Chapter 2. Topics in Hypothesis Testing

  • 2.1 Significance Levels 23

  • 2.2 Power 25

  • 2.3 One-Tailed and Two-Tailed Tests 26

  • 2.4 p-Values 27

  • 2.5 Sample Size Determination 27

  • 2.6 Multiple Testing 30

  • 2.7 Summary 40

2.1 Significance Levels

When conducting hypothesis testing, an erroneous conclusion is made if the null hypothesis is rejected when it is really true. This error is called a Type I error, and its probability is denoted by α, which is known as the 'significance level' of the test.

When setting up the hypothesis test, the rejection region is selected based on a predetermined value for α, usually a small value such as 0.05. This means that there is only a 5% chance of rejecting a true null hypothesis.

For example, suppose that administration of a drug was ...

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