Moreover, one should be cautious that extremely large studies may be more likely to find a formally statistical significant difference for a trivial effect that is not really meaningfully different from the null
http://plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124#article1.body1.sec8.p2

Instead of relying upon p-values, or other single-test metrics, one should rely upon concepts such as "uniformly most powerful" (UMP) unbiased tests, or "false discovery rates" (FDR), which acknowledge & optimize for multiple tests upon the same set of observations.

The author is correct, insofar as many published papers rely solely & too heavily upon t-test p-values.