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What is a p-value, precisely?

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Answer

  • The probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the one obtained.
  • It is NOT the probability that the null is true, nor the probability of a mistake.
  • A small p-value means the data are unlikely under H0.
  • Combine with effect size and confidence intervals — never rely on p-values alone.
Check yourself — multiple choice
  • The probability that H0 is true
  • The probability of observing data at least as extreme as ours if H0 is true
  • The probability that H1 is true
  • The Type I error rate

P(data  at  least  as  extreme  ∣  H0  true)P(\mathrm{data}\;\mathrm{at}\;\mathrm{least}\;\mathrm{as}\;\mathrm{extreme}\; \mid \;\mathrm{H0}\;\mathrm{true}).

#hypothesis-testing

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