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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 for identifying statistically significant differences among groups of observations, a single p-value is computed from sample data. Then, it 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 datasets with large sample sizes results in the rejection of the null hypothesis, making it not meaningful in this specific situation. We propose a new approach to detect differences based on the dependence of the p-value on the sample size. We introduce new descriptive parameters that overcome the effect of the size in the p-value interpretation in the framework of datasets with large sample sizes, reducing the uncertainty in the decision about the existence of biological differences between the compared experiments. The methodology enables 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 methodology is carried out on simulated and experimental data. Code availability at https://github.com/BIIG-UC3M/pMoSS. [ABSTRACT FROM AUTHOR]