Application of Benford's law: a valuable tool for detecting scientific papers with fabricated data? : A case study using proven falsified articles against a comparison group.

BACKGROUND: In naturally occurring numbers the frequencies of digits 1-9 in the leading position are counterintuitively distributed because the frequencies of occurrence are unequal. Benford-Newcomb's law describes the expected distribution of these frequencies. It was previously shown that known fraudulent articles consistently violated this law. OBJECTIVE: To compare the features of 12 known fraudulent articles from a single Japanese author to the features of 13 articles in the same research field from other Japanese authors, published during the same time period and identified with a Medline database search. RESULTS: All 25 articles were assessed to determine whether the data violated the law. Formulas provided by the law were used to determine the frequencies of occurrence for the first two leading digits in manually extracted numbers. It was found that all the known fraudulent papers violated the law and 6 of the 13 articles used for comparison followed the law. Assuming that the articles in the comparison group were not falsified or fabricated, the sensitivity of assessing articles with Benford-Newcomb's law was 100% (95% confidence interval CI: 73.54-100%) but the specificity was only 46.15% (95% CI: 19.22-74.87%) and the positive predictive value was 63.16% (95% CI: 38.36-83.71%). CONCLUSION: All 12 of the known falsified articles violated Benford-Newcomb's law, which indicated that this analysis had a high sensitivity. The low specificity of the assessment may be explained by the assumptions made about the articles identified for comparison. Violations of Benford-Newcomb's law about the frequencies of the leading digits cannot serve as proof of falsification but they may provide a basis for deeper discussions between the editor and author about a submitted work.

Effects of frontal transcranial direct current stimulation on emotional state and processing in healthy humans.

The prefrontal cortex is involved in mood and emotional processing. In patients suffering from depression, the left dorsolateral prefrontal cortex (DLPFC) is hypoactive, while activity of the right DLPFC is enhanced. Counterbalancing these pathological excitability alterations by repetitive transcranial magnetic stimulation (rTMS) or transcranial direct current stimulation (tDCS) improves mood in these patients. In healthy subjects, however, rTMS of the same areas has no major effect, and the effects of tDCS are mixed. We aimed to evaluate the effects of prefrontal tDCS on emotion and emotion-related cognitive processing in healthy humans. In a first study, we administered excitability-enhancing anodal, excitability-diminishing cathodal, and placebo tDCS to the left DLPFC, combined with antagonistic stimulation of the right frontopolar cortex, and tested acute emotional changes by an adjective checklist. Subjective emotions were not influenced by tDCS. Emotional face identification, however, which was explored in a second experiment, was subtly improved by a tDCS-driven excitability modulation of the prefrontal cortex, markedly by anodal tDCS of the left DLPFC for positive emotional content. We conclude that tDCS of the prefrontal cortex improves emotion processing in healthy subjects, but does not influence subjective emotional state.