Statistical inference

Hypotheses

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

Decisions
When a hypothesis is 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

 * 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
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


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.