Ioannidis turned this on its head and asked: assuming that the true difference in the brain volume is what the average of all the published studies says it is, how many of the published studies were big enough that they ought to have succesfully detected it?
He found 41 seperate meta-analyses for different brain regions in various disorders. These were published in 8 papers – because each paper reported on multiple regions. He only looked at meta-analyses published in the past 4 years, but these analyses will themselves have included older work. This means that this paper is a kind of meta-meta-analysis. He didn’t directly consider the raw brain scans at all.
The meta-analyses found many significant volume differences – but in 29 of those 41, there was an excess of significant papers. In other words, the papers were too small to have a good chance to detect the effect that they themselves found – suggesting that something funny was going on. Although, strangely, in 10/41 there were too few, and only in 2 were there the “right” number.