Use of the p-value as a size-dependent function to address practical differences when analyzing large datasets

Biomedical research has come to rely on p-values as a deterministic measure for data-driven decision making. In the largely extended null-hypothesis significance testing (NHST) for identifying statistically significant differences among groups of observations, a single p-value computed from sample data is routinely compared with a threshold, commonly set to 0.05, to assess the evidence against the hypothesis of having non-significant differences among groups, or the null hypothesis. Because the estimated p-value tends to decrease when the sample size is increased, applying this methodology to large datasets results in the rejection of the null hypothesis, making it not directly applicable in this specific situation. Herein, we propose a systematic and easy-to-follow method to detect differences based on the dependence of the p-value on the sample size. The proposed method introduces new descriptive parameters that overcome the effect of the size in the p-value interpretation in the framework of large datasets, reducing the uncertainty in the decision about the existence of biological/clinical differences between the compared experiments. This methodology enables both the graphical and quantitative characterization of the differences between the compared experiments guiding the researchers in the decision process. An in-depth study of the proposed methodology is carried out using both simulated and experimentally obtained data. Simulations show that under controlled data, our assumptions on the p-value dependence on the sample size holds. The results of our analysis in the experimental datasets reflect the large scope of this approach and its interpretability in terms of common decision-making and data characterization tasks. For both simulated and real data, the obtained results are robust to sampling variations within the dataset.