There are several cases of wrong use of statistical tests in the scientific literature. This cuts across various categories of journals (though commonest in low-quality journals). For instance, if you search the literature, there are more studies with ANOVA than Kruskall Wallis test even when assumptions for parametric tests (sample size) are violated. Another case, is LSD versus Bonferroni posthoc test. The use of LSD increases the rate of false positive errors. This can give rise to articles with a lot of false positive results. This may contribute to the increased failure of animal findings in clinical settings (That is, inability to translate preclinical research into clinical findings).
This problem arises because a lot of reviewers do not focus on statistical analyses during peer review. I am of the view that every journal should have an Editorial Board member who is knowledgeable in statistics and screens every manuscript for correctness of statistical tests. I would like to hear various views (insights) on this topic.