In this elaborate response to Wu (in Scientometrics, 2018), I maintain that null hypothesis significance testing (NHST) is logically flawed. Wu (2018) disagrees with this claim presented in Schneider (in Scientometrics 102(1):411–432, 2015). In this response, I examine the claim in more depth and demonstrate that since NHST is based on one conditional probability alone and framed in a probabilistic modus tollens framework of reasoning, it is by definition logically invalid. I also argue that disregarding this logically fallacy, as most researchers do, and treating the p value as a heuristic value for dichotomous decisions against the null hypothesis, is a risky business that often leads to false-positive claims.