There are many valid criticisms of P-values but the criticism that they are largely responsible for the reproducibility crisis has been accepted rather lightly in some quarters. Whatever the inferential statistic that is used, it is quite illogical to assume that as the sample size increases it will tend to show more evidence against the null hypothesis. This applies to Bayesian posterior probabilities as much as it does to P-values. In the context of P-values it can be referred to as the trend towards significance fallacy but more generally, for reasons I shall explain, it could be referred to as the anticipated evidence fallacy. The anticipated evidence fallacy is itself an example of the overstated evidence fallacy. I shall also discuss this fallacy and other relevant matters affecting reproducible science including the problem of false negatives.