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.

See also

• Inferential statistics decision-making tree
• Statistical inference (Wikipedia)
• Significance testing
• Statistical power
• Survey research and design in psychology/Lectures/Power & effect sizes