# Statistical inference

## Contents

## Hypotheses[edit]

- Null Hypothesis (H
_{0}): No differences or effect - Alternative Hypothesis (H
_{1}): Differences or effect

## Decisions[edit]

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

- Do not reject H
_{0},*p*is not significant (i.e. not below the critical alpha (α)) - Reject H
_{0},*p*is significant (i.e., below the critical α)

### Correct decisions[edit]

- Do not reject H
_{0}: Correctly retain H_{0}when there is no real difference/effect in the population - Reject H
_{0}(Power): Correctly reject H_{0}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 H_{0}, we risk making errors:

- Type I error: Incorrectly reject H
_{0}(i.e., there is no difference/effect in the population) - Type II error: Incorrectly fail to reject H
_{0}(i.e., there is a difference/effect in the population)

## Decision-making table[edit]

Cells represent:

- Correct acceptance of H
_{0} - Power (correct rejection of H
_{0}) = 1-β - Type I error (false rejection of H
_{0}) = α - Type II error (false acceptance of H
_{0}) = β

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