Abstract
Background. The p-curve is a plot of the distribution of p-values reported in a set of scientific studies. Comparisons between ranges of p-values have been used to evaluate fields of research in terms of the extent to which studies have genuine evidential value, and the extent to which they suffer from bias in the selection of variables and analyses for publication, p-hacking.Methods. p-hacking can take various forms. Here we used R code to simulate the use of ghost variables, where an experimenter gathers data on several dependent variables but reports only those with statistically significant effects. We also examined a text-mined dataset used by Head et al. (2015) and assessed its suitability for investigating p-hacking.Results. We show that when there is ghost p-hacking, the shape of the p-curve depends on whether dependent variables are intercorrelated. For uncorrelated variables, simulated p-hacked data do not give the “p-hacking bump” just below .05 that is regarded as evidence of p-hacking, though there is a negative skew when simulated variables are inter-correlated. The way p-curves vary according to features of underlying data poses problems when automated text mining is used to detect p-values in heterogeneous sets of published papers.Conclusions. The absence of a bump in the p-curve is not indicative of lack of p-hacking. Furthermore, while studies with evidential value will usually generate a right-skewed p-curve, we cannot treat a right-skewed p-curve as an indicator of the extent of evidential value, unless we have a model specific to the type of p-values entered into the analysis. We conclude that it is not feasible to use the p-curve to estimate the extent of p-hacking and evidential value unless there is considerable control over the type of data entered into the analysis. In particular, p-hacking with ghost variables is likely to be missed.
Highlights
The p-curve is a plot of the distribution of p-values reported in a set of scientific studies
Somewhat counterintuitively, ghost p-hacking induces a leftward skew in the p-curve when the dependent variables are intercorrelated, but not when they are independent
Directional t -tests were used; i.e., a variable was treated as a ghost variable only if there was a difference in the predicted direction, with greater mean for group 2 than for group 1
Summary
The p-curve is a plot of the distribution of p-values reported in a set of scientific studies. Understanding of the conceptual foundations of statistics has not always kept pace with software (Altman, 1991; Reinhart, 2015), leading to concerns that much reported science is not reproducible, in the sense that a result found in one dataset is not obtained when tested in a new dataset (Ioannidis, 2005) The causes of this situation are complex and the solutions are likely to. Two situations where reported p-values provide a distorted estimate of strength of evidence against the null hypothesis are publication bias and p-hacking Both can arise when scientists are reluctant to write up and submit unexciting results for publication, or when journal editors are biased against such papers. Concerns about publication bias are not new (Greenwald, 1975; Newcombe, 1987; Begg & Berlin, 1988), but scientists have been slow to adopt recommended solutions such as pre-registration of protocols and analyses
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