The small impact of p-hacking marginally significant results on the meta-analytic estimation of effect size

Abstract The label p-hacking (pH) refers to a set of opportunistic practices aimed at making statistically significant p values that should be non-significant. Some have argued that we should prevent and fight pH for several reasons, especially because of its potential harmful effects on the assessment of both primary research results and their meta-analytical synthesis. We focus here on the effect of a specific type of pH, focused on marginally significant studies, on the combined estimation of effect size in meta-analysis. We want to know how much we should be concerned with its biasing effect when assessing the results of a meta-analysis. We have calculated the bias in a range of situations that seem realistic in terms of the prevalence and the operational definition of pH. The results show that in most of the situations analyzed the bias is less than one hundredth (± 0.01), in terms of d or r. To reach a level of bias of five-hundredths (± 0.05), there would have to be a massive presence of this type of pH, which seems rather unrealistic. We must continue to fight pH for many good reasons, but our main conclusion is that among them is not that it has a big impact on the meta-analytical estimation of effect size.