As evidenced by numerous studies on statistical cognition (Kline, 2004; Beyth-Marom et al, 2008), even trained scientists have a hard time interpreting p-values, which frequently leads to misleading or incorrect conclusions.

few researchers can resist the temptation to conclude that there is no effect, a common fallacy called "accepting the null" which had frequently led to misleading or wrong scientific conclusions (Dienes, 2014, p.1).

Again, p is the probability of seeing results as extreme (or more extreme) as those actually observed if the null hypothesis were true. So p is computed under the assumption that the null hypothesis is true. Yet it is common for researchers, teachers and even textbooks to think of p as the probability of the null hypothesis being true (or equivalently, of the results being due to chance), an error called the "fallacy of the transposed conditional" (Haller and Krauss, 2002; Cohen, 1994, p.999).

Many researchers fail to appreciate that p-values are unreliable and vary widely across replications.

NHST as it is carried out today consists of this incoherent mix of Fisher and Neyman–Pearson methods (Gigerenzer, 2004).

p-values give a seductive illusion of certainty and truth (Cumming, 2012, Chap. 1). The sacred α = .05 criterion amplifies this illusion, since results end up being either "significant" or "non-significant".