An interesting effect that I recently stumbled upon: the publication bias.
According to the definition in Wikipedia:
Publication bias occurs when the publication of research results depends on their nature and direction.
Authors are more likely to submit, or editors accept, positive results, while negative or inconclusive results remain unpublished.
One consequence of it, is the decline effect: as studies with more and more data are conducted, they show that the size of the initial hypothesis / conclusion is getting smaller.
As usual, pictures are worth thousand words:
What seems to indicate that an effect size is decreasing when the study size increases, is in reality just caused by the publication bias: