# 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.