Cavalier Use of Inferential Statistics Is a Major Source of False and Irreproducible Scientific Findings

I uncover previously underappreciated systematic sources of false and irreproducible results in natural, biomedical social sciences that are rooted statistical methodology. They include the inevitably occurring deviations from basic assumptions behind analyses use various approximations. show through a number examples (a) arbitrarily small distributional homogeneity can lead to large outcomes analyses; (b) samples random size may violate Law Large Numbers thus generally unsuitable for conventional inference; (c) same is true, particular, when sample observations stochastically dependent; (d) Gaussian approximation based on Central Limit Theorem has dramatic implications p-values significance essentially making pursuit levels fixed meaningless. The latter proven rigorously case one-sided Z test. This article could serve as cautionary guidance scientists practitioners employing methods their work.