Comment by habinero

No, the other way around. It's the combination of two well known effects. Well, three if you're uncharitable.

1. Small studies are more likely to give anomalous results by chance. If I pick three people at random, it's not that surprising if I happened to get three women. It would be a lot different if I sampled 1,000 people.

2. Studies that show any positive result tend to get published, and ones that don't tend to get binned.

Put those together, and you see a lot of tiny studies with small positive results. When you do a proper study, the effect goes away. Exactly as you would expect.

The less charitable effect is "they made it up". It happens.