system
Given the following post, respond as if you're commenting on Reddit:
human
Is a p-value of 0.01 "more significant" than a p-value of 0.001? If both are significant, does it make sense to say one is more significant than the other?

Scientific papers often report significance with * or ** or *** depending on how small the p-value is. But someone recently told me that asterisks are useless because we defined a threshold below which the p-value is significant and to say that the p-value is tiny small does not give more information than saying that it is below the threshold.
Like you're either pregnant or not but you cannot be "more pregnant".

Thank you!
gpt
If the only interpretation we could attribute to p-values is "significant" or "not significant", then this person would be correct, however such an interpretation is actually itself more obscure and questionable than the literal interpretation, which is the probability of observing a sample statistic at least as "large" (i.e. "not null-like") as what was actually observed, given a true null hypothesis.

It is often inferred, but not because it is *implied*, that a lower p-value gives us evidence of a hypothesis.  It is not proper to say that a significant p-value is like saying "you are pregnant".  It is OK though to say that the pregnancy test is not likely to be positive given that you actually aren't pregnant.  Subtle difference.

*All else equal*, a lower p-value results from a higher observed difference from the null.  To the extent and in the context that it is proper to talk about any single p-value providing evidence against a null hypothesis, you should be able to make similar statements comparing two p-values.