Is the p-postulate (equal p-values provide equal evidence against the null) true? The p-postulate is the notion that equal p-values provide equal evidence against the null hypothesis.
Wagenmakers et al (2008) write: 

If p-values truly reflect evidence, a minimum requirement is that
  equal p-values provide equal evidence against the null hypothesis
  (i.e., the p-postulate). According to the p-postulate, p = .05 with 10
  observations constitutes just as much evidence against the null
  hypothesis as does p = .05 after 50 observations.

They cite Royall (1986) as the source for their definition of the p-postulate. They also go on saying that this postulate is false. Is it?



*

*Royall, R. N. (1986). The Effect of Sample Size on the Meaning of Significance Tests, The American Statistician, 40:4, 313-315  

*Wagenmakers, E.-J., Lee, M. D., Lodewyckx, T., & Iverson, G. (2008). Bayesian versus frequentist inference. In H. Hoijtink, I. Klugkist, and P. A. Boelen (Eds.), Bayesian Evaluation of Informative Hypotheses, pp. 181-207. Springer: New York.

 A: The Royall paper begins with two quotes that providing apparently contradictory interpretations of the p-value.  Both rely on interpreting the p-value in light of the sample size and as such both are flawed interpretations of the p-value.  
A p-value tells us one thing and one thing only--the probability of observing a statistic as extreme or more extreme than that observed in a sample as a result of random sampling error.  A p-value of .05 with a sample of 10 or a sample of 50 (or any sample size for that matter) yields the same interpretation in any case.  Under the assumptions of the model, a difference of the magnitude observed or greater would be observed in just 5% of samples if the null hypothesis were actually true.  
So, in response to your specific question and focusing on interpreting only the p-value, the answer is yes--equal p-values provide equal evidence against the null hypothesis at any sample size.  
This does not tell us anything about the magnitude of the difference or the effect size.  Indeed, all else being equal, the same difference in an observed effect size will yield lower p-values as sample size increases.  Strength of evidence against the null (p-value) and magnitude of the difference (effect size) should be interpreted together.
