I think studies that involve psychology have lots of “low tech” issues that can be exploited by bad statistics, including subjective metrics (self-reporting of mood, for example). I think that’s part of the reason for the reproducability crisis where famous findings can’t be replicated. (@nataliefrank has a good write-up here.)

The big data question is interesting, especially as it turns up now in biomedical and genomic research. In theory, science that uses big data should become more self-correcting, because there’s so much data to test a hypothesis with. But in practice, we may be making conclusions that can only be properly vetted by researchers with a strong statistics background. It’s outside of my experience, but I’m definitely interested in learning more.