Andrew Gelman’s blog (andrewgelman.com) often has interesting comments on different aspects of statistics. I particularly like this comment on the differences between values of .20 and .01 (copied from his blog entry “Ride a Crooked Mile” posted on 14 Jun 2017):
3. In their article, Krueger and Heck write, “Finding p = 0.055 after having found p = 0.045 does not mean that a bold substantive claim has been refuted (Gelman and Stern, 2006).” Actually, our point was much bigger than that. Everybody knows that 0.05 is arbitrary and there’s no real difference between 0.045 and 0.055. Our point was that apparent huge differences in p-values are not actually stable (“statistically significant”). For example, a p-value of 0.20 is considered to be useless (indeed, it’s often taken, erroneously, as evidence of no effect), and a p-value of 0.01 is considered to be strong evidence. But a p-value of 0.20 corresponds to a z-score of 1.28, and a p-value of 0.01 corresponds to a z-score of 2.58. The difference is 1.3, which is not close to statistically significant. (The difference between two independent estimates, each with standard error 1, has a standard error of sqrt(2); thus a difference in z-scores of 1.3 is actually less than 1 standard error away from zero!) So I fear that, by comparing 0.055 to 0.045, they are minimizing the main point of our paper.