Nearly every academic paper published since the 1960s has used statistics known to be faulty.
That sounds extreme, but it's actually not even controversial in the statistical literature.
In the 1950s, Ronald Fisher invented a statistical technique to solve the philosophical Problem of Induction. Neyman and Pearson developed a technique for statistical quality control in factories. Yet somehow, these two techniques were confused and merged into the Null Ritual of today, which is the neurotic pattern that every paper in many disciplines have to follow.
The Null Ritual is one of the clearest examples of academic consensus so far off the tracks that scholar treat the techniques in textbooks were religious devotion, rather than with critical awareness of what they are actually supposed to be. The end result? Nearly every field is rife with misuse of numbers, publication bias, misunderstandings and fake conclusions.
Note that pay-walled academic articles may be obtained by feeding their URLs to sites like Sci-Hub.