Is a p-value of 0.01 "more significant" than a p-value of 0.001? If both are significant, does it...

  • Question: 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". What do you say about this?
Answer:
What is significant is determined by the level set for your hypothesis test. All the p-value does is tell you the probability of getting a sample value at least that extreme given the null hypothesis is correct. So a smaller p-value would be more compelling evidence that the null hypothesis is not true, but you also have to make sure that the experiment and assumptions of the experiment are met otherwise the p-value could be of little value. It's also important to remember that things can be statistically significant but not practically significant.

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