How often are there statistical reporting errors in published research? Using a new automated method for scraping APA-formatted stats out of PDFs, Nuijten et al. (2015) found that over 10% of p-values were inconsistent with the reported details of the statistical test, and 1.6% were what they called "grossly" inconsistent, e.g. difference between the p-value and the test statistic meant that one implied statistical significance and the other did not (another summary here). Here are two key figures, first for proportion inconsistent by article and then for proportion of articles with an inconsistency:
These graphs are upsetting news. Around half of articles had at least one error by this analysis, which is not what you want from your scientific literature.* Daniel Lakens has a nice post suggesting that three errors account for many of the problems: incorrect use of < instead of =, use of one-sided tests without clear reporting as such, and errors in rounding and reporting.
Speaking for myself, I'm sure that some of my articles have errors of this type, almost certainly from copying and pasting results from an analysis window into a manuscript (say Matlab in the old days or R now).** The copy-paste thing is incredibly annoying. I hate this kind of slow, error-prone, non-automatable process.
So what are we supposed to do? Of course, we can and should just check our numbers, and maybe run statcheck (the R package Nuijten et al. created) on our own work as well. But there is a much better technical solution out there: write statistics into the manuscript in one executable package that automatically generates the figures, tables, and statistical results. In my opinion, doing this used to be almost as much of a pain as doing the cutting and pasting (and this is spoken as someone who writes academic papers in LaTeX!). But now the tools for writing text and code together have gotten so good that I think there's no excuse not to.