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You choose your level of significance before you do the experiment. “The level of statistical significance” – This is another one that can be tempting for me personally, but it’s wrong.“The probability that a repeat experiment would reach the same conclusion” – Wrong again.A low P-value encourages us to reject the hypothesis, but it doesn’t say anything about probabilities surrounding the hypothesis itself. “The probability that we would reject the hypothesis incorrectly” – Nope.The P-value assumes some chance, so it can’t be used to evaluate chance. What this really means, stated in full, is “the probability that our hypothesis is true and all deviations are explained by random error.” Again, it’s impossible to talk about the probability that a hypothesis is true using frequentist statistics. “The probability that the data is a fluke” – For me anyway, this is the interpretation that I really want to use, but it’s wrong.A high P-value means that our data is highly consistent with our hypothesis, nothing more.
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It’s actually impossible to talk about the probability that a hypothesis is true using frequentist statistics. “The probability that the hypothesis is true” – This one doesn’t mess me up too much, but it can be a source of confusion.This sounds simple enough, but it’s very tempting to interpret this in one of the following incorrect ways: The P-value is the probability that our data would be at least this inconsistent with the hypothesis, assuming the hypothesis is true. The P-value is one of the biggest sources of confusion in statistics, and it’s not uncommon for researchers to use the wrong definition: not when they compute it, but when they think about it.