Statistical inference

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  • Null Hypothesis (H0): No differences or effect
  • Alternative Hypothesis (H1): Differences or effect


When a hypothesis tested, a conclusion is drawn, based on sample data; either:

  • Do not reject H0, p is not significant (i.e. not below the critical alpha (α))
  • Reject H0, p is significant (i.e., below the critical α)

Correct decisions[edit]

  • Do not reject H0: Correctly retain H0 when there is no real difference/effect in the population
  • Reject H0 (Power): Correctly reject H0 when there is a real difference/effect in the population

Incorrect decisions: Type I and II errors[edit]

However, when we fail to reject or reject H0, we risk making errors:

  1. Type I error: Incorrectly reject H0 (i.e., there is no difference/effect in the population)
  2. Type II error: Incorrectly fail to reject H0 (i.e., there is a difference/effect in the population)

Decision-making table[edit]

Inferential Statistics Decision Making Table.png

Cells represent:

  1. Correct acceptance of H0
  2. Power (correct rejection of H0) = 1-β
  3. Type I error (false rejection of H0) = α
  4. Type II error (false acceptance of H0) = β

Traditional emphasis has been too much on Type I errors and not enough on Type II error – balance needed.

See also[edit]