Good Statistics Can't Save Science | Psychology Today

Alexander Danvers, researches emotions and social interactions says, High power statistical models can't replace scientific logic.

There is a revolution underway in how people evaluate the scientific merit of psychology studies, and many of the most important reforms have involved paying more attention to statistics.

For example, the comprehensive text on Statistical Power—a branch of statistics that lets researchers know how many participants they need to collect in an experiment for it to have a good chance of succeeding—was written in 1977. Only in the last decade have some influential journals started forcing people to use this information to justify the number of participants they collected in new experiments they report.

This is great for a nerd like myself with an aptitude for statistics, but it also tends to make the “Credibility Revolution” in psychology look like it’s basically about people who know statistics really well shouting at people who don’t to "get their math right."
But doing good science isn’t primarily about knowing statistics. What matters is drawing good conclusions about how the world works...

The work of Daniel Kahneman and Amos Tversky on decision-making (work that was the basis for a Nobel prize) often features examples like this. For example, they demonstrated what is referred to as “The Conjunction Fallacy ” using a question that almost always elicits the key effect in readers:
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Source: Psychology Today