What Have We (Not) Learnt from Millions of Scientific Papers with P Values?

P values linked to null hypothesis significance testing (NHST) is the most widely (mis)used method of statistical inference. Empirical data suggest that across the biomedical literature (1990–2015), when abstracts use P values 96% of them have P values of 0.05 or less. The same percentage (96%) applies for full-text articles. Among 100 articles in PubMed, 55 report P values, while only 4 present confidence intervals for all the reported effect sizes, none use Bayesian methods and none use false-discovery rate. Over 25 years (1990–2015), use of P values in abstracts has doubled for all PubMed, and tripled for meta-analyses, while for some types of designs such as randomized trials the majority of abstracts report P values. There is major selective reporting for P values. Abstracts tend to highlight most favorable P values and inferences use even further spin to reach exaggerated, unreliable conclusions. The availability of large-scale data on P values from many papers has allowed the development and applications of methods that try to detect and model selection biases, for example, p-hacking, that cause patterns of excess significance. Inferences need to be cautious as they depend on the assumptions made by these models and can be affected by the presence of other biases (e.g., confounding in observational studies). While much of the unreliability of past and present research is driven by small, underpowered studies, NHST with P values may be also particularly problematic in the era of overpowered big data. NHST and P values are optimal only in a minority of current research. Using a more stringent threshold, as in the recently proposed shift from P < 0.05 to P < 0.005, is a temporizing measure to contain the flood and death-by-significance. NHST and P values may be replaced in many fields by other, more fit-for-purpose, inferential methods. However, curtailing selection biases requires additional measures, beyond changes in inferential methods, and in particular reproducible research practices.