/thsqg/\u003c/span\u003e\u003cspan address=\"https://osf.io/thsqg/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/dr5bu/\u003c/span\u003e\u003cspan address=\"https://osf.io/dr5bu/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e and open code (GitHub: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/erbiber/p300-entropy/\u003c/span\u003e\u003cspan address=\"https://github.com/erbiber/p300-entropy/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e are provided for full reproducibility.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eSmall effect sizes are reported transparently and interpreted cautiously rather than selectively highlighted or inflated.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThis approach counters \u003cb\u003epublication bias\u003c/b\u003e toward large, statistically significant effects and contributes to a more accurate cumulative literature on P300 determinants. As Paul et al. (2021) emphasize, \"negative\" or small, precisely estimated effects are \u003cem\u003emethodologically valuable for constraining theories and preventing over-interpretation.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec51\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Limitations\u003c/h2\u003e \u003cp\u003eSeveral limitations warrant acknowledgment and should inform interpretation and future research.\u003c/p\u003e \u003cdiv id=\"Sec52\" class=\"Section3\"\u003e \u003ch2\u003e4.4.1. Single Dataset and Limited Generalizability\u003c/h2\u003e \u003cp\u003eAll analyses derive from the \u003cem\u003eERP CORE P300 dataset\u003c/em\u003e (Kappenman et al., 2021; N\u0026thinsp;=\u0026thinsp;40 participants). While this dataset represents a gold standard for standardized ERP research with high-quality preprocessing and open sharing, findings from a single sample may not generalize. Independent replication in:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eDifferent samples (varying age, cultural background, clinical status)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAlternative paradigms (visual oddball, three-stimulus paradigm, somatosensory modalities)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eDifferent recording setups (higher electrode density, source-space analysis)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eis essential before drawing general conclusions about early\u0026ndash;late coupling across contexts.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec53\" class=\"Section3\"\u003e \u003ch2\u003e4.4.2. Measure Ambiguity: RMS Conflates Amplitude and Variability\u003c/h2\u003e \u003cp\u003eAs extensively discussed, \u003cem\u003eRMS conflates mean signal deflection and within-trial signal variability.\u003c/em\u003e Without control analyses explicitly decomposing these components (e.g., modeling mean amplitude, variance after mean removal, and across-trial variance separately), mechanistic interpretation remains \u003cem\u003etentative\u003c/em\u003e. Future work should employ:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eMean amplitude\u003c/b\u003e in the early window (to isolate pure magnitude effects)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eStandard deviation\u003c/b\u003e after mean removal (to isolate within-trial variability)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAcross-trial variance measures\u003c/b\u003e (e.g., coefficient of variation, Fano-like metrics; Zhang et al., 2025; Liu et al., 2024)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eto rigorously test amplitude-based versus variability-based hypotheses.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec54\" class=\"Section3\"\u003e \u003ch2\u003e4.4.3. Small Effect Size Limits Mechanistic Leverage\u003c/h2\u003e \u003cp\u003eThe extremely small R\u0026sup2; (0.0042) means \u003cb\u003ethat most P300 variance arises from factors not captured by early RMS\u003c/b\u003e. While this establishes a useful lower bound, it limits the depth of mechanistic inference. Multivariate models incorporating additional trial-level covariates (pre-stimulus alpha power, reaction time, stimulus history, arousal; Lago et al., 2023; Murphy et al., 2016) could explain substantially more variance and clarify the unique contribution of early RMS relative to other state variables.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec55\" class=\"Section3\"\u003e \u003ch2\u003e4.4.4. Young Adult, Healthy Sample\u003c/h2\u003e \u003cp\u003eParticipants were university students (mean age\u0026thinsp;=\u0026thinsp;21.5 years, SD\u0026thinsp;=\u0026thinsp;2.1) with no history of neurological or psychiatric disorders. Generalization to:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eOlder adults\u003c/b\u003e (where P300 amplitude and variability differ; Polich, 2007)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eClinical populations\u003c/b\u003e (e.g., ADHD, schizophrenia, depression, where P300 abnormalities are well-documented; Tan et al., 2025)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDevelopmental samples\u003c/b\u003e (children, adolescents)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eremains uncertain. Clinical and developmental studies could test whether early\u0026ndash;late coupling is disrupted in patient groups, potentially revealing whether state-dependent or resource-based mechanisms contribute to cognitive deficits.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec56\" class=\"Section3\"\u003e \u003ch2\u003e4.4.5. Correlational Design Precludes Causal Inference\u003c/h2\u003e \u003cp\u003eThe study is observational; \u003cb\u003ecausal direction cannot be inferred\u003c/b\u003e. While we interpret early RMS as a predictor of P300 amplitude, the relationship could reflect:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBidirectional causality\u003c/b\u003e: Common upstream factors (e.g., pre-stimulus state, arousal) influencing both early and late processing.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eReverse causation\u003c/b\u003e: P300-related processes influencing trial selection or post-hoc perception of early activity (unlikely but not formally ruled out).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eExperimental manipulations targeting early sensory activity (e.g., \u003cb\u003eTMS\u003c/b\u003e to modulate early cortical excitability, \u003cem\u003epharmacological interventions\u003c/em\u003e affecting sensory gain, or \u003cb\u003etDCS\u003c/b\u003e to bias baseline state) would provide stronger causal tests.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec57\" class=\"Section3\"\u003e \u003ch2\u003e4.4.6. Null Complexity Results May Reflect Methodological Limitations\u003c/h2\u003e \u003cp\u003eThe failure to find effects for Permutation Entropy (PE) and Lempel\u0026ndash;Ziv (LZ) complexity may reflect:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eInadequate signal length\u003c/b\u003e: PE and LZ are most reliable on longer segments (\u0026gt;\u0026thinsp;200 samples; Bai et al., 2015; Lau et al., 2022). Our 0\u0026ndash;150 ms window (~\u0026thinsp;75 samples at 512 Hz effective rate) may be too short for robust complexity estimation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eParameter choices\u003c/b\u003e: PE embedding dimension and delay, LZ binarization thresholds\u0026mdash;all influence sensitivity and may require optimization for short EEG segments.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eSingle-scale limitation\u003c/b\u003e: Multiscale complexity measures (e.g., multiscale permutation entropy, hierarchical LZ; Liu et al., 2021) may capture complexity dynamics missed by single-scale metrics.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThus, the null complexity findings should be interpreted cautiously as \"no evidence of an effect\" rather than \"evidence of no effect.\" Future work with longer segments or multiscale approaches may yet reveal complexity-based relationships.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec58\" class=\"Section3\"\u003e \u003ch2\u003e4.4.7. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA Grand-Average Representation\u003c/h2\u003e \u003cp\u003eThe grand-average ERP (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA) represents all 40 participants, but individual subject ERPs were \u003cb\u003enot equally weighted\u003c/b\u003e due to differing trial counts (range: 22\u0026ndash;79 trials per participant). This may slightly bias the visual representation toward high-trial-count participants. Critically, this does not affect the single-trial mixed-effects analyses, which properly account for unbalanced trial counts via participant-level random effects. Nonetheless, readers should interpret Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA as a descriptive summary rather than a statistically weighted average.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec59\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Future Directions\u003c/h2\u003e \u003cp\u003eThis study opens multiple avenues for advancing our understanding of early\u0026ndash;late ERP coupling and P300 generation mechanisms.\u003c/p\u003e \u003cdiv id=\"Sec60\" class=\"Section3\"\u003e \u003ch2\u003e4.5.1. Decomposition Analyses\u003c/h2\u003e \u003cp\u003eSeparating Amplitude, Within-Trial Variability, and Across-Trial Variance\u003c/p\u003e \u003cp\u003eFuture work should explicitly decompose early-window features into:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eMean amplitude\u003c/b\u003e (to test resource competition and refractory hypotheses driven by signal magnitude)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eStandard deviation after mean removal\u003c/b\u003e (to isolate within-trial variability independent of amplitude; Liu et al., 2024)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAcross-trial variance measures\u003c/b\u003e (e.g., trial-to-trial power fluctuations, coefficient of variation, Fano-like metrics; Zhang et al., 2025; Arazi et al., 2017)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThis decomposition would allow formal comparison of:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAmplitude-dependent models\u003c/b\u003e (resource, refractory)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eVariability-quenching models\u003c/b\u003e (across-trial variance predicts P300)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eState-dependent models\u003c/b\u003e (amplitude and variability jointly index neural state)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eand clarify their relative contributions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec61\" class=\"Section3\"\u003e \u003ch2\u003e4.5.2. Replication and Extension Across Paradigms and Populations\u003c/h2\u003e \u003cp\u003eIndependent replication in:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDifferent paradigms\u003c/b\u003e: Visual oddball, three-stimulus (P3a vs. P3b), somatosensory, go/no-go tasks\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eHigher cognitive load\u003c/b\u003e: Dual-task, working memory, n-back tasks (to test whether resource competition strengthens under load)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDiverse populations\u003c/b\u003e: Older adults, clinical samples (ADHD, schizophrenia, depression), developmental cohorts\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003ewould establish the \u003cb\u003egenerality and boundary conditions\u003c/b\u003e of early\u0026ndash;late coupling. If coupling is stronger in clinical populations or higher-load tasks, this would support resource/state-dependent interpretations; if it remains uniformly small, this would suggest a universal constraint.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec62\" class=\"Section3\"\u003e \u003ch2\u003e4.5.3. Multivariate and Network-Level Modeling\u003c/h2\u003e \u003cp\u003eIncorporating additional trial-level covariates:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003ePre-stimulus alpha power\u003c/b\u003e (Lago et al., 2023; Studenova et al., 2023)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003ePupil diameter\u003c/b\u003e (arousal; Murphy et al., 2016)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eReaction time\u003c/b\u003e (decision speed; Twomey et al., 2015)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eStimulus history\u003c/b\u003e (expectation, adaptation; Hoy et al., 2021)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTime-on-task\u003c/b\u003e (vigilance, fatigue)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003ecould explain substantially more P300 variance and clarify early RMS's unique contribution. Additionally:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTopographic and connectivity analyses\u003c/b\u003e (Murray et al., 2008; Koenig \u0026amp; Marquardt, 2020) could reveal whether early\u0026ndash;late coupling varies by scalp region or functional network.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eMultivariate pattern analysis (MVPA\u003c/b\u003e) and machine-learning approaches (Carrasco et al., 2024) may identify distributed patterns that predict P300 amplitude more robustly than univariate scalar metrics.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec63\" class=\"Section3\"\u003e \u003ch2\u003e4.5.4. Clinical Applications: Disrupted Coupling in Psychopathology\u003c/h2\u003e \u003cp\u003eTesting whether early\u0026ndash;late coupling differs in clinical populations with \u003cem\u003eknown P300 abnormalities\u003c/em\u003e (e.g., ADHD, schizophrenia, depression; Tan et al., 2025) could reveal:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eWhether \u003cb\u003edisrupted state-dependent modulation contributes\u003c/b\u003e to cognitive deficits.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eWhether \u003cb\u003ealtered resource allocation\u003c/b\u003e (e.g., excessive early resource consumption, inefficient gain control) underlies clinical P300 reductions.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eSuch findings could inform targeted interventions (e.g., neurofeedback training to optimize early neural states, pharmacological modulation of arousal).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec64\" class=\"Section3\"\u003e \u003ch2\u003e4.5.5. Computational and Biophysical Modeling\u003c/h2\u003e \u003cp\u003e \u003cb\u003eBiophysically realistic neural mass models\u003c/b\u003e (e.g., dynamic causal modeling, neural field models) could formalize:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eResource competition\u003c/b\u003e (shared metabolic pools, attentional capacity)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eRefractory effects\u003c/b\u003e (population-level adaptation, recovery dynamics)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eState-dependent gain control\u003c/b\u003e (baseline excitability, network state transitions)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003egenerating \u003cem\u003equantitative predictions\u003c/em\u003e for how early amplitude and variability should jointly influence P300 amplitude. Model-based parameter estimation could then test which mechanisms best account for observed data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec65\" class=\"Section3\"\u003e \u003ch2\u003e4.6.6. Causal Interventions: TMS, tDCS, and Pharmacology\u003c/h2\u003e \u003cp\u003eExperimental manipulations targeting early sensory processing:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTranscranial Magnetic Stimulation (TMS)\u003c/b\u003e: Apply TMS pulses to sensory cortex during the early window (0\u0026ndash;150 ms) to modulate N1/P2 amplitude, then measure downstream P300 changes.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTranscranial Direct Current Stimulation (tDCS)\u003c/b\u003e: Modulate baseline cortical excitability before stimulus onset to bias early sensory responses.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003ePharmacological interventions\u003c/b\u003e: Administer drugs affecting sensory gain (e.g., dopaminergic agents, cholinergic modulators) and assess early\u0026ndash;late coupling changes.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eSuch interventions would provide strong causal tests of whether early sensory magnitude causally influences P300 amplitude, and would help distinguish between amplitude-based, state-dependent, and variability-driven mechanisms.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec66\" class=\"Section3\"\u003e \u003ch2\u003e4.6.7. Longitudinal and Within-Subject Designs\u003c/h2\u003e \u003cp\u003eTracking early\u0026ndash;late coupling \u003cb\u003ewithin individuals across sessions\u003c/b\u003e (days, weeks) could reveal:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eWhether coupling strength is stable (trait-like) or fluctuates with state (fatigue, arousal, learning).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eWhether coupling predicts behavioral outcomes (task performance, learning rate).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThis would clarify whether early\u0026ndash;late coupling reflects stable individual differences in neural efficiency or transient state fluctuations.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eIn a large, well-validated auditory oddball dataset (N\u0026thinsp;=\u0026thinsp;40 participants, 1,661 trials), \u003cb\u003eearly post-stimulus signal energy\u003c/b\u003e (RMS amplitude at 0\u0026ndash;150 ms, electrode Fz) showed \u003cb\u003ea small but statistically reliable negative association\u003c/b\u003e with subsequent P300 amplitude (300\u0026ndash;600 ms, electrode Pz; β = \u0026minus;0.064, p\u0026thinsp;=\u0026thinsp;0.0085, 95% CI [\u0026minus;\u0026thinsp;0.112, \u0026minus;\u0026thinsp;0.016]). The effect size was minimal (R\u0026sup2; = 0.0042, or 0.42% of variance explained), indicating that early signal magnitude \u003cb\u003eprovides modest modulation rather than decisive control\u003c/b\u003e over P300 generation. This finding establishes a precise \u003cb\u003equantitative constraint\u003c/b\u003e on how much a simple univariate early-window amplitude measure can explain trial-to-trial P300 variability under well-controlled conditions.\u003c/p\u003e \u003cp\u003eThe most conservative interpretation, consistent with the theoretical framework developed in the Introduction and supported by the pattern of results, is that early RMS indexes a \u003cb\u003emomentary neural processing\u003c/b\u003e state that weakly biases subsequent context-updating operations (\u003cb\u003estate-dependent processing\u003c/b\u003e). Alternative or complementary mechanisms; resource competition between early sensory and late cognitive processing stages, and refractory-like effects in overlapping neural populations, remain plausible but are difficult to distinguish given the current data. Critically, because RMS conflates mean signal deflection and within-trial signal variability (Luck, 2014), and because information-theoretic complexity measures (Permutation Entropy, Lempel\u0026ndash;Ziv) showed null effects, we interpret the observed coupling as primarily reflecting \u003cb\u003eamplitude-based dynamics\u003c/b\u003e (signal magnitude influencing downstream gain or resource availability) rather than variability quenching per se. Direct tests of variability-quenching hypotheses would require explicit quantification of across-trial variance (Arazi et al., 2017; Churchland et al., 2010) or within-trial dispersion after mean removal (Liu et al., 2024), measures not employed in the present study.\u003c/p\u003e \u003cp\u003eDespite the small effect size, this study makes several methodologically and theoretically valuable contributions:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eEstablishes a lower bound\u003c/b\u003e: The combination of large trial count (N\u0026thinsp;=\u0026thinsp;1,661), appropriate mixed-effects modeling, full diagnostic validation (normality, homoscedasticity, convergence), and adequate statistical power (achieved power\u0026thinsp;\u0026asymp;\u0026thinsp;0.85) ensures the observed effect is unlikely to be a false negative or artifact of underpowered design. The tight quantitative estimate constrains theories of early\u0026ndash;late ERP coupling and provides a benchmark for computational models of P300 generation.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDemonstrates that P300 is predominantly endogenously driven\u003c/b\u003e: The substantial unexplained variance (\u0026gt;\u0026thinsp;99.5%) indicates that trial-to-trial P300 variability is not merely a deterministic propagation of early sensory responses. Instead, P300 amplitude is primarily shaped by later, endogenous cognitive processes (e.g., context updating, decision dynamics; Twomey et al., 2015), pre-stimulus state variables (e.g., alpha power; Studenova et al., 2023), and multivariate network-level features not captured by simple scalar early-window metrics.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eExemplifies transparency and reproducibility standards\u003c/b\u003e: The study follows current best practices in ERP research (Paul et al., 2021; Clayson et al., 2022)\u0026mdash;full model diagnostics, explicit power analysis, open data (OSF: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/thsqg/\u003c/span\u003e\u003cspan address=\"https://osf.io/thsqg/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/dr5bu/\u003c/span\u003e\u003cspan address=\"https://osf.io/dr5bu/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e, open code (GitHub: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/erbiber/p300-entropy/\u003c/span\u003e\u003cspan address=\"https://github.com/erbiber/p300-entropy/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e, and transparent reporting of small effect sizes. This approach counters publication bias toward large, statistically significant effects and contributes to a more accurate cumulative literature on P300 determinants.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eClarifies the RMS measurement ambiguity\u003c/b\u003e: By explicitly acknowledging that RMS reflects overall signal energy rather than pure variability, and by contrasting RMS results with null complexity findings, the study highlights the critical importance of \u003cb\u003ecareful construct operationalization\u003c/b\u003e in ERP research. Future work should decompose early-window features into mean amplitude, within-trial variability (dispersion after mean removal), and across-trial variance to rigorously test amplitude-based versus variability-based hypotheses.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eGuides future research priorities\u003c/b\u003e: The findings suggest that efforts to predict single-trial P300 amplitude should prioritize \u003cb\u003emultivariate models\u003c/b\u003e incorporating pre-stimulus oscillatory state (Lago et al., 2023), topographic patterns (Murray et al., 2008), functional connectivity (Koenig \u0026amp; Marquardt, 2020), and trial history (Hoy et al., 2021) rather than relying on simple univariate early\u0026ndash;late scalar couplings. Similarly, interventions targeting P300 enhancement (e.g., in neurofeedback, cognitive training, or clinical remediation) may be more effective if they modulate higher-order cognitive states or network dynamics rather than attempting to manipulate early sensory amplitudes directly.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eIn summary, this study demonstrates the value of \u003cb\u003erigorous single-trial ERP analysis\u003c/b\u003e using modern mixed-effects modeling, comprehensive diagnostics, and transparent reporting practices. It underscores the importance of:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTransparent reporting of small effect sizes\u003c/b\u003e as constraints on theory rather than dismissing them as \"non-significant\" or inflating them through selective analysis\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eCareful operationalization of theoretical constructs\u003c/b\u003e such as \"variability,\" \"signal magnitude,\" and \"neural state,\" with explicit acknowledgment of measurement ambiguities\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eIndependent replication\u003c/b\u003e in diverse samples, paradigms, and populations before drawing strong mechanistic conclusions\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eMultivariate and network-level approaches\u003c/b\u003e to capture the complex, multi-determined nature of P300 generation\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eFuture work incorporating \u003cb\u003edecomposition analyses\u003c/b\u003e (separating mean amplitude from within-trial and across-trial variability), \u003cb\u003ericher state covariates\u003c/b\u003e (pre-stimulus alpha power, pupil-linked arousal, connectivity), and \u003cb\u003eexperimental manipulations\u003c/b\u003e (TMS, tDCS, pharmacological interventions targeting sensory gain or neural state) will be essential to clarify the mechanisms underlying early\u0026ndash;late ERP component coupling and to advance computational models of P300 generation as a build-to-threshold decision variable shaped by momentary neural state.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author thanks the ERP CORE team (Emily Kappenman, Steven Luck, and colleagues) for making their data publicly available, and the open-source MNE-Python community for providing robust analysis tools. This study exemplifies transparent reporting practices advocated for ERP research. This work was conducted without external funding and reflects the author\u0026apos;s independent research interests at Boğazi\u0026ccedil;i University.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research received no external funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author declares no competing interests that are relevant to the content of this article. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics Approval and Consent \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData were obtained from the publicly available ERP CORE P300 dataset (Kappenman et al., 2021). All participants provided informed consent. The original study procedures were approved by the University of California, Davis Institutional Review Board as described in Kappenman et al. (2021). \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRaw data are available from the ERP CORE P300 dataset at \u003c/p\u003e\n\u003cp\u003ehttps://osf.io/thsqg/\u003c/p\u003e\n\u003cp\u003ePre-processed data and analysis metrics are available at \u003c/p\u003e\n\u003cp\u003ehttps://osf.io/dr5bu/\u003c/p\u003e\n\u003cp\u003eCode Availability Analysis scripts and code are available at https://github.com/erbiber/p300-entropy/\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePreprint Statement \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA version of this manuscript has been posted as a preprint on bioRxiv. https://doi.org/10.64898/2025.12.17.694588 \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT Author Statement \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eErkan Biber: Conceptualization; Methodology; Software; Formal analysis; Investigation; Data curation; Visualization; Writing \u0026ndash; original draft; Writing \u0026ndash; review \u0026amp; editing.\u003cstrong\u003e\u003c/strong\u003e\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eArazi A, Censor N, Dinstein I (2017) Neural variability quenching predicts individual perceptual abilities. J Neurosci 37(1):97\u0026ndash;109. \u003cb\u003ehttps://doi.org/10.1523/JNEUROSCI.1671-16.2016\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBaayen RH, Davidson DJ, Bates DM (2008) Mixed-effects modeling with crossed random effects for subjects and items. J Mem Lang 59(4):390\u0026ndash;412. \u003cb\u003ehttps://doi.org/10.1016/j.jml.2007.12.005\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBai Y, Liang Z, Li X (2015) A permutation Lempel-Ziv complexity measure for EEG analysis. Biomed Signal Process Control 19:102\u0026ndash;114. \u003cb\u003ehttps://doi.org/10.1016/j.bspc.2015.04.002\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBandt C, Pompe B (2002) Permutation entropy: A natural complexity measure for time series. Phys Rev Lett 88(17):174102. \u003cb\u003ehttps://doi.org/10.1103/PhysRevLett.88.174102\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCarrasco CD, Milyavskaya M, Hofmann W (2024) Using multivariate pattern analysis to increase effect sizes for event-related potentials. Psychophysiology 61(7):e14570. \u003cb\u003ehttps://doi.org/10.1111/psyp.14570\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChurchland MM, Yu BM, Cunningham JP, Sugrue LP, Cohen MR, Corrado GS, Newsome WT, Clark AM, Hosseini P, Scott BB, Bradley DC, Smith MA, Kohn A, Movshon JA, Armstrong KM, Moore T, Chang SW, Snyder LH, Lisberger SG, Priebe NJ, Finn IM, Ferster D, Ryu SI, Santhanam G, Sahani M, Shenoy KV (2010) Stimulus onset quenches neural variability: A widespread cortical phenomenon. Nat Neurosci 13(3):369\u0026ndash;378. \u003cb\u003ehttps://doi.org/10.1038/nn.2501\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eClayson PE, Baldwin SA, Larson MJ (2013) How does noise affect amplitude and latency measurement of event-related potentials (ERPs)? A methodological critique and simulation study. Psychophysiology 50(2):174\u0026ndash;186. \u003cb\u003ehttps://doi.org/10.1111/psyp.12001\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eClayson PE, Carbine KA, Baldwin SA, Larson MJ (2019) Methodological reporting behavior, sample sizes, and statistical power in studies of event-related potentials: Barriers to reproducibility and replicability. Psychophysiology 56(11):e13437. \u003cb\u003ehttps://doi.org/10.1111/psyp.13437\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eClayson PE, Carbine KA, Baldwin SA, Olsen JA, Larson MJ (2022) Using generalizability theory and the ERP Reliability Analysis (ERA) Toolbox for assessing test-retest reliability of ERP scores Part 2: Application to metrics of cognitive control. Int J Psychophysiol 166:174\u0026ndash;187. \u003cb\u003ehttps://doi.org/10.1016/j.ijpsycho.2021.01.010\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCohen MX (2022) Decoding continuous variables from event-related potential (ERP) data with machine learning. Psychophysiology 59(1):e13941. \u003cb\u003ehttps://doi.org/10.1111/psyp.13941\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ede Ron J, van Geert PLC, Steenbakkers L (2023) Towards a general modelling framework of resource competition in cognitive development. Dev Rev 69:101109. \u003cb\u003ehttps://doi.org/10.1016/j.dr.2023.101109\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDonchin E (1981) Surprise!...Surprise? Psychophysiology 18(5):493\u0026ndash;513. \u003cb\u003ehttps://doi.org/10.1111/j.1469-8986.1981.tb01815.x\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGrady CL (2012) The cognitive neuroscience of ageing. Nat Rev Neurosci 13(7):491\u0026ndash;505. \u003cb\u003ehttps://doi.org/10.1038/nrn3256\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGramfort A, Luessi M, Larson E, Engemann DA, Strohmeier D, Brodbeck C, Goj L, Jas M, Brooks T, Parkkonen L, H\u0026auml;m\u0026auml;l\u0026auml;inen M (2013) MEG and EEG data analysis with MNE-Python. Front Neurosci 7:267. \u003cb\u003ehttps://doi.org/10.3389/fnins.2013.00267\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHeise MJ, Mon SK, Bowman LC (2022) Utility of linear mixed effects models for event-related potential research with infants and children. Dev Cogn Neurosci 54:101070. \u003cb\u003ehttps://doi.org/10.1016/j.dcn.2022.101070\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHoy CW, Steiner H, Knight RT (2021) Single-trial modeling separates multiple overlapping prediction errors during reward processing in human electrophysiology. Commun Biol 4:910. \u003cb\u003ehttps://doi.org/10.1038/s42003-021-02426-1\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKappenman ES, Farrens JL, Zhang W, Stewart AX, Luck SJ (2021) ERP CORE: An open resource for human event-related potential research. NeuroImage 225:117465. \u003cb\u003ehttps://doi.org/10.1016/j.neuroimage.2020.117465\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKoenig T, Marquardt C (2020) Electroencephalography and neuroimaging of brain oscillations in health and disease. Brain Topogr 33(2):157\u0026ndash;171. \u003cb\u003ehttps://doi.org/10.1007/s10548-020-00775-4\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKok A (2001) On the utility of P3 amplitude as a measure of processing capacity. Psychophysiology 38(3):557\u0026ndash;577. \u003cb\u003ehttps://doi.org/10.1017/S0048577201990559\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLago S, Stocco A, B\u0026ouml;lte J, Oltrogge E, Kliegl R (2023) Trial-by-trial fluctuations of pre-stimulus alpha power predict ERP amplitude during sentence comprehension. Psychophysiology 60(12):e14388. \u003cb\u003ehttps://doi.org/10.1111/psyp.14388\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLau ZJ, Pham T, Chen SHA, Makowski D (2022) Brain entropy, fractal dimensions and predictability: A review of complexity measures for EEG in healthy and neuropsychiatric populations. Eur J Neurosci 56(7):5047\u0026ndash;5069. \u003cb\u003ehttps://doi.org/10.1111/ejn.5772\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLavie N, Torralbo A (2010) Dilution: A theoretical burden or just load? A reply to Tsal and Benoni (2010). J Exp Psychol Hum Percept Perform 36(6):1657\u0026ndash;1664. \u003cb\u003ehttps://doi.org/10.1037/a0020733\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLempel A, Ziv J (1976) On the complexity of finite sequences. IEEE Trans Inf Theory 22(1):75\u0026ndash;81. \u003cb\u003ehttps://doi.org/10.1109/TIT.1976.1055501\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi X, Wang Y, Chen S, Zhao L, Ye X (2025) Attentional resource consumption of verbal-humor processing: Evidence from event-related potentials and event-related oscillations. Cogn Process 26(1):93\u0026ndash;112. https://doi.org/10.1007/s10339-024-00344-5\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu S, Wang X, Zhao L, Li J, Wang B, Jiang Y, Chen Y, Zhang Y (2021) Multiscale permutation Lempel\u0026ndash;Ziv complexity measure for biomedical signal analysis. Entropy 23(6):803. \u003cb\u003ehttps://doi.org/10.3390/e23060803\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu J, Zhao M, Wang K, Li J, Manyande A (2024) Analysis of modulations of mental fatigue on intra- and inter-subject EEG variability. J Neurosci Methods 407:110143. \u003cb\u003ehttps://doi.org/10.1016/j.jneumeth.2024.110143\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLuck SJ (2014) An introduction to the event-related potential technique, 2nd edn. MIT Press, Cambridge, MA\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMazaheri A, Nieuwenhuis ILC, van Dijk H, Jensen O (2009) Prestimulus alpha and mu activity predicts failure to inhibit motor responses. Hum Brain Mapp 30(6):1791\u0026ndash;1800. \u003cb\u003ehttps://doi.org/10.1002/hbm.20763\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMon SK, Durbin CE, Rappaport BI, Tejavibulya L, Weissman DG, Hennefield L, Barch DM (2024) Leveraging mixed-effects location scale models to assess the influence of covariates on event-related potential amplitude and variability. Psychophysiology 61(4):e14470. \u003cb\u003ehttps://doi.org/10.1111/psyp.14470\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMurphy PR, Boonstra E, Nieuwenhuis S (2016) Global gain modulation generates time-dependent urgency during perceptual choice in humans. Nat Commun 7:13526. \u003cb\u003ehttps://doi.org/10.1038/ncomms13526\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMurray MM, Brunet D, Michel CM (2008) Topographic ERP analyses: A step-by-step tutorial review. Brain Topogr 20(4):249\u0026ndash;264. \u003cb\u003ehttps://doi.org/10.1007/s10548-008-0054-5\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNeville HJ, Schmidt A, Kutas M (1986) Altered visual-evoked potentials in congenitally deaf adults. Brain Res 266(1):127\u0026ndash;132. \u003cb\u003ehttps://doi.org/10.1016/0006-8993(83)91314-8\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eO'Connell RG, Dockree PM, Kelly SP (2012) A supramodal accumulation-to-bound signal that determines perceptual decisions in humans. Nat Neurosci 15(12):1729\u0026ndash;1735. \u003cb\u003ehttps://doi.org/10.1038/nn.3248\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePaul M, Govaart GH, Schettino A (2021) Making ERP research more transparent: Guidelines for preregistration. Int J Psychophysiol 164:52\u0026ndash;63. \u003cb\u003ehttps://doi.org/10.1016/j.ijpsycho.2021.02.016\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePolich J (2007) Updating P300: An integrative theory of P3a and P3b. Clin Neurophysiol 118(10):2128\u0026ndash;2148. \u003cb\u003ehttps://doi.org/10.1016/j.clinph.2007.04.019\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJohannsen J, R\u0026ouml;der B, Kn\u0026ouml;sche TR, Rogenbuck F, Holz J, Ohl FW (2014) Uni- and crossmodal refractory period effects of event-related potentials provide insights into the development of multisensory processing. Front Hum Neurosci 8:552. https://doi.org/10.3389/fnhum.2014.00552\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStraub C, Finkelhor D, Hunter W, Dobrovolny KA (2020) Reproducibility of individual effect sizes in meta-analyses in psychology: Estimating the reliability of effect size estimates. PLoS ONE 15(5):e0233107. \u003cb\u003ehttps://doi.org/10.1371/journal.pone.0233107\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStudenova AA, Forster C, Engemann DA, Hensch T, Sander C, Mauche N, Hegerl U, Nikulin VV (2023) Event-related modulation of alpha rhythm explains the auditory P300 evoked response in EEG. eLife 12:e88367. \u003cb\u003ehttps://doi.org/10.7554/eLife.88367\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTan C, Li Y, Chen S, Wang X, Liu J (2025) P300 event-related potentials as diagnostic biomarkers for attention deficit hyperactivity disorder. Front Psychiatry 16:1590850. https://doi.org/10.3389/fpsyt.2025.1590850\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTwomey DM, Murphy PR, Kelly SP, O'Connell RG (2015) The classic P300 encodes a build-to-threshold decision variable. Eur J Neurosci 42(1):1636\u0026ndash;1643. \u003cb\u003ehttps://doi.org/10.1111/ejn.12936\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWolff A, de la Vega I, Zenon A, Pezzulo G, Boehler CN (2019) Neural variability quenching during decision-making: Neural individuality and its prestimulus complexity. NeuroImage 192:1\u0026ndash;14. \u003cb\u003ehttps://doi.org/10.1016/j.neuroimage.2019.02.070\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang LB, Hu L, Liu Y (2025) Neural variability reliably encodes interindividual differences in the perception of pain intensity. PLoS Biol 23(10):e3003470. \u003cb\u003ehttps://doi.org/10.1371/journal.pbio.3003470\u003c/b\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"brain-topography","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"btop","sideBox":"Learn more about [Brain Topography](http://link.springer.com/journal/10548)","snPcode":"10548","submissionUrl":"https://submission.nature.com/new-submission/10548/3","title":"Brain Topography","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"P300, event-related potential, single-trial analysis, linear mixed-effects models, neural state, state-dependent processing","lastPublishedDoi":"10.21203/rs.3.rs-8657074/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8657074/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe P300 event-related potential is a core index of attention and context updating, yet the trial-by-trial factors that modulate its amplitude remain incompletely characterized. This study tested whether early post-stimulus signal magnitude (0\u0026ndash;150 ms) predicts subsequent P300 amplitude (300\u0026ndash;600 ms) at the single-trial level. Using data from the ERP CORE auditory oddball dataset (N\u0026thinsp;=\u0026thinsp;40 participants; 1,661 trials), early activity was quantified as root mean square (RMS) amplitude at electrode Fz. A linear mixed-effects model with full model diagnostics and post-hoc power analysis revealed a statistically reliable negative association between early RMS and P300 amplitude (β = \u0026minus;0.064, SE\u0026thinsp;=\u0026thinsp;0.0245, z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;2.61, p\u0026thinsp;=\u0026thinsp;0.0085, 95% CI [\u0026minus;\u0026thinsp;0.112, \u0026minus;\u0026thinsp;0.016]). However, the effect size was minimal (R\u0026sup2; = 0.0042), explaining less than 0.5% of trial-level variance. Notably, the stimulus condition effect (Target vs. Standard) was approximately 13 times larger, indicating that early signal magnitude provides modest modulation rather than decisive control over P300 generation. Model diagnostics confirmed adequate assumptions (Shapiro-Wilk W\u0026thinsp;=\u0026thinsp;0.9995, p\u0026thinsp;=\u0026thinsp;0.97; achieved power\u0026thinsp;=\u0026thinsp;0.85). Exploratory complexity measures (Permutation Entropy, Lempel\u0026ndash;Ziv) were non-predictive, suggesting amplitude-dependent rather than complexity-based coupling. The most conservative interpretation is that early RMS reflects momentary neural state that weakly biases P300 amplitude, possibly through resource competition or refractory-like effects. These findings establish a quantitative constraint on early\u0026ndash;late ERP coupling, demonstrate that P300 is predominantly endogenously driven, and highlight the importance of distinguishing amplitude-based measures from trial-to-trial variability. Future work should decompose these components and incorporate pre-stimulus state covariates to clarify mechanisms.\u003c/p\u003e","manuscriptTitle":"Early Post-Stimulus Activity Negatively Predicts P300 Amplitude: A Single-Trial Analysis of the Auditory Oddball Task","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-27 11:27:07","doi":"10.21203/rs.3.rs-8657074/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-20T09:16:36+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-20T09:02:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"99004669865277761587205559805419166671","date":"2026-03-31T23:02:06+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-31T08:53:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"32280900287296455300690711478220555382","date":"2026-03-14T10:00:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-12T15:45:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-23T08:56:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-23T04:12:45+00:00","index":"","fulltext":""},{"type":"submitted","content":"Brain Topography","date":"2026-01-21T07:55:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"brain-topography","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"btop","sideBox":"Learn more about [Brain Topography](http://link.springer.com/journal/10548)","snPcode":"10548","submissionUrl":"https://submission.nature.com/new-submission/10548/3","title":"Brain Topography","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"4212c76e-dc4a-4bf1-a9ef-fb8d07705563","owner":[],"postedDate":"January 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-07T16:38:17+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-27 11:27:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8657074","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8657074","identity":"rs-8657074","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}